.TP2
.CM-----------------------------------------------------------------------















.CJ
#HNBO 3.0 Program Manual#N
.HR<<5//+1//32//58>>




#N(#INatural Bond Orbital / Natural Population Analysis /
Natural Localized Molecular Orbital Programs#N)





E. D. Glendening, A. E. Reed,\dagger  J. E. Carpenter,\ddagger  and F. Weinhold

#ITheoretical Chemistry Institute and Department of Chemistry,
University of Wisconsin, Madison, Wisconsin 53706#N





.LN50
.LM10
.RM80
.FJ
\dagger  #RPresent address: Bayer AG, Abteilung AV-IM-AM,
5090 Leverkusen, Bayerwerk, Federal Republic of Germany.

\ddagger  #RPresent address: Department of Chemistry, University of
California-Irvine, Irvine, California 92717.#N
.PN1r
.DF\np =\thsp \nthsp
.LM10
.RM80
.HF<<TABLE OF CONTENTS//3//10>>




.CJ
#HTable of Contents#N
.FJ



.TB
.FM<<6L4//0L55//0R5>>
.RW<< //#BTable of Contents//#Ii>>
.RW<< //#BPreface: HOW TO USE THIS MANUAL//#Iiii>>
.RW
.RW
.RW
.FM<<1L4//0L60//0R5>>
.RW<<#HA.//GENERAL INTRODUCTION AND INSTALLATION// >>
.RW=
.FM<<6L4//0L55//0R5>>
.RW<<#BA.1//INTRODUCTION TO THE NBO PROGRAM//#IA-1>>
.FM<<10L5//0L50//0R5>>
.RW<<#IA.1.1//What does the NBO Program Do?//#IA-1>>
.RW<<#IA.1.2//Structure of the NBO Program//#IA-3>>
.RW<<#IA.1.3//Input and Output//#IA-5>>
.RW<<#IA.1.4//General Capabilities and Restrictions//#IA-6>>
.RW<<#IA.1.5//References and Relationship to Previous Versions//#IA-7>>
.FM<<6L4//0L55//0R5>>
.RW<<#BA.2//INSTALLING THE NBO PROGRAM//#IA-10>>
.RW<<#BA.3//TUTORIAL EXAMPLE FOR METHYLAMINE//#IA-12>>
.FM<<10L5//0L50//0R5>>
.RW<<#IA.3.1//Running the Example//#IA-12>>
.RW<<#IA.3.2//Natural Population Analysis//#IA-13>>
.RW<<#IA.3.3//Natural Bond Orbital Analysis//#IA-16>>
.RW<<#IA.3.4//NHO Directional Analysis//#IA-20>>
.RW<<#IA.3.5//Perturbation Theory Energy Analysis//#IA-21>>
.RW<<#IA.3.6//NBO Summary//#IA-22>>
.ET




.TB
.FM<<1L4//0L60//0R5>>
.RW<<#HB.//NBO USER'S GUIDE// >>
.RW=
.FM<<6L4//0L55//0R5>>
.RW<<#BB.1//INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTS//#IB-1>>
.RW<<#BB.2//THE $NBO KEYLIST//#IB-2>>
.FM<<10L5//0L50//0R5>>
.RW<<#IB.2.1//Overview of $NBO Keywords//#IB-2>>
.RW<<#IB.2.2//Job Control Keywords//#IB-3>>
.RW<<#IB.2.3//Job Threshold Keywords//#IB-4>>
.RW<<#IB.2.4//Matrix Output Keywords//#IB-6>>
.RW<<#IB.2.5//Other Output Control Keywords//#IB-9>>
.RW<<#IB.2.6//Print Level Keywords//#IB-10>>
.RW<<#IB.2.7//Semi-Documented Additional Keywords//#IB-11>>
.FM<<6L4//0L55//0R5>>
.RW<<#BB.3//THE $CORE LIST//#IB-12>>
.RW<<#BB.4//THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)//#IB-14>>
.RW<<#BB.5//THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS)//#IB-16>>
.FM<<10L5//0L50//0R5>>
.RW<<#IB.5.1//Introduction to NBO Energetic Analysis//#IB-16>>
.RW<<#IB.5.2//The Nine Deletion Types//#IB-17>>
.RW<<#IB.5.3//Input for UHF Analysis//#IB-20>>
.RW
.RW
.RW
.FM<<6L4//0L55//0R5>>
.RW<<#BB.6//NBO KEYLIST ILLUSTRATIONS//#IB-21>>
.FM<<10L5//0L50//0R5>>
.RW<<#IB.6.1//Introduction//#IB-21>>
.RW<<#IB.6.2//NLMO Keyword//#IB-22>>
.RW<<#IB.6.3//DIPOLE Keyword//#IB-24>>
.RW<<#IB.6.4//Matrix Output Keywords//#IB-26>>
.RW<<#IB.6.5//BNDIDX Keyword//#IB-29>>
.RW<<#IB.6.6//RESONANCE Keyword: Benzene//#IB-32>>
.RW<<#IB.6.7//NOBOND Keyword: Hydrogen Fluoride//#IB-37>>
.RW<<#IB.6.8//3CBOND Keyword: Diborane//#IB-40>>
.RW<<#IB.6.9//NBO Directed Search ($CHOOSE Keylist)//#IB-44>>
.RW<<#IB.6.10//NBO Energetic Analysis ($DEL Keylist)//#IB-48>>
.RW<<#IB.6.11//Open-Shell UHF Output: Methyl Radical//#IB-52>>
.RW<<#IB.6.12//Effective Core Potential: Cu#d2#u Dimer//#IB-56>>
.FM<<6L4//0L55//0R5>>
.RW<<#BB.7//FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM//#IB-62>>
.FM<<10L5//0L50//0R5>>
.RW<<#IB.7.1//Introduction//#IB-62>>
.RW<<#IB.7.2//Format of the FILE47 Input File//#IB-63>>
.RW<<#IB.7.3//$GENNBO Keylist//#IB-65>>
.RW<<#IB.7.4//$COORD Keylist//#IB-66>>
.RW<<#IB.7.5//$BASIS Datalist//#IB-67>>
.RW<<#IB.7.6//$CONTRACT Datalist//#IB-69>>
.RW<<#IB.7.7//Matrix Datalists//#IB-71>>
.ET




.TB
.FM<<1L4//0L60//0R5>>
.RW<<#HC.//NBO PROGRAMMER'S GUIDE// >>
.RW=
.FM<<6L4//0L55//0R5>>
.RW<<#BC.1//INTRODUCTION//#IC-1>>
.RW<<#BC.2//OVERVIEW OF NBO.SRC SOURCE PROGRAM GROUPS//#IC-2>>
.RW<<#BC.3//LABELLED COMMON BLOCKS//#IC-4>>
.RW<<#BC.4//DIRECT ACCESS FILE AND OTHER I/O//#IC-14>>
.RW<<#BC.5//NAO/NBO/NLMO ROUTINES (GROUP I)//#IC-16>>
.FM<<10L5//0L50//0R5>>
.RW<<#IC.5.1//SR NBO Master Routine//#IC-16>>
.RW<<#IC.5.2//Job Initialization Routines//#IC-18>>
.RW<<#IC.5.3//NAO Formation Routines//#IC-19>>
.RW<<#IC.5.4//NBO/NLMO Formation Routines//#IC-22>>
.FM<<6L4//0L55//0R5>>
.RW<<#BC.6//ENERGY ANALYSIS ROUTINES (GROUP II)//#IC-26>>
.RW<<#BC.7//DIRECT ACCESS FILE (DAF) ROUTINES (GROUP III)//#IC-27>>
.RW<<#BC.8//FREE FORMAT INPUT ROUTINES (GROUP IV)//#IC-29>>
.RW<<#BC.9//OTHER SYSTEM INDEPENDENT I/O ROUTINES (GROUP V)//#IC-30>>
.RW<<#BC.10//GENERAL UTILITY ROUTINES (GROUP VI)//#IC-33>>
.RW<<#BC.11//SYSTEM-DEPENDENT DRIVER ROUTINES (GROUP VII)//#IC-36>>
.RW<<#BC.12//GENNBO AUXILLIARY ROUTINES//#IC-37>>
.RW<<#BC.13//ATTACHING NBO TO A NEW ESS PROGRAM//#IC-38>>
.RW
.RW
.RW
.FM<<6L4//0L55//0R5>>
.RW<< //#BAPPENDIX: Specific ESS Versions#N// >>
.RW<< //#BINDEX#N// >>
.ET
.HF<<HOW TO USE THIS MANUAL//3//10>>
.RL55






.LJ
#HPREFACE: HOW TO USE THIS MANUAL#N
.FJ



\np The NBO manual is divided into three major sections:

\np Section A (``General Introduction and Installation'')
contains general introductory and `one-time' information
for the novice user: what the program does, program structure and
relationship to driver electronic structure package, initial installation,
`quick start' sample input data, and a brief tutorial on sample output.

\np Section B (``NBO User's Guide'')
is for the intermediate user who has an installed program
and general familiarity with the standard (default) options of the NBO
program.  This section documents the list of #Ikeywords#N that can be used
to alter the standard NBO job options, 
with examples of the resulting output.  This 
section is mandatory for users who wish to use
the program to its full potential, to `turn off' or
`turn on' various NBO options for their specialized applications.

\np Section C (``NBO Programmer's Guide'')
is for accomplished programmers who
are interested in program logic and the detailed layout of
the source code.  This section describes the relationship of the
source code subprograms
to the published algorithms for NAO, NBO, and NLMO determination,
providing documentation at the level of individual
common blocks, functions, and subroutines.  This in turn serves as a
bridge to the `micro-documentation' included
as comment statements within the source code.  Section C also
provides guidelines for constructing `driver' routines to attach
the NBO programs to new electronic structure packages.

.PR10
.CM----------------------------------NBOA.MAN----------------------
.TP2
.HF<<A.1 INTRODUCTION TO THE NBO PROGRAM//3//10>>
.NF<<A-// >>
.PN1
.DF\degree =\*degree
.DF\np =\thsp \nthsp
.CM----------------------------------------------------------------
.CJ





#HSection A: GENERAL INTRODUCTION AND INSTALLATION#N
.FJ


.RL15
#BA.1 INTRODUCTION TO THE NBO PROGRAM#N

#IA.1.1 #IWhat Does the NBO Program Do?#N

\np The NBO program performs the analysis of a many-electron
molecular wavefunction in terms of localized electron-pair
`bonding' units.  The program carries out the determination of
natural atomic orbitals (NAOs), natural hybrid orbitals (NHOs),
natural bond orbitals (NBOs), and natural localized molecular
orbitals (NLMOs), and uses these to perform natural population
analysis (NPA), NBO energetic analysis, and other tasks pertaining
to localized analysis of wavefunction properties.  The NBO 
method makes use of only the first-order
reduced density matrix of the wavefunction, and hence is applicable
to wavefunctions of general mathematical form; in the open-shell
case, the analysis is performed in terms of ``different NBOs for
different spins,'' based on distinct density matrices for \alpha
and \beta  spin.\dagger   This
section provides a brief introduction to NBO algorithms and
nomenclature.

\np NBO analysis is based
on a method for optimally transforming a given wavefunction into
localized form, corresponding to the one-center (``lone pair'')
and two-center (``bond'') elements of the chemist's Lewis structure 
picture.  The NBOs are obtained as local block eigenfunctions 
of the one-electron density matrix, and are hence ``natural'' in the sense 
of L\umlaut owdin, having optimal convergence properties for describing the 
electron density.  The set of high-occupancy NBOs, each taken doubly
occupied, is said to represent the ``natural Lewis structure'' of
the molecule.  Delocalization effects appear as weak departures 
from this idealized localized picture.  

.DF\ha =#C#Ih#O#dA#u
.DF\hb =#C#Ih#O#dB#u
.DF\ca =#C#Ic#O#dA#u
.DF\cb =#C#Ic#O#dB#u
.DF\sab =\sigma #dAB#u
.DF\ssab =\sigma *#d#<AB#u
\np The various natural localized sets 
can be considered to result
from a sequence of transformations of the input atomic orbital basis set
{\chi #di#u},\ddagger 
.DF\@foot2 =
.LM+0
_______________
.LM+0

\dagger #C#RNote, however,
that some electronic structure packages do not make provision
for calculating the spin density matrices for some types of
open-shell wavefunctions (e.g., MCSCF wavefunctions calculated
by the GUGA formalism in the GAMESS system), so that NBO analysis
cannot be applied in these cases.#O

\ddagger #C#RIf the wavefunction is not calculated in an atom-centered
basis set, it would be necessary to first compute a wavefunction
for each isolated atom of the molecule (in the actual basis set
and geometry of the molecular calculation), then select the
most highly occupied natural orbitals of each atomic wavefunction
to compose a final set of linearly independent atom-centered basis
functions of the required dimensionality.  Since atom-centered
basis functions are the nearly universal choice for molecular
calculations, the current NBO program makes no provision for
this step.#O
.RL55
.ED
.CM------------------2 footnotes on this page--------------------------
.IF<<46//47//\@foot2 >>
.CM--------------------------------------------------------------------

.CJ
input basis \rarr  NAOs \rarr  NHOs \rarr  NBOs \rarr  NLMOs
.FJ

Each natural localized set forms a complete orthonormal 
set of one-electron functions 
for expanding the delocalized molecular 
orbitals (MOs) or forming matrix representations of one-electron 
operators.  The overlap of associated ``pre-orthogonal'' 
NAOs (PNAOs), lacking only the interatomic orthogonalization 
step of the NAO procedure, can be used to estimate the strength
of orbital interactions in the usual way.

\np The optimal condensation of occupancy in the natural
localized orbitals leads to partitioning into high- and
low-occupancy orbital types (reduction in dimensionality
of the orbitals having significant occupancy), as reflected 
in the orbital labelling.  The small set of most
highly-occupied NAOs, having a close
correspondence with the effective minimal basis set of semi-empirical
quantum chemistry, is referred to as the ``natural minimal basis''
(NMB) set.  The NMB (core + valence) functions are 
distinguished from the weakly occupied ``Rydberg'' 
(extra-valence-shell) functions that complete the span of the NAO space,
but typically make little contribution to molecular properties.  Similarly
in the NBO space,
the highly occupied NBOs of the natural Lewis structure
can be distinguished from the ``non-Lewis'' antibond and Rydberg
orbitals that complete the span of the NBO space.  Each pair of valence hybrids
\ha , \hb  in the NHO basis give rise to a bond (\sab ) and antibond (\ssab )
in the NBO basis,

.CJ
\sab  = \ca \ha  + \cb \hb

\ssab  = \cb \ha  \minus  \ca \hb

.FJ
the former a Lewis (L) and the latter a non-Lewis (NL) orbital.  The 
antibonds (valence shell non-Lewis orbitals) typically play the primary
role in departures (delocalization) from the idealized Lewis structure.

\np The NBO program also makes extensive provision for energetic
analysis of NBO interactions, based on the availability of a 1-electron
effective energy operator (Fock matrix) for the system.  Estimates
of energy effects are
based on second-order perturbation theory,
or on the effect of deleting certain orbitals or matrix elements and
recalculating the total energy.  NBO energy analysis is dependent
on the specific ESS to which the NBO program
is attached, as described in the Appendix.

\np The program is provided in a core set of NBO routines that can be
attached to an electronic structure system of the user's choice.  In
addition, specific `driver' routines are provided that facilitate
the attachment to popular #Iab initio#N and
semi-empirical packages (GAUSSIAN-8X, GAMESS, HONDO, AMPAC,
etc.).  These versions are described in
individual Appendices.


.RL55
#IA.1.2 #IStructure of the NBO Program#N

\np The overall logical structure of the NBO program and its attachment
to an electronic structure system (ESS) are 
illustrated in the block diagram, Fig. 1.  This figure illustrates how
the ESS and its scratch
files (in the upper part of the diagram) communicate through 
the interface routines RUNNBO, FEAOIN, and DELSCF 
with the main NBO modules and associated direct access file (in
the lower part).

\np The main NBO program is represented by modules labelled ``NBO''
and ``NBOEAN.''  These refer to the construction of NBOs (including
natural population analysis, construction of NAOs, NLMOs, etc.) and to
NBO energy analysis, respectively.  Each module consists
of subroutines and functions that perform the required 
operations.  These two modules communicate with the
direct-access disk file NBODAF (LFN 48, labelled ``FILE48''
elsewhere in this manual) that is created and
maintained by the
NBO routines.   Details of the NBO and NBOEAN
modules, common blocks, and direct-access file are described 
in the Programmer's Guide,
Section C.

\np The NBO program blocks communicate with the attached
ESS through three system-dependent `driver' subroutines 
(RUNNBO, FEAOIN, DELSCF).  The purpose of these drivers
is to load needed information about the wavefunction and
various matrices into the FILE48 direct access file
and NBO common blocks.  Although the ESS
is usually thought of as `driving' the NBO program, 
from the point of view of the NBO program the 
ESS is merely a `device' that provides
initial input (e.g., a density matrix and label information) or
other feedback (a calculated energy value) upon
request.  Each such ESS device therefore requires special drivers
to make this feedback possible.  Versions of the driver subroutines are
included for several popular packages.  The driver routines are 
described in more detail in the Programmer's Guide, Section C.
.CM-------------------------Figure 1-------------------------------------
.RL55
.DF\@line1 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf 0>>
.ED
.DF\@line2 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf  0//
'\line2 ' 2//+0 +\!lf 0>>
.ED
.DF\@line3 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf  0//
'\line2 ' 2//+0 +\!lf 0//'\line3 ' 2//+0 +\!lf 0>>
.ED
.DF\@line4 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf  0//
'\line2 ' 2//+0 +\!lf 0//'\line3 ' 2//+0 +\!lf 0//'\line4 ' 2//
+0 +\!lf 0>> 
.ED
.DF\@line5 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf  0//
'\line2 ' 2//+0 +\!lf 0//'\line3 ' 2//+0 +\!lf 0//'\line4 ' 2//
+0 +\!lf 0//'\line5 ' 2//+0 +\!lf 0>> 
.ED
.DF\!dpx =68
.DF\!dpy =120
.DF\!lf =\!dpy
.DF\!ipen =1
.BX<<3//15//75//8//35>>
.CM----draw box at 10,55 and save coords of bottom
.DF\!hl =45
.DF\!vl =8
.DF\!nl =3
.DF\line1 =ab initio or
.DF\line2 =semi-empirical
.DF\line3 =program (ESS)
.DF\!wess =12
.DF\!wid =\!wess
.GS$box
.DF\!hess =\!dhl
.DF\!vess =\!dbot
.CM----draw scratch disk
.DF\!hs =-15
.DF\!hl =\!hl +\!hs
.DF\!hscr =\!hl
.DF\!vscr =\!vl
.DF\!a =4
.DF\!b =0.5
.DF\!ht =3.5
.DF\text =SCRATCH
.GS$cyl
.DF\!hl =\!hl -\!hs
.CM----draw line from ESs to scratch
.DF\!h1 =\!hess -\!wess *\!dpx /2
.DF\!v1 =(\!vscr +1)*\!dpy
.DF\!h2 =(\!hscr +\!a )*\!dpx
.DF\!v2 =\!v1
.GS$gline
.CM----move to bottom of ESS box
.DF\!vl =\!vl +3
.CM----draw runnbo box & save coords
.DF\!vl =\!vl +3
.DF\!nl =1
.DF\line1 =RUNNBO
.DF\!wid =8
.DF\!ipen =5
.GS$box
.DF\!ipen =1
.DF\!hrun =\!dhl
.DF\!trun =\!dtop
.DF\!brun =\!dbot
.CM----move to bottom of box
.DF\!vl =\!vl +1
.CM----draw line from bottom of ess to top of runnbo
.DF\!h1 =\!hess
.DF\!v1 =\!vess
.DF\!h2 =\!hrun
.DF\!v2 =\!trun 
.GS$gline
.CM----draw FEAOIN box & save coords
.DF\!hl =45-15
.DF\!vl =\!vl +5
.DF\!hfetch =\!hl
.DF\!vfetch =\!vl
.DF\!nl =1
.DF\line1 =FEAOIN
.DF\!wid =8
.DF\!ipen =5
.GS$box
.DF\!ipen =1
.DF\!hfet =\!dhl
.DF\!tfet =\!dtop
.DF\!bfet =\!dbot
.CM----draw dashed line from scratch to feaoin
.DF\!h1 =\!hscr *\!dpx
.DF\!v1 =(\!vscr +3.5+\!b )*\!dpy
.DF\!h2 =\!h1
.DF\!v2 =\!tfet
.DF\!ipen =7
.GS$gline
.DF\!ipen =1
.CM----draw NBO box & save coords
.DF\!hl =45-5
.DF\!hnbo =\!hl
.DF\!vnbo =\!vl
.DF\!wid =5
.DF\!nl =1
.DF\line1 =NBO
.GS$box
.DF\!hnbo =\!dhl
.DF\!tnbo =\!dtop
.DF\!bnbo =\!dbot
.CM----draw horizontal line from FEAOIN to to NBO
.DF\!h1 =\!hfet +4*\!dpx
.DF\!v1 =\!tnbo +0.5*(\!bnbo -\!tnbo )
.DF\!h2 =\!hnbo -2.5*\!dpx
.DF\!v2 =\!v1
.GS$gline
.CM----draw line from bottom of runnbo to to top of nbo
.DF\!h1 =\!hrun
.DF\!v1 =\!brun
.DF\!h2 =\!hnbo
.DF\!v2 =\!tnbo
.GS$gline
.CM----draw NBOEAN box & store coords
.DF\!hl =45+5
.DF\!hean =\!hl
.DF\!wid =8
.DF\!nl =1
.DF\line1 =NBOEAN
.GS$box
.DF\!hean =\!dhl
.DF\!tean =\!dtop
.DF\!bean =\!dbot
.CM---draw line from bottom of runnbo to top of nboean
.DF\!h1 =\!hrun
.DF\!v1 =\!brun
.DF\!h2 =\!hean
.DF\!v2 =\!tean
.GS$gline
.CM---draw DELSCF box & save coords
.DF\!hl =45+15
.DF\!hdel =\!hl
.DF\!wid =8
.DF\!nl =1
.DF\line1 =DELSCF
.DF\!ipen =5
.GS$box
.DF\!ipen =1
.DF\!hdel =\!dhl
.DF\!tdel =\!dtop
.DF\!bdel =\!dbot
.CM-----draw line from bottom of runnbo to top of delscf
.DF\!h1 =\!hrun
.DF\!v1 =\!brun
.DF\!h2 =\!hdel
.DF\!v2 =\!tnbo
.GS$gline
.CM-----draw NBODAF cylinder
.DF\!hl =45
.DF\!vl =\!vl +5
.DF\!a = 4
.DF\!b =0.5
.DF\text =NBODAF
.GS$cyl
.DF\!hdaf =\!dhl
.DF\!tdaf =\!dvl
.CM-----draw line from bottom of delscf to top of daf
.DF\!h1 =\!hdel
.DF\!v1 =\!bdel
.DF\!h2 =\!hdaf
.DF\!v2 =\!tdaf
.DF\!ipen =1
.GS$gline
.CM-----draw line from bottom of nboean to top of daf
.DF\!h1 =\!hean
.DF\!v1 =\!bean
.GS$gline
.CM-----draw line from bottom of nbo to top of daf
.DF\!h1 =\!hnbo
.DF\!v1 =\!bnbo
.GS$gline
.CM-----draw line from bottom of feaoin to top of daf
.DF\!h1 =\!hfet
.DF\!v1 =\!bfet
.GS$gline
.DF\!ipen =1
.CM-----draw dashed line from ESS to DELSCF
.DF\!h1 =\!hess +6*\!dpx
.DF\!v1 =\!vess -\!dpy
.DF\!h2 =\!hdel
.DF\!v2 =\!v1
.DF\!ipen =7
.GS$gline
.DF\!h1 =\!h2
.DF\!v1 =\!v2
.DF\!v2 =\!tdel
.GS$gline
.DF\!ipen =1
.GT$onward
.CM$gline ---------------------------------------------------------
.GR<<\!h1 \!v1 0//\!h2 \!v2 \!ipen >>
.RT
.CM$box ----------------------------------------------------------
.CM draw box centered below pointer, and return to pointer origin
.CM---------set \!nl = no. lines, \!wid = width (characters),
.CM---------and \line1 , \line2 , ...
.DF\!lfh =\!dpy /2
.DF\!dhl =\!hl *\!dpx
.DF\!dvl =\!vl *\!dpy
.DF\!dwid =\!wid *\!dpx
.DF\!dht =(\!nl +0.5)*\!dpy
.DF\!dhlfwid =\!dwid /2
.DF\!test1 =0.5-ABS((\!nl -1))
.DF\!test2 =0.5-ABS((\!nl -2))
.DF\!test3 =0.5-ABS((\!nl -3))
.DF\!test4 =0.5-ABS((\!nl -4))
.DF\!test5 =0.5-ABS((\!nl -5))
.IF<<\!test1 >>THEN<<\@line1 >>
.IF<<\!test2 >>THEN<<\@line2 >>
.IF<<\!test3 >>THEN<<\@line3 >>
.IF<<\!test4 >>THEN<<\@line4 >>
.IF<<\!test5 >>THEN<<\@line5 >>
.GR<<\!dhl +0 0//+0 -\!lfh 0//+\!dhlfwid +0 \!ipen //+0 -\!dht \!ipen //
-\!dwid +0 \!ipen //+0 +\!dht \!ipen //+\!dhlfwid +0 \!ipen >>
.DF\!dbot =\!dvl +(\!nl -1.25)*\!dpy +\!lfh
.DF\!dtop =\!dbot -\!dht
.RT
.CM$cyl -----------------------------------------------------
.CM set \!a =hor. radius, \!b = vert. radius, \!ht =height
.CM.DF\!a =4
.CM.DF\!b =0.5
.CM.DF
.DF\!dhl =\!hl *\!dpx
.DF\!dvl =\!vl *\!dpy
.DF\!t =0
.DF\!twopi =2*3.1415926
.DF\!dht =\!ht *\!dpy
.DF\!dhlfht =\!dht /2 -\!dpy /2
.DF\!radius =\!a *\!dpx
.DF\!diam =2*\!radius
.DF\!a2 =\!a *\!a
.DF\!b2 =\!b *\!b
.DF\!x =\!a *COS(\!t *\!twopi )
.DF\!y =-SQR(\!b2 *(1-\!x *\!x /\!a2 ))
.DF\!ym =-\!y
.GR<<\!dhl \!dvl 0//
F \!x \!y \!t 0.0001 0.5 .05 \!dpx \!dpy  0 1 \!ipen //+\!radius +0 0//
F \!x \!ym \!t 0.0001 0.5 .05 \!dpx \!dpy  0 1 \!ipen //
+0 +\!dht  \!ipen //+\!diam  -\!dht  0//+0 +\!dht  \!ipen //-\!radius  +0 0//
F \!x \!ym \!t 0.0001 -0.5 -0.05 \!dpx \!dpy  0 1 \!ipen //
+\!radius -\!dhlfht  0//'\text ' 2//+0 +\!lf 0//'file' 2>>
.RT
.CM----------------------------------------------------------------
.CM$onward
.LM15
.RM75
.FJ
.LN37
#BFigure 1:#N Schematic diagram depicting flow of information 
between the electronic
structure system (ESS) and the NBO program, 
and the commun#|ication lines connecting these programs to
the ESS scratch file
(called the ``dictionary file,'' ``read-write file,''
etc., in various systems) and the NBO direct access file (NBODAF).  Heavier 
box borders mark the ESS-specific driver 
routines (RUNNBO, FEAOIN,
DELSCF) that directly interface the ESS program.  The heavy dashed
lines denote calls from the NBO program `backward' to the ESS program
for information needed to carry out its tasks.  Otherwise, the sequential
flow of program control is generally from top to bottom
and from left to right in the diagram.
.LM10
.RM80
.FJ
.CM------------------end of Figure 1----------------------------------


.RL55
#IA.1.3 #IInput and Output#N

\np From the user's point of view, the #_input#/ to the NBO program
attached to an ESS program consists simply of one or
more keywords (an NBO #Ikeylist#N) included in the ESS input
file.  In effect, the NBO program reads these keywords to set
various job options, then interrogates the ESS program through
the DELSCF and FEAOIN drivers for additional information
concerning the wavefunction.  The general form of NBO keylists and
the specific functions associated with each keyword are detailed
in the User's Guide, Section B.  The method of 
including NBO keylists in the input file for each
ESS is detailed in the specific Appendix for the ESS.

\np The following information is passed from
the ESS to the NBO program (transparent to the user):
.LM+5
.RM-5

.OS<<3//1.>>
The one-electron density matrix #BD#N (or density matrices in the
open-shell case) in the chosen atomic orbital (AO) basis set;

.OS<<3//2.>>
The AO overlap matrix #BS#N, and label information identifying the
symmetry (angular momentum type) and location (number of the atom
to which affixed) for each AO;

.OS<<3//3.>>
Atomic number (nuclear charge) of each atom.

.LM-5
.RM+5
Certain additional information is written on the FILE48 direct
access file and may be used
in response to specific job
options,
such as the AO Fock matrix #BF#N, if energy analysis is requested; the
AO dipole matrix #BM#N, if dipole moment analysis is requested; or
information concerning the mathematical form of the AOs (orbital
exponents, contraction coefficients, etc.), if orbital plotting
information is requested
to be saved as input for a contour plotting program.

\np The principal #_output#/ from the NBO program 
consists of the tables and summaries describing
the results of NBO analysis, included in the ESS output
file.  Sample NBO output is described in Section A.2.4  
below.  If requested, the NBO program may also write out transformation
matrices or other data to disk files.  The NBO program also
creates or updates two files, the direct-access 
file (FILE48) and the `archive' file (FILE47) that
can be used to repeat NBO analysis with different options,
without running the ESS program to recalculate the 
wavefunction.  Necessary details of these files are given
in Section B.7 and the Programmer's Guide,
Section C.


.RL55
#IA.1.4 #IGeneral Capabilities and Restrictions#N

\np Principal capabilities of the NBO program are:

.LM+5
.RM-5
.OS<<3//1.>>
Natural population, natural bond orbital, and natural localized
molecular orbital analysis of SCF, MCSCF, CI, and M\not oller-Plesset
wavefunctions (main subroutine: NBO);

.OS<<3//2.>>
For RHF closed-shell and UHF wavefunctions only,
energetic analysis of the wavefunction in terms of the interactions
(Fock matrix elements) between NBOs (main subroutine: NBOEAN);

.OS<<3//3.>>
Localized analysis of molecular dipole moment in terms of NLMO
and NBO bond moments and their interactions (main subroutine: DIPANL).

.LM-5
.RM+5
\np A highly transportable subset of standard FORTRAN 77 is employed,
with no special compiler extensions of any vendor,
and all variable names of six characters or less.  Common
abbreviations used in naming subprograms, variables, and keywords are:

.LM+10
.OS<<6//S>>
= overlap matrix
.OS<<6//DM>>
= density matrix (or D)
.OS<<6//F>>
= Fock matrix
.OS<<6//DI>>
= dipole matrix (or DXYZ, or DX, DY, DZ)
.OS<<6//NPA>>
= Natural Population Analysis
.OS<<6//NAO>>
= Natural Atomic Orbital
.OS<<6//NBO>>
= Natural Bond Orbital
.OS<<6//NLMO>>
= Natural Localized Molecular Orbital
.OS<<6//PNAO>>
= pre-orthogonal NAO (i.e., omit interatomic orthogonalization)
.OS<<6//PNHO, PNBO, PNLMO = pre-orthogonal  NHO, etc. (formed from PNAOs)>>
\thsp

.LM-10
\np Most of the NBO storage is allocated dynamically, to conform to
the minimum required for the molecular system under study.  However,
certain NBO common blocks of fixed dimensionality are used for
integer storage.  These are currently dimensioned to accomodate
up to 99 atoms and 500 basis functions.  Section C.3 describes how
these restrictions can be altered.  The program is not set up to
handle complex wavefunctions, but can treat any real RHF, ROHF, UHF, MCSCF
(including GVB), CI, or M\not oller-Plesset-type wavefunction
(i.e., any form of wavefunction for which the requisite density
matrices are available) for ground or excited states of general
open- or closed-shell molecules.  Effective core potentials
(``pseudo#|potentials'') can be handled, including complete neglect
of core electrons as assumed in semi-empirical treatments.  The
atomic orbital basis functions (up to #If#N orbitals in angular
symmetry) may be of general Slater-type, contracted Gaussian-type,
or other general composition,
including the ``effective'' ortho#|normal valence-shell AOs of
semi-empirical treatments.  AO basis functions are
assumed to be normalized, but in general non-orthogonal.


.RL55
#IA.1.5 #IReferences and Relationship to Previous Versions#N

\np This program (``version 3.0'') is an extension of previous versions of the
NBO method incorporated in the semi-empirical program #IBONDO#N
[F. Weinhold, #IQuantum Chemistry Program Exchange No. 408#N
(1980); ``version 1.0'']
and in a GAUSSIAN-82 implementation [A. E. Reed and F. Weinhold, #IQCPE 
Bull. #B5#N, 141 (1985); ``version 2.0''], and should be considered to supplant
those versions.  Version 3.0 also supplants the various specific versions 
(``the GAMESS version,'' ``the AMPAC version,'' etc.) 
that have been informally created and distributed to individual users outside
the QCPE framework.

Principal contributors to the development of
the NBO methods and programs (1975-1990) are

.TB
.FM<<10L20//5L25>>
.RW<<T. K. Brunck//A. E. Reed>>
.RW<<J. P. Foster//J. E. Carpenter>>
.RW<<A. B. Rives//E. D. Glendening>>
.RW<<R. B. Weinstock//F. Weinhold>>
.ET

Principal references to the development and applications of NAO/NBO/NLMO
methods are:

.LM+3
.OS<<3//#_Natural Bond Orbitals:#/>>

J. P. Foster and F. Weinhold, #IJ. Am. Chem. Soc. #B102#N, 7211-7218
(1980). 

.OS<<3//#_Natural Atomic Orbitals and Natural Population Analysis:#/>>

A. E. Reed and F. Weinhold, #IJ. Chem. Phys. #B78#N, 4066-4073 (1983);
A. E. Reed, R. B. Weinstock, and F. Weinhold, #IJ. Chem. Phys. #B83#N,
735-746 (1985).  

.OS<<3//#_Natural Localized Molecular Orbitals:#/>>

 A. E. Reed and F. Weinhold, #IJ. Chem. Phys. #B83#N, 1736-1740 (1985).

.OS<<3//#_Open-Shell NBO:#/>>

J. E. Carpenter and F. Weinhold, #IJ. Molec. Struct. (Theochem) #B169#N,
41-62 (1988); J. E. Carpenter, #IPh. D. Thesis#N, University of Wisconsin,
Madison, 1987.

.OS<<3//#_Review Articles:#/>>

A. E. Reed, L. A. Curtiss, and F. Weinhold, #IChem. Rev. #B88#N, 
899-926 (1988); F. Weinhold and J. E. Carpenter, in, R. Naaman
and Z. Vager (eds.), ``The Structure of Small Molecules and
Ions,'' (Plenum, New York, 1988), pp. 227-236.

.LM10
\np The principal enhancements of version 3.0 include:

.LM+5
.RM-5
.OS<<3//1.>>
#IGeneralized Program Interface.#N
Overall program organization (Fig. 1) has been modified to
standardize communication with the main ESS program.  This
insures that all special ESS ``versions'' of the NBO program 
now have consistent options and capabilities
(as long as the option is meaningful in the context of the ESS), and enables
the program to be offered in a greater number of specialized ESS versions
than were previously available.

.OS<<3//2.>>
#INAO/NPA Summary Table.#N
New tables give improved display of NAOs and 
natural populations, including
the ``natural electron configuration'' of
each atom (i.e., the occupancy and type of NAOs describing
the atomic electron configuration of each atom).  The new NAO
summary tables (Section A.3.2)
include an SCF atomic orbital energy (if available),
a conventional atomic orbital label (1#Is#N,
2#Is#N, 2#Ip#N, etc., in accordance with the labelling
in isolated atoms), and a shell designation (Cor = core, Val = valence, 
or Ryd = Rydberg) to aid characterization of the NAO.

.OS<<3//3.>>
#INBO Summary Table.#N
A new NBO summary table (Section A.3.6) has been 
provided to summarize the energetics
and delocalization patterns of the principal NBOs.  This succinctly
combines the most important information from the full NBO table, diagonal
NBO Fock matrix elements, and
2nd-order energy analysis.

.OS<<3//4.>>
#IBond Bending Analysis.#N
The program includes a new analysis of hydrid directionality
and bond ``bending'' (keyword BEND, Section A.3.4).

.OS<<3//5.>>
#IDipole Moment Analysis.#N
The program includes new optional provision (keyword DIPOLE, Section
B.6.3) for
analysis of the molecular dipole moment in terms of localized
NLMOs and NBOs.

.OS<<3//6.>>
#IPrint options.#N
The program offers new structured printing options (Section B.2.4) that give
greater convenience and flexibility in controlling printed output,
with improved provision for printing matrices or
basis transformations involving general NAO, NHO, NBO, NLMO or
pre-orthogonal (PNAO, PNHO, PNBO, PNLMO) basis sets.

.OS<<3//7.>>
#IOrbital Contour Info.#N
The program makes optional provision (keyword PLOT, Section B.2.5) for
writing out files that can be used by an orbital plotting
program (available separately through QCPE) to 
draw contour diagrams of the NBOs or
other natural localized orbitals.

.OS<<3//8.>>
#IEffective Core Potentials.#N
The program now handles effective core potentials (pseudo#|potentials),
or the complete neglect of core levels characteristic of semi-empirical
wavefunctions (Section B.6.12).

.LM-5
.RM+5
The program also includes three changes to 
correct problems of the previous version (which may have
affected a small number of users):

.LM+5
.RM-5
.OS<<3//9.>>
#IUnpolarized Cores.#N
NAOs identified as ``core'' orbitals are now auto#|matically carried over
as unhybridized 1-center core NBOs 
(Section B.3).  This has virtually no effect on
the form or occupancy of a core NBO, but averts the (rare) problem of 
unphysical mixing between core and
valence lone pairs when the occupancies are `accidentally'
degenerate (usually, both very close to 2.000...)
within the numerical machine precision.  A warning message
is printed when the core occupancy is less than 1.9990, indicating
a possible ``core polarization'' effect of physical significance.

.OS<<3//10.>>
#IExcited State Antibond Labels.#N
The program now directly investigates the nodal structure of an NBO (by
examining the overlap matrix in the PNHO basis) before assigning it a
label as a ``bond'' (unstarred) or ``antibond'' (starred) NBO.  In previous
versions, these labels were assigned on the basis of the presumed higher
occupancy of the in-phase bond combination, which 
was generally true for ground
states, but not for excited states.  The program now
prints a warning message whenever it encounters the ``anomalous''
situation of an out-of-phase antibond NBO having higher occupancy than
the corresponding in-phase bond NBO, indicative of an excited-state
configuration.  [WARNING: the overlap test cannot be applied to
semi-empirical methods with orthogonal AOs (e.g., AMPAC), 
so antibond labels for these methods are assigned, as in previous
versions, on the basis of occupancy.]

.OS<<3//11.>>
#IAlternative Resonance Structures.#N The program now institutes a
search for alternative Lewis (`resonance') structures when two or
more structures may be competitive, and returns the
structure of lowest non-Lewis occupancy.  This corrects a possible
dependence on atomic numbering in cases of strong delocalization.

.LM-5
.RM+5
Despite these changes and extensions, version 3.0 has been
designed to be upward compatible with v. 2.0, as nearly as 
possible.  Previous users of NBO 2.0 should find that their jobs
run similarly (i.e., most keywords 
continue to function
as in previous versions).  Thus, experienced 
NBO users should find little difficulty
in adapting to, and experimenting with, 
the new capabilities of the program.
.HF<<A.2 INSTALLING THE NBO PROGRAM//3//10>>


.RL55
#BA.2 INSTALLING THE NBO PROGRAM#N

\np The NBO programs and manual are provided on a distribution tape.  The 
tape contains three files: the TechSet code of this
manual (file NBO.MAN), a file containing the core NBO source routines
and supporting driver routines (file NBO.SRC), and the Fortran
``enabler'' program (file ENABLE.FOR).  

\np In overview, the installation procedure involves the following steps
(the details of each step being dependent on your operating system):

.LM+5
.OS<<3//1.>>
#IEnabling the NBO routines.#N  Copy the contents of the distribution
tape onto your system.  Using your system Fortran 77 compiler, compile
and link the enabler program to create the ENABLE.EXE executable;
for example, the VMS commands to create ENABLE.EXE are
 #T
     FOR ENABLE
     LINK ENABLE

#NNow, run the ENABLE program (e.g., type ``RUN ENABLE'' in
a VMS system), and 
answer the prompt
 #T
     NBO program version to enable?

#Nby selecting from the available offerings.  Each ESS package is
associated with a 3-letter identifier
(``G88'' for GAUSSIAN-88, ``GMS'' for GAMESS,
``AMP'' for AMPAC, etc.).  The ENABLE program will create
a file #IXXX#NNBO.FOR (where `#IXXX#N' is the identifier)
that incorporates the appropriate drivers for
your ESS.  

.OS<<3//2.>>
#ICompiling the NBO routines.#N  Using your system Fortran 77 compiler,
compile the #IXXX#NNBO.FOR file to an object code file (say, 
#IXXX#NNBO.OBJ).  [Compiler
errors (if any) should be fixed before proceeding.  Please notify the
authors if you encounter undue difficulties in this step.]

.OS<<3//3.>>
#IModifying the ESS routines.#N  In general, the ESS source Fortran code
must be modified to call the NBO routines near the
point where the ESS performs Mulliken Population Analysis or evaluates
properties of the final wavefunction.  The modification generally
consists of inserting a single statement (viz., ``CALL RUNNBO'') in
one subroutine of your ESS system.  See the appropriate Appendix
of this Manual for detailed information on exactly how to modify
the ESS code for your chosen system.

.OS<<3//4.>>
#IRebuilding the integrated ESS/NBO program.#N  Re-compile your modified
ESS programs and link the resulting object file (say, ESS.OBJ) with
the #IXXX#NNBO.OBJ file to form the 
final ESS.EXE executable.  In general, this
step will closely follow the initial installation procedure for
your ESS, with the exception that the #IXXX#NNBO.OBJ file must be included
in the link statement (or deposited in one of the libraries accessed
by the linker, etc.).

.LM10
Note that installation of the NBO programs into your ESS system in no way
affects the way your system processes standard input files.  The only
change involves enabling the reading of NBO keylists 
(if detected in your input
file), performance of the tasks requested in the keylist, and return 
of control to the parent ESS program in the state in which the
NBO call was encountered.

\np If you are interfacing the NBO programs to a new ESS package (not
represented in the driver routines provided with this distribution),
see Section C for guidance on how to create drivers for your ESS
to provide the necessary information.  Alternatively, see
Section B.7 for a description of the input file to GENNBO,
the stand-alone version of the NBO program.

\np The TechSet-coded version of this manual, NBO.MAN, can be
printed on an HP LaserJet printer 
(`F' cartridge) with the TECHSET 
technical typesetting program [ACS Software, American Chemical Society, 
Marketing Communications
Dept., 1155 Sixteenth Street, N.W., Washington, D.C. 20036].
.HF<<A.3 TUTORIAL EXAMPLE FOR METHYLAMINE//3//10>>


.RL55
#BA.3 TUTORIAL EXAMPLE FOR METHYLAMINE#N

#IA.3.1 Running the Example#N

\np This section provides an introductory `quick start' tutorial 
on running a simple NBO job and interpreting the output.  The example
chosen is that of methylamine (CH#d3#uNH#d2#u) in
Pople-Gordon idealized geometry, treated at the #Iab initio#N
RHF/3-21G level.  This simple split-valence
basis set consists of 28 AOs (nine each
on C and N, two on each H), extended by 13 AOs beyond
the minimal basis level.

\np Input files to run this job (or its nearest equivalent) with
each ESS are given in the Appendix.  (The output shown below was
created with the GAMESS system.)  In most cases, you can modify
the standard ESS input file to produce NBO output by
simply including the line
 #T
     $NBO $END

#Nat the end of the file.  This is an `empty' NBO keylist, specifying
that NBO analysis should be carried out at the #Idefault#N level.

\np The default NBO output produced by this example is shown below,
just as it appears in your output file.  The 
start of the NBO section is marked
by a standard header and storage info:

.HR<<5//+0//5//85>>
.CM----------------------output file----------------------------------------
.DF\@seg =
.RL9
*******************************************************************************
            N A T U R A L   A T O M I C   O R B I T A L   A N D
         N A T U R A L   B O N D   O R B I T A L   A N A L Y S I S
*******************************************************************************

Job title:  Methylamine...RHF/3-21G//Pople-Gordon standard geometry             

Storage needed:  2505 in NPA,  2569 in NBO ( 750000 available)
.ED
.DF\!lm =5
.DF\!rm =88
.LM\!lm
.RM\!rm
 #T
\@seg

.LM10
.RM80
.HR<<5//+0//5//85>>

#NNote that all NBO output is formatted to a maximum 80-character
width for convenient display on a computer terminal.  The NBO heading
echoes any requested keywords (none for the present default case)
and shows an estimate of the memory requirements 
(in double precision words) for the separate 
steps of the NBO process, compared
to the total allocated memory available through your ESS
process.  Increase the memory allocated to your
ESS process if the estimated NBO requests exceed the available storage.
.RL55
.FJ
#IA.3.2 Natural Population Analysis#N

#N\np The next four NBO output segments 
summarize the results of natural population
analysis (NPA).  The first segment is the main NAO table, as shown
below:  

.HR<<5//+0//5//85>>
.DF\@seg =
NATURAL POPULATIONS:  Natural atomic orbital occupancies 
                                                         
 NAO Atom #  lang   Type(AO)    Occupancy      Energy    
---------------------------------------------------------
  1    C  1  s      Cor( 1s)     1.99900     -11.04184
  2    C  1  s      Val( 2s)     1.09038      -0.28186
  3    C  1  s      Ryd( 3s)     0.00068       1.95506
  4    C  1  px     Val( 2p)     0.89085      -0.01645
  5    C  1  px     Ryd( 3p)     0.00137       0.93125
  6    C  1  py     Val( 2p)     1.21211      -0.07191
  7    C  1  py     Ryd( 3p)     0.00068       1.03027
  8    C  1  pz     Val( 2p)     1.24514      -0.08862
  9    C  1  pz     Ryd( 3p)     0.00057       1.01801

 10    N  2  s      Cor( 1s)     1.99953     -15.25950
 11    N  2  s      Val( 2s)     1.42608      -0.71700
 12    N  2  s      Ryd( 3s)     0.00016       2.75771
 13    N  2  px     Val( 2p)     1.28262      -0.18042
 14    N  2  px     Ryd( 3p)     0.00109       1.57018
 15    N  2  py     Val( 2p)     1.83295      -0.33858
 16    N  2  py     Ryd( 3p)     0.00190       1.48447
 17    N  2  pz     Val( 2p)     1.35214      -0.19175
 18    N  2  pz     Ryd( 3p)     0.00069       1.59492

 19    H  3  s      Val( 1s)     0.81453       0.13283
 20    H  3  s      Ryd( 2s)     0.00177       0.95067

 21    H  4  s      Val( 1s)     0.78192       0.15354
 22    H  4  s      Ryd( 2s)     0.00096       0.94521

 23    H  5  s      Val( 1s)     0.78192       0.15354
 24    H  5  s      Ryd( 2s)     0.00096       0.94521

 25    H  6  s      Val( 1s)     0.63879       0.20572
 26    H  6  s      Ryd( 2s)     0.00122       0.99883

 27    H  7  s      Val( 1s)     0.63879       0.20572
 28    H  7  s      Ryd( 2s)     0.00122       0.99883
.ED
.LM\!lm
.RM\!rm
 #T
.RS#~
\@seg
.RS~#

.LM10
.RM80
.HR<<5//+0//5//85>>

#NFor each 
of the 28 NAO functions, this table lists the atom
to which NAO is attached (in the numbering scheme of the ESS program),
the angular momentum type `lang' (#Is#N, #Ip#dx#u#N, etc., in the coordinate
system of the ESS program), the orbital type (whether core, valence, or
Rydberg, and a conventional
hydrogenic-type label), the orbital occupancy (number of
electrons, or `natural 
population' of the orbital), and the orbital energy (in the favored units
of the ESS program, in this case atomic units: 1 a.u. = 627.5 
kcal/mol).  [For example, NAO 4 (the highest energy C orbital of the
NMB set) is the valence shell 2#Ip#N#dx#u orbital on carbon, occupied
by 0.8909 electrons, whereas NAO 5 is a Rydberg 
3#Ip#N#dx#u orbital with only 0.0014 electrons.]  Note that the 
occupancies of the Rydberg (Ryd) NAOs are
typically much lower than those of the core (Cor) plus
valence (Val)
NAOs of the natural minimum basis set, reflecting 
the dominant role of the NMB orbitals 
in describing molecular properties. 

\np The principal quantum numbers for the
NAO labels (1#Is#N, 2#Is#N, 3#Is#N, etc.) are assigned on the
basis of the energy order if a Fock matrix is available, or on the
basis of occupancy otherwise.  A message is printed warning of
a `population inversion' if the occupancy and energy
ordering do not coincide.

.CM------------------------------------------------------------------------
.DF\@seg =
Summary of Natural Population Analysis:                  
                                                         
                                      Natural Population 
              Natural   -----------------------------------------------
   Atom #     Charge        Core      Valence    Rydberg      Total
-----------------------------------------------------------------------
     C  1   -0.44079      1.99900     4.43848    0.00331     6.44079
     N  2   -0.89715      1.99953     5.89378    0.00384     7.89715
     H  3    0.18370      0.00000     0.81453    0.00177     0.81630
     H  4    0.21713      0.00000     0.78192    0.00096     0.78287
     H  5    0.21713      0.00000     0.78192    0.00096     0.78287
     H  6    0.35999      0.00000     0.63879    0.00122     0.64001
     H  7    0.35999      0.00000     0.63879    0.00122     0.64001
=======================================================================
  * Total *  0.00000      3.99853    13.98820    0.01328    18.00000
.ED

.RL19
#NThe next segment is an atomic summary showing the 
natural atomic charges (nuclear
charge minus summed
natural populations of NAOs on the atom) and total
core, valence, and Rydberg populations on each atom:

.HR<<5//+0//5//85>>
.LM\!lm
.RM\!rm
 #T
.RS#~
\@seg
.RS~#

.LM10
.RM80
.HR<<5//+0//5//85>>

#NThis table succinctly describes the molecular
charge distribution in terms of NPA charges.  [For example,
the carbon atom of methylamine is assigned a net NPA 
charge of \minus 0.441
at this level; note also the slightly less positive charge
on H(3) than on the other two methyl hydrogens: +0.184 vs. +0.217.]
.DF\@seg =
                                Natural Population      
--------------------------------------------------------
  Core                       3.99853 ( 99.9632% of   4)
  Valence                   13.98820 ( 99.9157% of  14)
  Natural Minimal Basis     17.98672 ( 99.9262% of  18)
  Natural Rydberg Basis      0.01328 (  0.0738% of  18)
--------------------------------------------------------
.ED

.RL15
#NNext follows a summary of the NMB and NRB populations
for the composite
system, summed over atoms:

.HR<<5//+0//5//85>>
 #T
.LM\!lm
.RM\!rm
\@seg

.LM10
.RM80
.HR<<5//+0//5//85>>

#NThis exhibits the high percentage contribution (typically, > 99%) 
of the NMB set to the molecular charge distribution.  [In the present
case, for example, the 13 Rydberg orbitals of the 
NRB set contribute only 0.07%
of the electron density, whereas the 15 NMB functions account
for 99.93% of the total.]

.RL16
#NFinally, the natural populations are summarized as an effective
valence electron configuration (``natural electron configuration'')
for each atom:
.DF\@seg =
   Atom #          Natural Electron Configuration
----------------------------------------------------------------------------
     C  1      [core]2s( 1.09)2p( 3.35)
     N  2      [core]2s( 1.43)2p( 4.47)
     H  3            1s( 0.81)
     H  4            1s( 0.78)
     H  5            1s( 0.78)
     H  6            1s( 0.64)
     H  7            1s( 0.64)
.ED

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.RS~#

.LM10
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#NAlthough the occupancies of the atomic orbitals are non-integer
in the molecular environment, the effective atomic configurations
can be related to idealized atomic states in
`promoted' configurations.  [For example, the carbon atom in
the above table is most nearly described by an idealized
1s#u2#d2s#u1#d2p#u3#d electron configuration.]


.RL55
#IA.3.3 Natural Bond Orbital Analysis#N

#N\np The next segments of the output summarize the results 
of NBO analysis.  The first segment reports on details of the search for
an NBO natural Lewis structure: 

.DF\@seg =
NATURAL BOND ORBITAL ANALYSIS:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    1.90    17.95048   0.04952      2   6   0   1     0      0    0.02
-----------------------------------------------------------------------------

Structure accepted: No low occupancy Lewis orbitals
.ED
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#NNormally, there is but one cycle of the NBO search (cf. the
``RESONANCE'' keyword, Section B.6.6).  The table summarizes
a variety of information for each cycle:
the occupancy thresh#|old for a `good' pair in the NBO search; 
the total populations of Lewis and non-Lewis
NBOs; the number of core (CR), 2-center bond (BD), 
3-center bond (3C), and lone pair (LP) NBOs in
the natural Lewis structure; the number of low-occupancy Lewis (L)
and `high-occupancy' (> 0.1e) non-Lewis (NL) orbitals; and the
maximum deviation (`Dev') of any formal bond order from a 
nominal estimate (NAO Wiberg bond index) for the structure.  [If
the latter exceeds 0.1, additional NBO searches are initiated
(indicated by the parenthesized number under `Cycle') for alternative
Lewis structures.]  The Lewis 
structure is accepted if all orbitals of the formal Lewis structure
exceed the occupancy thresh#|old (default, 1.90 electrons).

.RL22
\np #NNext follows a more detailed breakdown of the Lewis and non-Lewis
occupancies into core, valence, and Rydberg shell contributions:
.DF\@seg =
WARNING:  1 low occupancy (<1.9990e) core orbital  found on  C 1

--------------------------------------------------------
  Core                      3.99853 ( 99.963% of   4)
  Valence Lewis            13.95195 ( 99.657% of  14)
 ==================       ============================
  Total Lewis              17.95048 ( 99.725% of  18)
 -----------------------------------------------------
  Valence non-Lewis         0.03977 (  0.221% of  18)
  Rydberg non-Lewis         0.00975 (  0.054% of  18)
 ==================       ============================
  Total non-Lewis           0.04952 (  0.275% of  18)
--------------------------------------------------------
.ED

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#NThis shows the general quality of the natural Lewis structure
description in terms of the percentage of the total electron
density (e.g., in the above case, about 99.7%).  The table also
exhibits the relatively important role of the valence non-Lewis
orbitals (i.e., the six valence antibonds, NBOs 23-28) relative to
the extra-valence orbitals (the 13 Rydberg NBOs 10-22) in the
slight departures from a localized Lewis structure model.  (In
this case, the table also includes a warning about a carbon core
orbital with slightly less than double occupancy.)

.DF\@seg =
    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (1.99858) BD ( 1) C 1- N 2      
               ( 40.07%)   0.6330* C 1 s( 21.71%)p 3.61( 78.29%)
                                       -0.0003 -0.4653 -0.0238 -0.8808 -0.0291
                                       -0.0786 -0.0110  0.0000  0.0000
               ( 59.93%)   0.7742* N 2 s( 30.88%)p 2.24( 69.12%)
                                       -0.0001 -0.5557  0.0011  0.8302  0.0004
                                        0.0443 -0.0098  0.0000  0.0000
  2. (1.99860) BD ( 1) C 1- H 3      
               ( 59.71%)   0.7727* C 1 s( 25.78%)p 2.88( 74.22%)
                                       -0.0002 -0.5077  0.0069  0.1928  0.0098
                                        0.8396 -0.0046  0.0000  0.0000
               ( 40.29%)   0.6347* H 3 s(100.00%)
                                       -1.0000 -0.0030
  3. (1.99399) BD ( 1) C 1- H 4      
               ( 61.02%)   0.7812* C 1 s( 26.28%)p 2.80( 73.72%)
                                        0.0001  0.5127 -0.0038 -0.3046 -0.0015
                                        0.3800 -0.0017  0.7070 -0.0103
               ( 38.98%)   0.6243* H 4 s(100.00%)
                                        1.0000  0.0008
  4. (1.99399) BD ( 1) C 1- H 5      
               ( 61.02%)   0.7812* C 1 s( 26.28%)p 2.80( 73.72%)
                                        0.0001  0.5127 -0.0038 -0.3046 -0.0015
                                        0.3800 -0.0017 -0.7070  0.0103
               ( 38.98%)   0.6243* H 5 s(100.00%)
                                        1.0000  0.0008
  5. (1.99442) BD ( 1) N 2- H 6      
               ( 68.12%)   0.8253* N 2 s( 25.62%)p 2.90( 74.38%)
                                        0.0000  0.5062  0.0005  0.3571  0.0171
                                       -0.3405  0.0069 -0.7070 -0.0093
               ( 31.88%)   0.5646* H 6 s(100.00%)
                                        1.0000  0.0020
  6. (1.99442) BD ( 1) N 2- H 7      
               ( 68.12%)   0.8253* N 2 s( 25.62%)p 2.90( 74.38%)
                                        0.0000  0.5062  0.0005  0.3571  0.0171
                                       -0.3405  0.0069  0.7070  0.0093
               ( 31.88%)   0.5646* H 7 s(100.00%)
                                        1.0000  0.0020
  7. (1.99900) CR ( 1) C 1             s(100.00%)p 0.00(  0.00%)
                                        1.0000 -0.0003  0.0000 -0.0002  0.0000
                                        0.0001  0.0000  0.0000  0.0000
  8. (1.99953) CR ( 1) N 2             s(100.00%)p 0.00(  0.00%)
                                        1.0000 -0.0001  0.0000  0.0001  0.0000
                                        0.0000  0.0000  0.0000  0.0000
  9. (1.97795) LP ( 1) N 2             s( 17.85%)p 4.60( 82.15%)
                                        0.0000  0.4225  0.0002  0.2360 -0.0027
                                        0.8749 -0.0162  0.0000  0.0000
 10. (0.00105) RY*( 1) C 1             s(  1.57%)p62.84( 98.43%)
                                        0.0000 -0.0095  0.1248 -0.0305  0.7302
                                       -0.0046  0.6710  0.0000  0.0000
 11. (0.00034) RY*( 2) C 1             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0146  0.9999
 12. (0.00022) RY*( 3) C 1             s( 56.51%)p 0.77( 43.49%)
                                        0.0000 -0.0023  0.7517 -0.0237  0.3710
                                       -0.0094 -0.5447  0.0000  0.0000
 13. (0.00002) RY*( 4) C 1             s( 41.87%)p 1.39( 58.13%)
 14. (0.00116) RY*( 1) N 2             s(  1.50%)p65.53( 98.50%)
                                        0.0000 -0.0062  0.1224  0.0063  0.0371
                                        0.0197  0.9915  0.0000  0.0000
 15. (0.00044) RY*( 2) N 2             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000 -0.0132  0.9999
 16. (0.00038) RY*( 3) N 2             s( 33.38%)p 2.00( 66.62%)
                                        0.0000  0.0133  0.5776  0.0087 -0.8150
                                       -0.0121 -0.0405  0.0000  0.0000
 17. (0.00002) RY*( 4) N 2             s( 65.14%)p 0.54( 34.86%)
 18. (0.00178) RY*( 1) H 3             s(100.00%)
                                       -0.0030  1.0000
 19. (0.00096) RY*( 1) H 4             s(100.00%)
                                       -0.0008  1.0000
 20. (0.00096) RY*( 1) H 5             s(100.00%)
                                       -0.0008  1.0000
 21. (0.00122) RY*( 1) H 6             s(100.00%)
                                       -0.0020  1.0000
 22. (0.00122) RY*( 1) H 7             s(100.00%)
                                       -0.0020  1.0000
 23. (0.00016) BD*( 1) C 1- N 2      
               ( 59.93%)   0.7742* C 1 s( 21.71%)p 3.61( 78.29%)
                                       -0.0003 -0.4653 -0.0238 -0.8808 -0.0291
                                       -0.0786 -0.0110  0.0000  0.0000
               ( 40.07%)  -0.6330* N 2 s( 30.88%)p 2.24( 69.12%)
                                       -0.0001 -0.5557  0.0011  0.8302  0.0004
                                        0.0443 -0.0098  0.0000  0.0000
 24. (0.01569) BD*( 1) C 1- H 3      
               ( 40.29%)   0.6347* C 1 s( 25.78%)p 2.88( 74.22%)
                                        0.0002  0.5077 -0.0069 -0.1928 -0.0098
                                       -0.8396  0.0046  0.0000  0.0000
               ( 59.71%)  -0.7727* H 3 s(100.00%)
                                        1.0000  0.0030
 25. (0.00769) BD*( 1) C 1- H 4      
               ( 38.98%)   0.6243* C 1 s( 26.28%)p 2.80( 73.72%)
                                       -0.0001 -0.5127  0.0038  0.3046  0.0015
                                       -0.3800  0.0017 -0.7070  0.0103
               ( 61.02%)  -0.7812* H 4 s(100.00%)
                                       -1.0000 -0.0008
 26. (0.00769) BD*( 1) C 1- H 5      
               ( 38.98%)   0.6243* C 1 s( 26.28%)p 2.80( 73.72%)
                                       -0.0001 -0.5127  0.0038  0.3046  0.0015
                                       -0.3800  0.0017  0.7070 -0.0103
               ( 61.02%)  -0.7812* H 5 s(100.00%)
                                       -1.0000 -0.0008
 27. (0.00426) BD*( 1) N 2- H 6      
               ( 31.88%)   0.5646* N 2 s( 25.62%)p 2.90( 74.38%)
                                        0.0000 -0.5062 -0.0005 -0.3571 -0.0171
                                        0.3405 -0.0069  0.7070  0.0093
               ( 68.12%)  -0.8253* H 6 s(100.00%)
                                       -1.0000 -0.0020
 28. (0.00426) BD*( 1) N 2- H 7      
               ( 31.88%)   0.5646* N 2 s( 25.62%)p 2.90( 74.38%)
                                        0.0000 -0.5062 -0.0005 -0.3571 -0.0171
                                        0.3405 -0.0069 -0.7070 -0.0093
               ( 68.12%)  -0.8253* H 7 s(100.00%)
                                       -1.0000 -0.0020
.ED

.RL20
#NNext follows the main listing of NBOs, displaying the form and occupancy
of the complete set of NBOs that span the input AO space:  
 #T

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#NFor each NBO (1-28), the
first line of printout
shows the occupancy (between 0 and 2.0000 electrons) and unique label
of the NBO.  This 
label gives the type
(``BD'' for 2-center bond, ``CR'' for 1-center core pair, ``LP'' for 1-center
valence lone pair, ``RY*'' for 1-center Rydberg, and ``BD*'' for 2-center
antibond, the unstarred and starred labels corresponding to Lewis
and non-Lewis NBOs, respectively), a serial number (1, 2,... if there is a
single, double,... bond between the pair of atoms), and the atom(s) to
which the NBO is affixed.  [For example, the first NBO in the sample
output is the  2-center bond (with 1.99858 electrons)
between carbon (atom 1) and nitrogen (atom 2), the \sigma #dCN#u 
bond.]  The next lines summarize
the natural atomic hybrids #Ih#N#dA#u
of which the NBO is composed, giving the
percentage (100|#Ic#N#dA#u|#u2#d) of the NBO on each hybrid (in parentheses),
the polarization coefficient #Ic#N#dA#u, the atom label, and a hybrid
label showing the #Isp#N#u\lambda #d composition 
(percentage #Is#N-character, #Ip#N-character, etc.) of
each #Ih#N#dA#u.  [For example, the \sigma #dCN#u NBO 
is formed from an #Isp#N#u3.61#d hybrid (78.3%
#Ip#N-character) on carbon interacting with an #Isp#N#u2.24#d hybrid
(69.1% #Ip#N-character) on nitrogen,

.CJ
\sigma #dCN#u = 0.633(#Isp#N#u3.61#d)#dC#u + 0.774(#Isp#N#u2.24#d)#dN#u 
.FJ

corresponding roughly to the qualitative concept 
of interacting #Isp#N#u3#d hybrids (75% #Ip#N-character) and the higher
electronegativity (larger polarization coefficient) of N.]  Below 
each NHO label is the set of
coefficients that specify how the NHO is written explicitly as a linear
combination of NAOs on the atom.  The order of NAO coefficients follows
the numbering of the NAO tables.  [For example, in the first NBO entry,
the carbon hybrid #Ih#N#dC#u 
of the \sigma #dCN#u bond has largest coefficients for the 2#und#d
and 4#uth#d NAOs, corresponding to the approximate description

.CJ
#Ih#N#dC#u \~=  \minus 0.4653(2#Is#N)#dC#u \minus  0.8808(2#Ip#N#dx#u)#dC#u
.FJ

in terms of the valence NAOs of the carbon atom.]  In 
the CH#d3#uNH#d2#u example, the NBO search
finds the C-N bond (NBO 1), three C-H bonds (NBOs 2, 3, 4), two N-H
bonds (NBOs 5, 6), N lone pair (NBO 9), and C and N
core pairs (NBOs 7, 8) of the expected Lewis structure.  NBOs 10-28
represent the residual non-Lewis NBOs of low occupancy.  In this
example, it is also interesting to note the slight asymmetry of the three
\sigma #dCH#u NBOs, and the slightly higher occupancy 
(0.01569 #Ivs.#N 0.0077
electrons) in the \sigma *#<#dC#d1#uH#d3#u#u antibond 
(NBO 24) lying #Itrans#N to the
nitrogen lone pair.
.RL55
#IA.3.4 NHO Directional Analysis#N

\np The next segment of output
summarizes the angular properties of
the natural hybrid orbitals:  

.DF\@seg =
NHO Directionality and "Bond Bending" (deviations from line of nuclear centers)

        [Thresholds for printing:  angular deviation  >  1.0 degree]
                                   hybrid p-character > 25.0%
                                   orbital occupancy  >  0.10e

                      Line of Centers        Hybrid 1              Hybrid 2
                      ---------------  -------------------   ------------------
          NBO           Theta   Phi    Theta   Phi    Dev    Theta   Phi    Dev
===============================================================================
  1. BD ( 1) C 1- N 2    90.0    5.4     --     --    --      90.0  182.4   3.0
  3. BD ( 1) C 1- H 4    35.3  130.7    34.9  129.0   1.0      --     --    --
  4. BD ( 1) C 1- H 5   144.7  130.7   145.1  129.0   1.0      --     --    --
  5. BD ( 1) N 2- H 6   144.7  310.7   145.0  318.3   4.4      --     --    --
  6. BD ( 1) N 2- H 7    35.3  310.7    35.0  318.3   4.4      --     --    --
  9. LP ( 1) N 2          --     --     90.0   74.8   --       --     --    --
.ED

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#NThe `direction' of a hybrid is specified 
in terms of the polar (\theta ) and 
azimuthal (\phi ) angles (in the ESS coordinate system) of the vector
describing its #Ip#N-component.  The hybrid direction is
compared with the direction of the line of centers between the two
nuclei to determine the `bending' of the bond, expressed as
the deviation angle (``Dev,'' in degrees) between these two directions.  For
example, in the CH#d3#uNH#d2#u case shown above, the nitrogen NHO
of the \sigma #dCN#u bond (NBO 1) is bent away 
from the line of C-N
centers by 3.0\degree , whereas the carbon NHO is approximately 
aligned with the C-N axis (within the 1.0\degree  threshold for 
printing).  The N-H bonds (NBOs 5, 6) are 
bent even further (4.4\degree ).  The information in this table
is often useful in anticipating the direction of geometry changes
resulting from geometry optimization (viz., likely reduced pyramidalization
of the -NH#d2#u group to relieve the nitrogen bond `kinks' found
in the tetrahedral Pople-Gordon geometry).


.RL55
#IA.3.5 Perturbation Theory Energy Analysis#N

\np The next segment summarizes the second-order perturbative estimates
of `donor-acceptor' (bond-antibond) interactions in the NBO basis:
.DF\@seg =
Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis

    Threshold for printing:   0.50 kcal/mol
                                                         E(2)  E(j)-E(i) F(i,j)
     Donor NBO (i)              Acceptor NBO (j)       kcal/mol   a.u.    a.u. 
===============================================================================

within unit  1
  2. BD ( 1) C 1- H 3     / 14. RY*( 1) N 2              0.84    2.18    0.038
  3. BD ( 1) C 1- H 4     / 26. BD*( 1) C 1- H 5         0.52    1.39    0.024
  3. BD ( 1) C 1- H 4     / 27. BD*( 1) N 2- H 6         3.03    1.37    0.057
  4. BD ( 1) C 1- H 5     / 25. BD*( 1) C 1- H 4         0.52    1.39    0.024
  4. BD ( 1) C 1- H 5     / 28. BD*( 1) N 2- H 7         3.03    1.37    0.057
  5. BD ( 1) N 2- H 6     / 10. RY*( 1) C 1              0.56    1.78    0.028
  5. BD ( 1) N 2- H 6     / 25. BD*( 1) C 1- H 4         2.85    1.51    0.059
  6. BD ( 1) N 2- H 7     / 10. RY*( 1) C 1              0.56    1.78    0.028
  6. BD ( 1) N 2- H 7     / 26. BD*( 1) C 1- H 5         2.85    1.51    0.059
  7. CR ( 1) C 1          / 16. RY*( 3) N 2              0.61   13.11    0.080
  7. CR ( 1) C 1          / 18. RY*( 1) H 3              1.40   11.99    0.116
  7. CR ( 1) C 1          / 19. RY*( 1) H 4              1.55   11.99    0.122
  7. CR ( 1) C 1          / 20. RY*( 1) H 5              1.55   11.99    0.122
  8. CR ( 1) N 2          / 10. RY*( 1) C 1              1.51   16.23    0.140
  8. CR ( 1) N 2          / 12. RY*( 3) C 1              0.84   16.77    0.106
  8. CR ( 1) N 2          / 21. RY*( 1) H 6              0.61   16.26    0.089
  8. CR ( 1) N 2          / 22. RY*( 1) H 7              0.61   16.26    0.089
  9. LP ( 1) N 2          / 24. BD*( 1) C 1- H 3         8.13    1.13    0.086
  9. LP ( 1) N 2          / 25. BD*( 1) C 1- H 4         1.46    1.14    0.037
  9. LP ( 1) N 2          / 26. BD*( 1) C 1- H 5         1.46    1.14    0.037
.ED

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#NThis is carried out by examining all possible
interactions between
`filled' (donor) Lewis-type NBOs and `empty' (acceptor) non-Lewis
NBOs, and estimating their energetic importance by 2nd-order perturbation
theory.  Since these interactions lead to loss of occupancy from the
localized NBOs of the idealized Lewis structure into 
the empty non-Lewis orbitals (and thus, to departures from the
idealized Lewis structure description), they are referred to
as `delocalization' corrections to the zeroth-order natural Lewis
structure.  For each donor NBO (#Ii#N) and acceptor NBO (#Ij#N), 
the stabilization energy E(2) associated with delocalization
(``2e-stabilization'') #Ii \rarr  j#N is estimated as

.CJ
.DF\denom =\epsilon #dj#u \minus  \epsilon #di#u
E(2) = \Delta E#dij#u = q#di#u \quo <<F(i,j)#u2#d//\denom >>
.FJ

where #Iq#N#di#u is the donor orbital occupancy,
\epsilon #di#u, \epsilon #dj#u are diagonal elements (orbital energies)
and F(i,j) is the off-diagonal NBO Fock matrix element.  [In the example
above, the #In#N#dN#u \rarr  \sigma *#<#dCH#u interaction between the
nitrogen lone pair (NBO 8) and the antiperiplanar C#d1#u-H#d3#u antibond
(NBO 24) is seen to give the strongest
stabilization, 8.13 kcal/mol.]  As the heading
indicates, entries are included in this table only when the interaction
energy exceeds a default threshold of 0.5 kcal/mol.
.RL55
#IA.3.6 NBO Summary#N

\np Next appears a condensed summary of the principal NBOs, showing the
occupancy, orbital energy, and the qualitative pattern of delocalization
interactions associated with each:
.DF\@seg =
Natural Bond Orbitals (Summary):

                                                    Principal Delocalizations
          NBO              Occupancy    Energy      (geminal,vicinal,remote)
===============================================================================
Molecular unit  1  (CH5N)
  1. BD ( 1) C 1- N 2       1.99858    -0.89908
  2. BD ( 1) C 1- H 3       1.99860    -0.69181    14(v)
  3. BD ( 1) C 1- H 4       1.99399    -0.68892    27(v),26(g)
  4. BD ( 1) C 1- H 5       1.99399    -0.68892    28(v),25(g)
  5. BD ( 1) N 2- H 6       1.99442    -0.80951    25(v),10(v)
  6. BD ( 1) N 2- H 7       1.99442    -0.80951    26(v),10(v)
  7. CR ( 1) C 1            1.99900   -11.04131    19(v),20(v),18(v),16(v)
  8. CR ( 1) N 2            1.99953   -15.25927    10(v),12(v),21(v),22(v)
  9. LP ( 1) N 2            1.97795    -0.44592    24(v),25(v),26(v)
 10. RY*( 1) C 1            0.00105     0.97105
 11. RY*( 2) C 1            0.00034     1.02120
 12. RY*( 3) C 1            0.00022     1.51414
 13. RY*( 4) C 1            0.00002     1.42223
 14. RY*( 1) N 2            0.00116     1.48790
 15. RY*( 2) N 2            0.00044     1.59323
 16. RY*( 3) N 2            0.00038     2.06475
 17. RY*( 4) N 2            0.00002     2.25932
 18. RY*( 1) H 3            0.00178     0.94860
 19. RY*( 1) H 4            0.00096     0.94464
 20. RY*( 1) H 5            0.00096     0.94464
 21. RY*( 1) H 6            0.00122     0.99735
 22. RY*( 1) H 7            0.00122     0.99735
 23. BD*( 1) C 1- N 2       0.00016     0.57000
 24. BD*( 1) C 1- H 3       0.01569     0.68735
 25. BD*( 1) C 1- H 4       0.00769     0.69640
 26. BD*( 1) C 1- H 5       0.00769     0.69640
 27. BD*( 1) N 2- H 6       0.00426     0.68086
 28. BD*( 1) N 2- H 7       0.00426     0.68086
      -------------------------------
             Total Lewis   17.95048  ( 99.7249%)
       Valence non-Lewis    0.03977  (  0.2209%)
       Rydberg non-Lewis    0.00975  (  0.0542%)
      -------------------------------
           Total unit  1   18.00000  (100.0000%)
          Charge unit  1    0.00000
.ED

.HR<<5//+0//5//85>>
 #T
.LM\!lm
.RM\!rm
\@seg

.LM10
.RM80
.HR<<5//+0//5//85>>

#NThis table allows one to quickly identify the principal delocalizing
acceptor orbitals associated with each donor NBO, and their
topological relationship to this NBO, i.e., whether attached to the same
atom (geminal, ``g''), to an adjacent bonded atom (vicinal, ``v''), or
to a more remote (``r'') site.  These acceptor NBOs will generally 
correspond to the principal `delocalization tails' of the NLMO
associated with the parent donor NBO.  [For example, in the table above,
the nitrogen lone pair (NBO 9) is seen to be the lowest-occupancy
(1.97795 electrons) and highest-energy 
(\minus 0.44592 a.u.) Lewis NBO, and to
be primarily
delocalized into antibonds 24, 25, 26 (the vicinal \sigma *#<#dCH#u
NBOs).  The summary at the bottom of the table shows that the
Lewis NBOs 1-9 describe about 99.7% of the total electron density,
with the remaining non-Lewis density found primarily in the
valence-shell antibonds (particularly, NBO 24).]

.CM-----------------------------NBOB.MAN---------------------------
.TP2
.DF\np =\thsp \nthsp
.DF\degree =\*degree
.HF<<B.1 INTRODUCTION TO THE NBO USER'S GUIDE//3//10>>
.NF<<B-// >>
.PN1
.CM----------------------------------------------------------------





.CJ
#HSection B: NBO USER'S GUIDE#N
.FJ


#BB.1 INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTS#N

\np Section B constitutes the general 
user's guide to the NBO program.  It
assumes that the user has an installed 
electronic structure system (ESS) with attached NBO program,
a general idea of what the 
NBO method is about, and some
acquaintance with standard NBO terminology and output data.  If you are
completely inexperienced in these areas, read Section A
(General Introduction and Installation) for the necessary background
to this Section.

\np The User's Guide describes how to use the NBO program
by modifying your input file to the ESS program
to get some NBO output.  The modification consists of adding a list
of #Ikeywords#N in a prescribed #Ikeylist#N format.  Four distinct
keylist ($KEY) types are recognized ($NBO, $CORE, $CHOOSE, and $DEL), and
these will be described in turn in Sections B.2-B.5.  Some of the details
of inserting NBO keylists into the input file depend on the details
of your ESS method, and are described in the appropriate Appendix for
the ESS.  However, the general form of NBO keylists and the meaning and
function of each keyword are identical for all versions (insofar as the
option is meaningful for the ESS), and are described herein.  

\np The four keylist types have common rules of syntax:  Keylist
delimiters are identified by a ``$'' prefix.  Each keylist
begins with the parent keylist name (e.g., ``$NBO''), followed
by any number of keywords, and ended
with the word ``$END''; for example,
 #T
     $NBO   keyword1   keyword2   . . .   $END      !comment

#N(The allowed keyword entries for each type of keylist are described
in Sections B.2-B.5.)  The keylist is ``free format,'' with keywords
separated by commas or any number of spaces.  An NBO option is
activated by simply including its keyword in the appropriate keylist.  The
order of keywords in the principal $NBO keylist
does not matter, but multiple keylists must be given
in the order (1) $NBO, (2) $CORE, (3) $CHOOSE, (4) $DEL of presentation
in Sections B.2-B.5.  Keywords may be typed in upper or lower case,
and will be echoed near the top of the NBO output.  A $KEY list can
be continued to any number of lines, but all the entries of a $KEY list must
appear in a distinct set of lines, starting with the $KEY name on the
first line and ending with the closing $END on the last line (i.e.,
no two $KEY lists should share parts of the same line).  As the
above example
indicates, any line in the keylist input may terminate with an exclamation
point (!) followed by `comment' of your choice; the ``!'' is 
considered to terminate
the line, and the trailing `comment' is ignored by the program.
.HF<<B.2 THE $NBO KEYLIST//3//10>>


.RL55
#BB.2 THE $NBO KEYLIST#N

#IB.2.1 Overview of $NBO keywords#N

\np The $NBO keylist is the principal means of specifying NBO
job options and controlling output, and must precede 
any other keylist ($CORE, $CHOOSE,
or $DEL) in your input file.  The allowed keywords that can
appear in a $NBO keylist are grouped as follows:

.RL5
.LM+5
#IJob Control Keywords:#N
.LM+0
.TB
.FM<<5L15//0L15//0L15//0L15>>
.RW<<NPA//NBOSUM//NOBOND//SKIPBO>>
.RW<<NBO//RESONANCE//3CBOND//NLMO>>
.ET
.LM+0
#IJob Threshold Keywords:#N
.LM+0
.TB
.FM<<5L40>>
.RW<<BEND(=ang,pct,occ)>>
.RW<<E2PERT(=val)>>
.RW<<DIPOLE(=val)>>
.ET
.LM+0
.RL13
#IMatrix Output Keywords:#N
.LM+0
.TB
.FM<<5L10//0L10//0L10//0L10//0L10>>
.RW<<AONAO//NAONHO//NHONBO//NBONLMO//NLMOMO>>
.RW<<AONHO//NAONBO//NHONLMO//NBOMO// >>
.RW<<AONBO//NAONLMO//NHOMO// // >>
.RW<<AONLMO//NAOMO// // // >>
.RW<<AOMO// // // // >>
.RW<<AOPNAO//AOPNHO//AOPNBO//AOPNLMO// >>
.FM<<5L10//0L10//0L10//0L10>>
.RW<<DMAO//FAO//DIAO//SAO>>
.RW<<DMNAO//FNAO//DINAO//SPNAO>>
.RW<<DMNHO//FNHO//DINHO//SPNHO>>
.RW<<DMNBO//FNBO//DINBO//SPNBO>>
.RW<<DMNLMO//FNLMO//DINLMO//SPNLMO>>
.ET
.LM+0
.RL3
#IOther Output Control Keywords:#N
.LM+0
.TB
.FM<<5L10//0L10//0L10//0L10>>
.RW<<LFNPR//DETAIL//BNDIDX//AOINFO>>
.RW<<PLOT//ARCHIVE//NBODAF// >>
.ET
.LM+0
.RL2
#IPrint Level Control:#N
.LM+5
PRINT=n
.LM-5

.LM-5
Keywords are first listed and described according to these formal
groupings in Sections B.2.2-B.2.6.  Section B.6 illustrates 
the effect of commonly used $NBO 
keywords (as well as other $KEY lists) on the
successive stages of NAO/NBO/NLMO transformation and subsequent
energy or dipole analysis, with sample output for these keyword
options.

\np Some keywords of the $NBO keylist
require (or allow) numerical values or other parameters
to specify their exact function.  In this
case, the numerical value or parameter must immediately follow the keyword
after an equal sign (=) or any number of blank spaces.  Examples:
 #T
     E2PERT=2.5   LFNPR 16  NBOMO=W25

#N(The equal sign is recommended, and will be used in the remaining
examples.)

[\np Although the general user's interaction with the NBO programs is usually
through the documented keywords of Sections B.2.2-B.2.6, some additional
`semi-documented' keywords are listed in Section B.2.7 which may be of
interest to the specialist.]
.RL55
#IB.2.2 Job Control Keywords#N

\np The keywords in this group activate or deactivate 
basic tasks to be performed by
the NBO programs, or change the way the NBO search is conducted.  Each
keyword is described in terms of the option it activates (together with an 
indication of where the option is useful):

.LM+12
.OS<<12//#IKEYWORD#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//22//80>>

.OS<<12//NPA>>
Request Natural Population Analysis and printing of NPA summary
tables (Section A.3.2).  This keyword also activates calculation
of NAOs, except for semi-empirical ESS methods.

.OS<<12//NBO>>
Request calculation of NBOs and printing of the main NBO table
(Section A.3.3).

.OS<<12//NBOSUM>>
Request printing of the NBO summary table (Section A.3.6).  This
combines elements of the NBO table and 2nd-order perturbation
theory analysis table (see below) in a convenient form for recognizing
the principal delocalization patterns.

.OS<<12//RESONANCE>>
Request search for highly delocalized structures 
(Section B.6.6).  The NBO search
normally aborts when one or more Lewis NBOs has less
than the default occupancy threshold of
1.90 electrons for a `good' electron
pair.  When the RESONANCE keyword is activated, this threshold
is successively lowered in 0.10 decrements to 1.50,
and the NBO search repeated to find the best Lewis structure
within each occupancy threshold.  The program returns with the best
overall Lewis structure (lowest total non-Lewis occupancy) found
in these searches.  (Useful for benzene and other highly
delocalized molecules.)

.OS<<12//NOBOND>>
Request that no bonds (2-center NBOs) are to be formed in the
NBO procedure (Section B.6.7).  The 
resulting NBOs will then simply be 1-center
atomic hybrids.  (Useful for highly ionic species.)

.OS<<12//3CBOND>>
Request search for 3-center bonds (Section B.6.8).  The normal 
default is to search
for only 1- and 2-center NBOs.  (Useful for diborane and other
electron-deficient `bridged' species.)

.OS<<12//SKIPBO>>
Skip the computation of NBOs, i.e., only determine NAOs and
perform natural population analysis.  (Useful when only NPA is
desired.)

.OS<<12//NLMO>>
Compute and print out the summary table of Natural Localized
Molecular Orbitals (Section B.6.2).  NLMOs are similar to Boys or 
Edmiston-Ruedenberg LMOs, but more efficiently calculated.  (Useful
for `semi-localized' description of an SCF or correlated 
wavefunction.)  Activated automatically by all keywords that pertain
to NLMOs (e.g., AONLMO, SPNLMO, DIPOLE).
.HR<<1//+1//10//80>>

.LM10

Note that the SKIPBO keyword has higher precedence than other
keywords in this list, so that keywords with which it is
implicitly in conflict (e.g., NBO, 3CBOND, NLMO) will be ignored
if SKIPBO is included in the $NBO keylist.
.RL55
#IB.2.3 Job Threshold Keywords#N
.BM61

\np The keywords in this group also activate new tasks to be
performed by the NBO program, but these keywords may be modified
by one or more parameters (thresholds) that control the precise
action to be taken.  (In each case the keywords may also be used
without parameters, accepting the default values [in brackets].)

.LM30
.OS<<20//#IKEYWORD  parameter(s)#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//18>>
.HR<<1//+1//19//29>>
.HR<<1//+1//30//80>>

.OS<<20//BEND      ang, pct, occ>>
Request the NHO Directional Analysis table (Section A.3.4).  The
three parameters [and default values] have the following
significance:

.LM+10
.OS<<8//ang [1.0]>> 
=  threshold angular deviation for printing
.OS<<8//pct [25]>>
=  threshold percentage #Ip#N-character for printing
.OS<<8//occ [0.1]>>
=  threshold NBO occupancy for printing
.LM-10

#NParameter values may be separated by a space or a comma.

  Example:#T     BEND=2,10,1.9

#NThis example specifies that the bond-bending table should
only include entries for angular deviations of at least 2\degree  (ang),
hybrids of at least 10% #Ip#N-character (pct), and NBOs of occupancy
at least 1.9 electrons (occ).

.RL13
.OS<<20//E2PERT       eval>>
Request the Perturbation Theory Energy Analysis 
table (Section A.3.5), where

.LM+10
.OS<<8//eval [0.5]>>
=  threshold energy (in kcal/mol) for printing

.LM-10
Entries will be printed for NBO donor-acceptor interaction energies
that exceed the `eval' threshold.

  Example:#T     E2PERT=5.0

#NThis example would print only interactions of at least 5 kcal/mol
(i.e., only the single entry for the 8.13 kcal/mol
#In#N#dN#u \rarr  \sigma *#<#dCH#u interaction in the output
of Section A.3.5).

.RL16
.OS<<20//DIPOLE       dval>>
Request the Molecular Dipole Moment Analysis table (Section B.6.3), where

.LM+10
.OS<<9//dval [0.02]>>
= threshold dipole moment (Debye) for printing

.LM-10
The program will carry out a decomposition of the total molecular
dipole moment in terms of localized NLMO and NBO
contributions, including all terms whose contribution (in vector norm)
exceeds the `dval' threshold.

  Example:#T     DIPOLE=0.1

#NThis example would print out dipole contributions of all NBOs (and
their delocalization interactions) of magnitude \ge  0.1\thsp D.
.LM10
.HR<<1//+1//10//80>>


.BM60
#NBoth the BEND and E2PERT keywords are activated by default
at the standard PRINT level option (see Section B.2.6); to get an
example of dipole moment analysis, include the keylist
 #T
     $NBO  DIPOLE  $END

#Nin your input file.  Note that the DIPOLE keyword leads to an
analysis in terms of both NBOs and NLMOs, so that the NLMO keyword
(Section B.2.2) is automatically activated in this case.
.RL55
.LM10
#IB.2.4 Matrix Output Keywords#N

\np The keywords in this group activate the printing of various
matrices to the output file, or their writing
to (or reading from) external disk files.  The large number
of keywords in this group provide great flexibility in printing
out the details of the successive transformations,
.DF\steps1 =input AOs \rarr  (PNAOs) \rarr  NAOs \rarr  NHOs \rarr  
.DF\steps2 =NBOs \rarr  NLMOs \rarr  canonical MOs

.CJ
\steps1  \steps2
.FJ

or the matrices of various operators in the natural
localized basis sets.  This ordered sequence of transformations
forms the basis for naming the keywords.


#_Keyword Names#/

\np The keyword for printing the matrix for a particular basis
transformation, IN \rarr  OUT, is constructed from the 
corresponding acronymns
for the two sets in the generic form ``INOUT''.  For example,
the transformation AO \rarr  NBO is keyed as ``AONBO'', 
while that from NBOs to
NLMOs is correspondingly ``NBONLMO''.  The transformations are
always specified in the ordered sequence shown above (i.e., ``AONBO''
is allowed, but ``NBOAO'' is an unrecognized `backward' 
keyword).  Keywords are recognized for #Iall possible#N transformations
from the input AOs to other sets 
(NAO, NHO, NBO, NLMO, MO, or the pre-orthogonal PNAO, PNHO, PNBO,
PNLMO sets) in the
overall sequence leading to canonical MOs, i.e.,

.LM+15
.OS<<12//#IAO basis:#N>>
AONAO  AONHO  AONBO  AONLMO  AOMO  
.LM+0
AOPNAO  AOPNHO  AOPNBO  AOPNLMO
.LM10

and from each of the orthonormal natural localized sets to sets
lying to the right in the sequence, i.e.,
.RL8

.LM+15
.OS<<12//#INAO basis:#N>>  
NAONHO  NAONBO  NAONLMO  NAOMO

.OS<<12//#INHO basis:#N>>  
NHONBO  NHONLMO  NHOMO

.OS<<12//#INBO basis:#N>>  
NBONLMO  NBOMO

.OS<<12//#INLMO basis:#N>> 
NLMOMO
.LM10

The matrix T#dIN,OUT#u for a specified IN \rarr  OUT transform has
rows labelled by the IN set and columns labelled by the OUT set.

\np One can also print out the matrix representations of the Fock
matrix (F), density matrix (DM), or dipole moment matrix (DI)
in the input AO set or any of the natural localized sets (NAO,
NHO, NBO, or NLMO).  The corresponding keyword is constructed by
combining the abbreviation (M) for the operator with that
for the set (SET) in the generic form ``MSET''.  For example,
to print the Fock matrix (F) in the NBO set, use the
keyword ``FNBO'', or to print the dipole matrix in the NLMO
basis, use ``DINLMO''.  (For the dipole matrix keywords, all
three vector components will be printed.)  One can also print 
out elements of the overlap matrix (S) in the input AO basis 
or any of the `pre-orthogonal' sets
(PNAO, PNHO, PNBO, or PNLMO), using, e.g., ``SPNAO'' for the
overlap matrix in the PNAO basis.  The complete set of allowed
keywords for operator matrices is:

.RL7
.LM+20
.OS<<15//#IFock matrix:#N>>  
FAO  FNAO  FNHO  FNBO  FNLMO

.OS<<15//#Idensity matrix:#N>>  
DMAO  DMNAO  DMNHO  DMNBO  DMNLMO

.OS<<15//#Idipole matrix:#N>>  
DIAO  DINAO  DINHO  DINBO  DINLMO

.OS<<15//#Ioverlap matrix:#N>>  
SAO  SPNAO  SPNHO  SPNBO  SPNLMO
.LM10

Other desired transformations
can be readily obtained from the keyword transformations
by matrix multiplication.


.RL10
#_Keyword Parameters#/

\np Each generic matrix keyword (``MATKEY'') can include
a parameter that specifies the output operation to
be performed on the matrix.  The allowed MATKEY parameters
are of two types (three for AONAO, NAONBO; see below):
 
.LM+20
.OS<<15//MATKEY=P[c]>>
(print out the matrix in the standard output file, 'c' columns)

.OS<<15//MATKEY=W[n]>>
(write out the matrix to disk file #In#N)
.LM10

#NThe first (P[c]) parameter is used to control output to the standard
output file.  When the MATKEY keyword is inserted in the $NBO keylist with
no parameters, the matrix is by default printed (in its
entirety) in the standard output file.  Thus, ``MATKEY=P''
would be equivalent to ``MATKEY'', with no parameters.  The complete
`P[c]' form of the print parameter serves to truncate the 
printed matrix output
to a specified number of columns [c].  For example, to print out
only the first 16 columns of a matrix, use the form
 #T
     MATKEY=P16         (print 16 columns)

#NFor certain matrices, one can also restrict 
printing to only the valence (VAL) or
Lewis (LEW) columns with modified `[c]' 
specifiers.  For the transformations
to MOs, use the form
 #T
     MATKEY=PVAL        (print core + valence MO columns only)

#Nwhere ``MATKEY'' is AOMO, NAOMO, NHOMO, NBOMO, or NLMOMO (only).  This
will print out only the occupied MOs 
and the lowest few unoccupied MOs, e.g., the six lowest virtual MOs of
the methylamine example (Section A.3), though
not necessarily those with pre#|dominant valence character.  Similarly,
for the transformations to NBOs or NLMOs, use the form
 #T
     MATKEY=PLEW        (print Lewis orbital columns only)

#Nwhere ``MATKEY'' is AONBO, NHONBO, NAONBO, AONLMO, NAONLMO, 
NHONLMO, NBONLMO (or AOMO, NAOMO, NHOMO, NBOMO, NLMOMO).  This
prints out the Lewis NBOs or occupied MOs only, e.g., only the nine
occupied NBOs or MOs of the methylamine example.  Judicious use of
these print parameters keeps printed
output within reasonable bounds
in calculations with large basis sets.

#NThe second type of MATKEY parameter (W[n]) is used to
write the matrix (in its entirety) to a specified disk
file [n].  By default, each keyword transformation matrix is associated with
a particular logical file number (LFN) in the range 31-49, as shown in
the table below:

.TB
.FM<<5C10//2C6//5C10//2C6//5C10//2C6>>
.RW<<#I //default// //default// //default>>
.RW<<matrix//LFN//matrix//LFN//matrix//LFN#N>>
.FM<<5L18//5L18//5L18>>
.RW<<_//_//_>>
.FM<<5L10//2C6//5L10//2C6//5L10//2C6>>
.RW<<AONAO//33//NHONBO//49//DMNHO//49>>
.RW<<AONHO//35//NHONLMO//49//DMNBO//49>>
.RW<<AONBO//37//NHOMO//49//DMNLMO//49>>
.RW<<AONLMO//39//NBONLMO//49//DIAO//49>>
.RW<<AOMO//40//NBOMO//49//DINAO//49>>
.RW<<AOPNAO//32//NLMOMO//49//DINHO//49>>
.RW<<AOPNHO//34//FAO//49//DINBO//49>>
.RW<<AOPNBO//36//FNAO//49//DINLMO//49>>
.RW<<AOPNLMO//38//FNHO//49//SAO//49>>
.RW<<NAONHO//49//FNBO//49//SPNAO//49>>
.RW<<NAONBO//42//FNLMO//49//SPNHO//49>>
.RW<<NAONLMO//49//DMAO//41//SPNBO//49>>
.RW<<NAOMO//49//DMNAO//49//SPNLMO//49>>
.ET

#NWhen the ``MATKEY=Wn'' keyword is inserted in the $NBO keylist with
no `n' specifier, the matrix is by default written out (in its
entirety) to this LFN.  Thus, ``MATKEY=W'' 
is equivalent to ``MATKEY=Wn'' if ``n'' is the default LFN for
that keyword.  Use the ``Wn'' parameter to direct output to
any non-default LFN disk file.  For example, the keyword
 #T
     AONBO=W22

#Nwould write out the AO \rarr  NBO transformation to LFN = 22 (rather
than the default LFN = 37). 

\np The format of the printed output under the print `P' parameter
differs from that written to an external file under
the `W' parameter.  The `P' output (intended for a human reader)
includes an identifying label for each row, and gives the 
numerical entries to somewhat lesser precision (F8.4 format) than
the corresponding `W' output (F15.9 format), which is usually
intended as input to another program.  Use the ``MATKEY=W6''
keyword to route the more precise `W' form of the matrix to
the standard output file, LFN 6.

\np For the AONAO, NAONBO matrices (only), one can also include a 
read parameter (R),
 #T
     AONAO=Rn
     NAONBO=Rn

#Nwhich causes the matrix to be input to the
program from LFN #In#N.  This 
parameter has the
effect of `freezing' orbitals to a
set prescribed in the input file (thus 
bypassing the NBO optimization of these orbitals for the molecular
system).  For example, the keyword ``NAONBO=R44'' would have the
effect of freezing the NAO \rarr  NBO 
transformation coefficients to the form specified in LFN 44 (perhaps
written with the ``NAONBO=W44'' keyword in a previous calculation
on isolated molecules, and now to be used in a calculation on a
molecular complex).  Similarly, the keyword ``AONAO=R45'' could
be used to force the analysis of an excited state to be
carried out in terms of the NAOs of the ground state (previously 
written out with the ``AONAO=W45''
keyword).
.RL55
#IB.2.5 Other Output Control Keywords#N

\np The keywords in this group also help to control
the I/O produced 
by a specified set of job options, and thus supplement the
keywords of the previous section.  However, the keywords
of this section `steer' the flow of information that is
routinely produced by the NBO program (or can be passed through
from the ESS program) without materially affecting the actual
jobs performed by the NBO program.  The options associated with
each keyword are tabulated below:

.LM+12
.OS<<12//#IKEYWORD#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//22//80>>

.OS<<12//LFNPR=n>>
Set the logical file number (LFN) for NBO program output.  The default
LFN is #In#N = 6, the usual LFN for output from the ESS program.  This
option can be used to steer the NBO section of the job output to a
desired file.
 
  Example:#T  LFNPR=25   (re-direct NBO output to LFN 25)
 #N
.OS<<12//DETAIL>>
Request additional details of the NBO search.  This option (primarily
for programming and debugging purposes) records details of the 
NBO loops over atoms
and atom pairs, enroute to the final NBOs.

.OS<<12//BNDIDX>>
Request print-out of the NAO-Wiberg Bond Index 
array and related valency indices (Section B.6.5).  The elements of
this array are the sums of squares of off-diagonal density matrix
elements between pairs of atoms in the NAO basis, and are the NAO
counterpart of the Wiberg bond index [K. Wiberg, Tetrahedron #B24#N,
1083-1096 (1968)].  (This bond index is routinely used
to `screen' atom pairs for possible bonding in the NBO
search, but the values
are not printed unless the BNDIDX keyword is activated.)

.OS<<12//AOINFO>>
Request writing of information concerning the AO basis set (geometrical
positions, orbital exponents, contraction coefficients, etc.) to an
external file, LFN 31.  This is a portion of the information needed
by the ORB#|PLOT orbital contour plotting programs (cf. ``PLOT''
keyword below.)

.RL4
.NH
.OS<<12//PLOT>>
Request writing of #Iall#N files required by orbital contour plotting
programs ORB#|PLOT.  This activates the AOINFO keyword, as well
as all the necessary matrix output keywords (AONBO=W37, etc.) 
that could be required for ORBPLOT.
.HY

.OS<<12//ARCHIVE=n>>
Request writing the FILE47 `archive' file to external disk
file LFN = #In#N (or, if ``=n'' is not present, to the default
LFN = 47).  This file can serve as the input file to run the
GENNBO program in stand-alone mode, to repeat the NBO analysis
(possibly with new job options) without repeating the calculation
of the wavefunction (Section B.7).

.OS<<12//NBODAF=n>>
Request writing the NBO direct access file (DAF) to external
disk file LFN = #In#N (or, if ``=n'' is not present, to the
default LFN =48).
.LM10
.HR<<1//+1//10//80>>
.RL55
#IB.2.6 Print Level Keywords#N

\np The keyword ``PRINT=n'' (#In#N = 0-4) can be used to give
convenient, flexible control of all NBO output in terms of
a specified print level #In#N.  This keyword
activates groups of keywords in a heirarchical manner, and
thus incrementally increases the volume of output, ranging
from #Ino#N NBO output (PRINT=0) to a considerable volume of
detail (PRINT=4).  The keywords associated with each
print level are tabulated below [default value, PRINT=2]:

.LM+5
.TB
.FM<<0C8//2L45>>
.RW<<#Iprint level#N//#Iadditional output or activated keywords#N>>
.RW<<_//_>>
.FM<<0C8//2L55>>
.RW<<0//suppress #Iall#N output from the NBO program>>
.RW<<1//activate NPA and NBO keywords>>
.RW<<[2]//activate BEND, NBOSUM, and E2PERT keywords>>
.RW<<3//activate NLMO, DIPOLE, and BNDIDX keywords>>
.RW<<4//activate all(!) keywords>>
.ET
.LM10

For each print level #In#N, the NBO output will include items activated
by the listed keywords, as well as all items from lower
print levels.

\np When additional keywords 
are included with a ``PRINT=n'' keyword
in the $NBO keylist, the NBO output includes the additional keyword
items as well as those implied by the print level.  This can be used
to tailor the NBO output to virtually any selection of output
items.  For example, the keylist
 #T
     $NBO  PRINT=2  NLMO  FNBO=P  NAOMO=P11  $END

#Nwould add to the standard methylamine output file of Section A.3
an NLMO summary table, the Fock matrix in
the NBO basis, and the transformation coefficients
for the first 11 molecular orbitals in terms of NAOs.  Similarly,
to produce the NPA listing only, one could use
 #T
     $NBO  PRINT=1  SKIPBO  $END

#Nor
 #T
     $NBO  PRINT=0  NPA  $END

#N[There is actually a slight difference between 
the two examples:  The
NBOs are determined by default (once the $NBO keylist is encountered),
even if all output is suppressed with PRINT=0; in the first example,
the keyword SKIPBO bypasses NBO determination, whereas in
the second example the NBOs are still determined `in background.']
.RL55
#IB.2.7 Semi-Documented Additional Keywords#N

\np Some additional keywords are listed below that may of use
to specialists or program developers:

.LM+15
.OS<<15//#IKEYWORD#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//25//80>>

.OS<<15//THRESH=val>>
Set the threshold of orbital occupancy desired for bond
orbital selection.  If this is not included, the default
occupancy [1.90] will be used (or values decreasing from 1.90
to 1.50 by 0.10 steps,
if the RESONANCE keyword is included).

.OS<<15//PRJTHR=val>>
Set the projection threshold [default 0.20] to determine if
a `new' hybrid orbital has too high overlap with hybrids
previously found.

.OS<<15//MULAT>>
Print total gross Mulliken populations by atom.

.OS<<15//MULORB>>
Print gross Mulliken populations, by orbital and atom.

.OS<<15//RPNAO>>
Revises PAO to PNAO transformation matrix by post-multiplying
by #BT#N#dRyd#u and #BT#N#dred#u [see the NPA paper:
A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys. #B83#N,
735-746 (1985)].

.OS<<15//PAOPNAO>>
Input or output of pure AO (PAO) to pre-NAO (PNAO) transformation.  The
PAOs are AOs of pure angular momentum symmetry (rather than
cartesian gaussians).  This keyword can be used with read (`R'),
write (`W', default LFN 43) or print (`P') parameters.

.OS<<15//BOAO>>
Print out the bond-order matrix (Fock-Dirac density matrix) in the
basis set of input AOs.  This keyword can be used with write
(`W', default LFN 49) or print (`P') parameters.
.HR<<1//+1//10//80>>


.LM10
.HF<<B.3 THE $CORE LIST//3//10>>
.RL55
#BB.3 THE $CORE LIST#N

\np In the Lewis structure picture, the inner `core' electron pairs
are pictured as occupying orbitals having essentially 
isolated atomic orbital character.  In NBO parlance, these core orbitals
correspond to 1-center unhybridized NAOs of near-maximum occupancy,
which are isolated on each center before the main NBO search
begins for localized valence electron pairs.  A warning message
is printed if the occupancy of a presumed closed-shell
core NBO falls below 1.9990 electrons (or 0.9990 in the open-shell 
case), indicative of a possible core-valence mixing effect of
physical significance.

\np [In previous versions
of the NBO program, core orbitals having the expected pure atomic
character are found in essentially all
cases, except where an `accidental' degeneracy in occupancy of
core and valence lone pairs leads to undesirable core-valence
mixing; the present version explicitly isolates core pairs 
as unhybridized NAOs prior
to the main NBO search to prevent this unphysical effect.]

\np The NBO program contains a table giving the nominal number of
core orbitals to be isolated on each type of atom (e.g., 1#Is#N for
first-row atoms Li-Ne, 1#Is#N, 2#Is#N, 2#Ip#N for second-row atoms
Na-Ar, etc.).  At times, however, it is interesting to examine the
effect of allowing core orbitals to mix into the bonding hybrids, or
to hybridize (polarize) among themselves.  This can be accomplished
by including a $CORE keylist to specify the number of core
orbitals to be isolated on each atomic center, thus modifying
the nominal core table.  Unlike other NBO keylists, the $CORE list
includes only integers (rather than keywords) to specify the
core modifications, but the rules 
are otherwise similar to those for
other keylists.  The $CORE list (if included) must follow the $NBO
keylist and precede the $CHOOSE or $DEL keylists.

.RL10
\np The format of the $CORE modification list is:

.LM+15
.OS<<10//first line:>>
The keyword ``$CORE''

.OS<<10//next lines:>>
Pairs of integers, one pair for each center.  The first integer
indicates the atomic center (in the numbering of the main ESS)
and the second is the number of core orbitals to be isolated on
that atom.  Note that atomic centers not included in the CORE list
are assigned default cores.

.OS<<10//last line:>>
The keyword ``$END'', to indicate the end of core input.

.LM-15
The entire list may also be condensed to a single line, 
but the word ``$CORE'' must occur as the first word of the line
and ``$END'' as
the last word; that is, the core
modification keylist cannot continue on a line that contains other
keylist information.

\np The core orbitals are isolated by occupancy, the most occupied NAOs
being first selected, and full subshells are isolated at a time.  Thus,
for example, to select the five orbitals of the
#In#N = 1 and #In#N = 2 shells
as core orbitals, it would make no difference 
to select ``3'' or ``4'' (instead
of ``5''), since all three of these
choices would specify a core containing a 1#Is#N, 2#Is#N, and 
all three 2#Ip#N orbitals.  The $CORE modification list 
is read only once, and applies to both
\alpha  and \beta  spin manifolds in an open-shell calculation.

.RL6
An example, appropriate for Ni(1)-C(2)-O(3) with the indicated numbering
of atoms, is shown below:
 #T
     $CORE
       1   5
     $END

#NThis would direct the NBO program to isolate only 5 core orbitals
on Nickel (atom 1), rather than the nominal 9 core orbitals.  In
other words, only 1#Is#N, 2#Is#N, and 2#Ip#N orbitals will be considered
as core orbitals in the search for NBOs of NiCO, allowing the 3#Is#N
and 3#Ip#N orbitals to mix with valence NAOs in bond formation.  Since
the carbon and oxygen atoms were not included in the modification list,
the nominal set of core orbitals (1#Is#N only) is isolated on each
of these atoms.  

.RL8
[The alternative example
 #T
     $CORE   1  0    2  0    3  0   $END

#N(no cores) would allow all NAOs to be included in the NBO search;
this would be equivalent to the default treatment in 
the earlier version of the program (see Section A.1.5).]
.HF<<B.4 THE $CHOOSE KEYLIST//3//10>>
.RL55
#BB.4 THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)#N

\np A $CHOOSE keylist requests that the NBO search be directed
to find a particular Lewis structure (`resonance structure') 
chosen by the user.  (This
is useful for testing the accuracy of alternative resonance structure
representations of the wavefunction, relative to the optimal
Lewis structure returned in a free NBO search.)  In the
$CHOOSE list, a resonance structure is specified by indicating
where lone pairs and bonds (including multiple bonds) are to
be found in the molecule.  In some cases, the user may wish to
specify only the location of bonds, letting the NBO algorithm
seek the best location for lone pairs, but it is usually safest to
completely specify the resonance structure, both lone 
pairs and bonds. 

\np The format of the $CHOOSE list is:

.LM+15
.OS<<10//first line:>>
The keyword ``$CHOOSE''

.OS<<10//next line:>>
The keyword ``ALPHA'' (only for open-shell wavefunction)

.OS<<10//next lines:>>
If one-center (`lone') NBOs are to be searched for, type the
keyword ``LONE'' followed by a list of pairs of numbers, the
first number of each pair being the atomic center and the 
second the number of valence lone pairs on that atom.  Terminate the 
list with ``END''.  (Note that only the occupied #Ivalence#N lone pairs
should be entered, since the number of core orbitals on each
center is presumed known.)

If two-center (`bond') NBOs are to be searched for, type
the keyword ``BOND'', followed by the list of bond specifiers,
and terminated by ``END''.  Each bond specifier is one of the
letters

.LM+10
.OS<<5//``S''>>
single bond
.OS<<5//``D''>>
double bond
.OS<<5//``T''>>
triple bond
.OS<<5//``Q''>>
quadruple bond
.LM-10

followed by the two atomic centers of the bond (e.g., ``D 9 16'' for
a double bond between atoms 9 and 16).

If three-center NBOs are to be searched for, type
the keyword ``3CBOND'', followed by the list of 3-c bond
specifiers, and terminated by ``END''.  Each 3-c bond specifier
is again one of the letters ``S'' (single), ``D'' (double), ``T''
(triple), or ``Q'' (quadruple), followed by three integers for
the three atomic centers (e.g., ``S 4 8 10'' for a single
three-center bond 4-8-10).  (Note that the 3CBOND keyword 
of the $NBO keylist is implicitly activated
if 3-c bonds are included in a $CHOOSE list.)

.OS<<10//next line:>>
The word ``END'' to signal the end of the \alpha  spin list.

.OS<<10//next line:>>
The keyword ``BETA'' (for open-shell wavefunctions)

.OS<<10//next lines:>>
The input for \beta  spin, same format as above.  The overall $CHOOSE
list should always end with the ``$END'' keyword.

.RL16
.LM10
Two examples will serve to illustrate the $CHOOSE format (each is
rather artificial, inasmuch as the specified $CHOOSE structure
corresponds to the `normal' structure that would be found by
the NBO program):

.LM+5
.DF\dots =#+.\thsp .\thsp .#-
.OS<<4//(1)>> 
The closed-shell H-bonded complex FH\dots CO,
with atom numbering F(1)-H(2)\dots C(3)-O(4), might be specified as
 #T
     $CHOOSE
        LONE  1  3
              3  1
              4  1     END
        BOND  S  1  2
              T  3  4  END
     $END

#NThis would direct the NBO program to search for three lone pairs
on atom F(1), one lone pair on atom C(3), one lone pair on atom 
O(4), one bond between F(1)-H(2), and three bonds between C(3)-O(4).

.RL18
.OS<<4//(2)>>
The open-shell FH\dots O#d2#u complex, with
atom numbering F(1)-H(2)#+...#-O(3)-O(4),  
and with the unpaired electrons on O#d2#u being of 
\alpha  spin, might be specified as
 #T
     $CHOOSE
       ALPHA
         LONE  1  3
               3  3
               4  3     END
         BOND  S  1  2
               S  3  4  END
       END
       BETA
         LONE  1  3
               3  1
               4  1     END
         BOND  S  1  2
               T  3  4  END
       END
     $END

.LM10
#NNote that this example incorporates the idea of ``different Lewis
structures for different spins,'' with a distinct pattern of localized
1-c (`lone') and 2-c (`bond') functions for \alpha  and \beta  spin.

\np As with other keylists, the $CHOOSE keylist can be condensed to
a smaller number of lines, as long as no line is shared with another
keylist.  The order of keywords within the $CHOOSE keylist should
be as shown above (i.e., ALPHA before BETA, LONE before BOND, etc.),
but the order of entries within a LONE or BOND list is
immaterial.  A $CORE keylist (if present) must precede the $CHOOSE list.
.HF<<B.5 THE $DEL KEYLIST//3//10>>
.RL55
#BB.5 THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS)#N

#IB.5.1 Introduction to NBO Energetic Analysis#N

\np The fourth and final type of keylist is a `deletions' ($DEL)
keylist, to activate NBO energetic analysis.  This analysis is
performed by (1) deleting specified elements (or blocks of elements)
from the NBO Fock matrix, (2) diagonalizing this new Fock matrix
to obtain a new density matrix, and (3) passing this density matrix
to the SCF routines for a single pass through the SCF energy
evaluator.  The difference between this `deletion' energy and
the original SCF energy provides a useful measure of the
energy contribution of the deleted terms.  Since a Fock matrix
is required, the energetic analysis is performed for RHF and
UHF wavefunctions only.

\np Input for the NBO energetic analysis is through the $DEL keylist,
which specifies the deletions to be performed.  Multiple analyses
(deletions) can be performed during a single job, with each deletion
included in the overall $DEL keylist.  The nine distinct
types of deletions input are described in Section B.5.2 below.

\np The deletions keylist begins with the ``$DEL'' keyword.  For 
the analysis of UHF wavefunctions, the deletions for
the \alpha  and \beta  spin manifolds must be separately 
specified (see Section B.5.3).  Otherwise, the input for closed
shells RHF and UHF is identical.  The input is free format and
the input for a single deletion can be spread over as many lines
as desired.  The desired deletions should be listed one after the
other.  After the last deletion, the word ``$END'' signals the
end of the keylist.


.RL15
.LM+10
.RM-10
.BX<<3//18//72//+0//+13>>

.CJ
#BWARNING#N
.FJ

If symmetry is used, one must be careful to only do deletions
that will preserve the symmetry of the electronic 
wavefunction!!  If this is not done, the energy of the
deletion will be incorrect because the assumption is made in
evaluating the energy that the original symmetry still exists,
and the variational principle may be violated.  (For example,
if symmetry is used for ethane, is is permissible to do
a ``NOSTAR'' deletion, but not the deletion of a single C-H
antibond.)  The remedy is not to use symmetry in the SCF
calculation.
.LM10
.RM80


\np In describing the deletion types, use is made of the terms
``molecular unit'' and ``chemical fragment.''  The NBO program
looks at the chemical bonding pattern produced by the bonding NBOs
and identifies the groups of atoms that are linked together
in distinct ``molecular units'' (usually synonymous with ``molecules''
in the chemical sense).  The first atom that is not in molecular
unit 1 will be in molecular unit 2, and so forth.  For example, if
the list of atoms is C(1), H(2), F(3), O(4), and bonding NBOs are
found between C(1)-O(4) and H(2)-F(3), then molecular unit 1
will be CO and molecular unit 2 will be HF.  A ``chemical fragment''
is taken to be any subset of the atoms, usually (but not
necessarily) in the same molecular unit, and usually (but not
necessarily) connected
by bond NBOs.  Typically, a chemical fragment might be 
specified to be a single atom, the four atoms of a
methyl group, or any other `radical' of a molecular unit, identified
by giving the atom numbers of which the fragment consists.
.RL55
#IB.5.2 The Nine Deletion Types#N

\np The keywords and format to specify each of the nine allowed
deletion types are described below:


#_(1) Deletion of entire orbitals.#/

This is called for by typing ``DELETE'', then the number of orbitals
to be deleted, then the keyword ``ORBITAL'' (or ``ORBITALS''), then
the list of the orbitals to be deleted.

  Example:     #TDELETE  3  ORBITALS  15  18  29

#N[See also deletion types (4) and (7) for deleting sets of orbitals.]

.RL15
.LM+10
.RM-10
.BX<<3//18//72//+0//+11>>

.CJ
#BWARNING#N
.FJ

The ``single-pass'' method of evaluating deletion energies is
appropriate only for deletions of #Ilow#N-occupancy (non-Lewis)
orbitals, for which the loss of self-consistency in the Coulomb
and exchange potentials (due to redistribution of the electron
density of deleted orbitals) is small compared to the net
energy change of deletion.  It is fundamentally erroneous
to delete #Ihigh#N-occupancy (Lewis) orbitals by this
procedure.
.LM10
.RM80



#_(2) Deletion of specific Fock matrix elements.#/

This is called for by typing ``DELETE'', then the number of elements
to be deleted, then the keyword ``ELEMENT'' (or ``ELEMENTS''), then
the list of the elements to be deleted (each as a pair of integers).

  Example:     #TDELETE  3  ELEMENTS  1 15  3 19  23 2

#NThis example would result in the zeroing of the following Fock
matrix elements:  (1,15), (15,1), (3,19), (19,3), (23,2), (2,23).  [See
also deletion types (3), (5), (6), (8), (9) for deleting sets of elements.]


#_(3) Deletion of off-diagonal blocks of the Fock matrix.#/

Each block is specified by two sets of orbitals, and all Fock
matrix elements in common between these two sets are set to
zero.  This is called for by typing ``ZERO'', then the number
of off-diagonal blocks to be zeroed, and then, for each block,
the following:

.RL6
.LM+5
(1) the dimensions of the block, separated by the word ``BY'' (e.g.,
``6 BY 3'' if the first set has 6 orbitals and the second set
has 3 orbitals);

(2) the list of orbitals in the first set;

(3) the list of orbitals in the second set.

.LM-5
.RL8
An example is shown below:
 #T
     ZERO  2  BLOCKS  2  BY  5
                               3  4
                               9  10  11  14  19
                      3  BY  2
                               1  2  7
                              20  24

#NThis will set the following Fock matrix elements to zero:

.LM+5
(3,9), (3,10), (3,11), (3,14), (3,19),
(9,3), (10,3), (11,3), (14,3), (19,3),
(4,9), (4,10), (4,11), (4,14), (4,19),
(9,4), (10,4), (11,4), (14,4), (19,4),
(1,20), (1,24), (2,20), (2,24), (7,20), (7,24)
(20,1), (24,1), (20,2), (24,2), (20,7), (24,7)
.LM-5

[Usually, in studying the total delocalization from one
molecular unit to another, it is much easier to use deletion
type (8) below.  Similarly, in studying the total delocalization
from one chemical fragment to another, it is easier to use
deletion type (9).]


#_(4) Deletion of all Rydberg and antibond orbitals.#/

The Rydberg and antibond orbitals are the non-Lewis NBO orbitals
that have stars in their labels (RY*, BD*) in the NBO analysis
output.  To delete all these orbitals, simply enter ``NOSTAR''.  The
result of this deletion is the energy of the idealized NBO natural
Lewis structure, with all Lewis NBOs doubly occupied.  (Unlike other
deletions, in which there is a slight loss of variational
self-consistency due to the redistributed occupancy of the deleted
orbitals, the result of a ``NOSTAR'' deletion corresponds rigorously
to the variational expectation value of the determinant of doubly
occupied Lewis NBOs).


.RL4
#_(5) Deletion of all vicinal delocalizations.#/

To delete all Fock matrix elements between Lewis NBOs and the
vicinal non-Lewis NBOs, simply enter ``NOVIC''.


.RL4
#_(6) Deletion of all geminal delocalizations.#/

To delete all Fock matrix elements between Lewis NBOs and the
geminal non-Lewis NBOs, simply enter ``NOGEM''.


.RL6
#_(7) Deletion of all starred (antibond/Rydberg) orbitals on a
particular molecular unit.#/

This is called for by typing ``DESTAR'', then the number of 
molecular units to be de#|starred, then the keyword ``UNIT'' 
(or ``UNITS''), then the list of units.

  Example:     #TDESTAR  2  UNITS  3  4
 #N

.RL13
#_(8) Zeroing all delocalization from one molecular unit to another.#/

This is called for by typing ``ZERO'', then the number of delocalizations
to zero, then the keyword ``DELOCALIZATION'' (can be abbreviated
to ``DELOC''), and then, for each delocalization, the word ``FROM'',
the number of the donor unit, the word ``TO'', and
the number of the acceptor unit.

  Example:     #TZERO  2  DELOC  FROM 1 TO 2   FROM 2 TO 1

#NThe above example would zero #Iall#N intermolecular
delocalizations between units 1 and 2 (i.e., both 1 \rarr  2 and
2 \rarr  1).  The
effect is to remove all Fock matrix elements between high-occupancy
(core/lone pair/bond) NBOs of the donor unit to the low-occupancy
(antibond/Rydberg) NBOs of the acceptor unit.  The donor and acceptor
units may be the same.


.RL4
#_(9) Zeroing all delocalization from one chemical fragment to another.#/

This is called for by typing ``ZERO'', then the number of inter-fragment
delocalizations to be zeroed, then the words ``ATOM BLOCKS'',
and then, for each delocalization,
the following:
.LM+5

(1) the number of atoms in the two fragments, separated by the word ``BY''
(e.g., ``6  BY  3'' if the first fragment has 6 atoms and the second
has 3 atoms);

(2) the list of atoms in the first fragment;

(3) the list of atoms in the second fragment.
.LM-5

For example, to zero all delocalizations between the fragments
defined by atoms (1,2) and by atoms (3,4,5), the $DEL entries would be
 #T
     ZERO  2  ATOM BLOCKS
              2  BY  3
                       1  2
                       3  4  5
              3  BY  2
                       3  4  5
                       1  2

#NIn this example, the first block removes the (1,2) \rarr  (3,4,5)
delocalizations, while the second removes the (3,4,5) \rarr  (1,2)
delocalizations.

\np For additional examples of $DEL input, see Section B.6.10.
.RL55
#IB.5.3 Input for UHF Analysis#N

\np Deletions of the alpha and beta Fock matrices can be done
independently.  The deletions are input as above (Section B.5.2) for
RHF closed shell, but they must be specified separately for alpha
and beta in the UHF case.

\np The deletion to be done on the alpha Fock matrix must be preceded
by the keyword ``ALPHA'', and the deletion of the beta Fock matrix
must be preceded by the keyword ``BETA''.  (Actually, only the first
letter ``A'' or ``B'' is searched for by the program.)  The ALPHA
deletion must precede the BETA deletion.  The BETA deletion
may be the same as the ALPHA deletion, or different.

\np NOTE:  The types of the \alpha  NBOs often differ from those of
the \beta  NBOs, so that distinct \alpha , \beta  deletions
lists are generally required.  For example, O#d2#u (triplet) has one bond in
the \alpha  system and three in the \beta  system, if the unpaired
electrons are in the \alpha  system.

\np Here are three examples to illustrate UHF open-shell deletions:

.RL4
Example 1:
 #T
     ALPHA  ZERO  1  DELOC  FROM  1  TO  2
     BETA   NOSTAR

.RL4
#NExample 2:
 #T
     ALPHA  ZERO  1  DELOC  FROM  1  TO  2
     BETA   ZERO  0  DELOC

.RL4
#NExample 3:
 #T
     ALPHA  DELETE  0  ORBITALS
     BETA   DELETE  1  ORBITAL  8

#NIf no deletion is done, this must be specified using zero (0) with
one of the deletion input formats, as shown in Examples 2,3 above.
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS//3//10>>
.RL55
#BB.6 NBO KEYLIST ILLUSTRATIONS#N


#IB.6.1 Introduction#N

\np This section illustrates the output produced by several
important keyword options of the NBO 
keylists ($NBO, $CHOOSE, $DEL, $CORE lists), 
supplementing the illustrations 
of Section A.3.  Excerpts are provided
rather than full output, since, e.g., NPA analysis is
unaffected by keywords that modify the NBO search.  Keywords
of general applicability are illustrated with the
methylamine example (RHF/3-21G, Pople-Gordon geometry) of
Section A.3, which should be consulted for further 
information.  More specialized keywords (RESONANCE, 3CBOND, etc.)
are illustrated with prototype molecules (benzene, diborane, etc.) 
chosen for the keyword.

\np Sections B.6.2-B.6.8 illustrate representative examples
from the $NBO keyword groups, including NLMO, DIPOLE, BNDIDX,
RESONANCE, NOBOND, 3CBOND, and matrix output 
keywords.  Section B.6.9 and B.6.10 similarly illustrate
the use of the $CHOOSE and $DEL keylists.  Section B.6.11
illustrates the output for open-shell UHF cases, emphasizing
features associated with the ``different Lewis 
structures for different spins'' representation of \alpha  and
\beta  spin manifolds.  Section B.6.12 shows the effect of using
effective core potentials for Cu#d2#u, also illustrating
aspects of the inclusion of #Id#N functions.
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (NLMO)//3//10>>
.RL55
#IB.6.2 NLMO Keyword#N

\np When the NLMO keyword is activated, the program computes the
NLMOs and prints out three tables summarizing their form.  For
the RHF/3-21G methylamine example (cf. Section A.3), the principal
NLMO table is shown below:
.DF\@seg =
NATURAL LOCALIZED MOLECULAR ORBITAL (NLMO) ANALYSIS:

Maximum off-diagonal element of DM in NLMO basis:   0.00000

Hybridization/Polarization Analysis of NLMOs in NAO Basis:
NLMO/Occupancy/Percent from Parent NBO/ Atomic Hybrid Contributions
-------------------------------------------------------------------------------
  1. (2.00000)  99.9290%  BD ( 1) C 1- N 2      
                          40.039%  C 1 s( 21.54%)p 3.64( 78.46%)
                          59.891%  N 2 s( 30.98%)p 2.23( 69.02%)
                           0.015%  H 3 s(100.00%)
                           0.021%  H 6 s(100.00%)
                           0.021%  H 7 s(100.00%)
  2. (2.00000)  99.9301%  BD ( 1) C 1- H 3      
                          59.675%  C 1 s( 25.44%)p 2.93( 74.56%)
                           0.040%  N 2 s(  1.99%)p49.22( 98.01%)
                          40.258%  H 3 s(100.00%)
  3. (2.00000)  99.6996%  BD ( 1) C 1- H 4      
                          60.848%  C 1 s( 25.25%)p 2.96( 74.75%)
                           0.093%  N 2 s( 13.08%)p 6.65( 86.92%)
                           0.014%  H 3 s(100.00%)
                          38.861%  H 4 s(100.00%)
                           0.017%  H 5 s(100.00%)
                           0.158%  H 6 s(100.00%)
  4. (2.00000)  99.6996%  BD ( 1) C 1- H 5      
                          60.848%  C 1 s( 25.25%)p 2.96( 74.75%)
                           0.093%  N 2 s( 13.08%)p 6.65( 86.92%)
                           0.014%  H 3 s(100.00%)
                           0.017%  H 4 s(100.00%)
                          38.861%  H 5 s(100.00%)
                           0.158%  H 7 s(100.00%)
  5. (2.00000)  99.7206%  BD ( 1) N 2- H 6      
                           0.113%  C 1 s(  5.15%)p18.41( 94.85%)
                          67.929%  N 2 s( 25.82%)p 2.87( 74.18%)
                           0.137%  H 4 s(100.00%)
                           0.014%  H 5 s(100.00%)
                          31.793%  H 6 s(100.00%)
  6. (2.00000)  99.7206%  BD ( 1) N 2- H 7      
                           0.113%  C 1 s(  5.15%)p18.41( 94.85%)
                          67.929%  N 2 s( 25.82%)p 2.87( 74.18%)
                           0.014%  H 4 s(100.00%)
                           0.137%  H 5 s(100.00%)
                          31.793%  H 7 s(100.00%)
  7. (2.00000)  99.9499%  CR ( 1) C 1           
                          99.951%  C 1 s(100.00%)p 0.00(  0.00%)
                           0.013%  H 3 s(100.00%)
                           0.013%  H 4 s(100.00%)
                           0.013%  H 5 s(100.00%)
  8. (2.00000)  99.9763%  CR ( 1) N 2           
                           0.010%  C 1 s( 22.30%)p 3.48( 77.70%)
                          99.980%  N 2 s(100.00%)p 0.00(  0.00%)
  9. (2.00000)  98.8972%  LP ( 1) N 2           
                           0.440%  C 1 s(  1.05%)p94.15( 98.95%)
                          98.897%  N 2 s( 17.85%)p 4.60( 82.15%)
                           0.489%  H 3 s(100.00%)
                           0.085%  H 4 s(100.00%)
                           0.085%  H 5 s(100.00%)
.ED

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#NFor each of the nine occuplied NLMOs, the table shows first the
NLMO occupancy (necessarily 2.0000 at SCF level, as in the
present example), the percentage
of the total NLMO composition represented by this parent NBO
(usually > 99%), and the label of the `parent' 
NBO.  Below this, there follows an NAO decomposition
of the NLMO, showing the percentage of the NLMO on each atom
and the hybrid composition ratios (effective
#Isp#N#u\lambda #d character and percentage #Is-#N and 
#Ip#N-character) of the NAOs.  For 
example, NLMO 9 is the most delocalized NLMO
of the table, having only about a 98.9% contribution from
the localized N(2) parent lone pair NBO,
with `delocalization tails' composed
primarily of contributions (~0.4% each) from C(1) and H(3), and 
smaller contributions (~0.09%) from H(4) and H(5).  This 
corresponds to what might have been anticipated from the
NBO summary table (Section A.3.6) or perturbation theory
energy analysis table (Section A.3.5), which showed that
the N(2) lone pair, NBO 9, is principally delocalized
onto NBO 24, the vicinal C(1)-H(3) antibond [with lesser
delocalizations onto NBOs 25, 26, the C(1)-H(4) and C(1)-H(5)
antibonds].
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (DIPOLE)//3//10>>
.RL55
.BM62
#IB.6.3 DIPOLE Keyword#N

\np The DIPOLE keyword activates the NBO/NLMO analysis of the
molecular dipole moment, as shown below for the example
of RHF/3-21G methylamine (cf. Section A.3):
.DF\@seg =
Dipole moment analysis:

[Print threshold: Net dipole > 0.02 Debye]

                                NLMO bond dipole            NBO bond dipole
                            -------------------------  ------------------------
         Orbital              x     y     z   Total      x     y     z   Total
===============================================================================
  1. BD ( 1) C 1- N 2       -0.76 -0.08  0.00  0.76    -0.76 -0.09  0.00  0.77

  2. BD ( 1) C 1- H 3        0.49  1.90  0.00  1.96     0.50  1.90  0.00  1.97
                                            deloc  14:  0.03 -0.01  0.00  0.03
                                            deloc  25: -0.01  0.00  0.02  0.02
                                            deloc  26: -0.01  0.00 -0.02  0.02

  3. BD ( 1) C 1- H 4        0.67 -0.77 -1.50  1.81     0.71 -0.79 -1.50  1.84
                                            deloc  27: -0.05  0.00  0.00  0.05
                                            deloc  26: -0.02  0.03 -0.03  0.04
                                            deloc  24: -0.01 -0.02  0.00  0.02

  4. BD ( 1) C 1- H 5        0.67 -0.77  1.50  1.81     0.71 -0.79  1.50  1.84
                                            deloc  28: -0.05  0.00  0.00  0.05
                                            deloc  25: -0.02  0.03  0.03  0.04
                                            deloc  24: -0.01 -0.02  0.00  0.02

  5. BD ( 1) N 2- H 6       -0.45  0.44  0.86  1.06    -0.50  0.44  0.89  1.11
                                            deloc  25:  0.06 -0.01 -0.02  0.06

  6. BD ( 1) N 2- H 7       -0.45  0.44 -0.86  1.06    -0.50  0.44 -0.89  1.11
                                            deloc  26:  0.06 -0.01  0.02  0.06

  7. CR ( 1) C 1             0.00  0.00  0.00  0.00     0.00  0.00  0.00  0.00

  8. CR ( 1) N 2             0.00  0.01  0.00  0.01     0.00  0.00  0.00  0.00

  9. LP ( 1) N 2            -0.63 -2.85  0.00  2.91    -0.88 -2.93  0.00  3.06
                                            deloc  24:  0.16  0.09  0.00  0.18
                                            deloc  25:  0.03  0.01  0.01  0.03
                                            deloc  26:  0.03  0.01 -0.01  0.03
                                            deloc  10:  0.02 -0.02  0.00  0.03
                           ----------------------------------------------------
        Net dipole moment   -0.45 -1.67  0.00  1.73    -0.71 -1.82  0.00  1.95
Delocalization correction                               0.27  0.14  0.00  0.30
                           ----------------------------------------------------
      Total dipole moment   -0.45 -1.67  0.00  1.73    -0.45 -1.67  0.00  1.73
.ED

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.RL5
#NThe bottom line of the table shows the individual (x,y,z) vector components 
(\minus 0.45,\minus 1.67,0.00)
and length (1.73 D) of the total molecular dipole moment, in the coordinate
system of the ESS program.  This is decomposed in the main body of
the table into the individual contributions of ``NLMO bond dipoles''
(which strictly add to give the net molecule dipole at the SCF level)
and ``NBO bond dipoles'' (which must be added with their
off-diagonal `deloc' contributions to give the net molecular 
moment).  Each NLMO or NBO bond dipole 
vector \vect \mu #dAB #u is evaluated as
.DF\mab =\vect \mu #dAB#u
.DF\mabe =\mab #<#<#<#u#u(elec)#d#d
.DF\mabn =\mab #<#<#<#u#u(nuc)#d#d
.DF\sab =\sigma #dAB#u
.DF\si =\sigma #di#u
.DF\sj =\sigma #dj#u
.DF\dk =\sigma #dk#u
.DF\sinlmo =\si #<#u#u(NLMO)#d#d
.DF\cii =#Ic#N#dii#u
.DF\cji =#Ic#N#dji#u
.DF\cki =#Ic#N#dki#u
.CJ

\mab  = \mabe  + \mabn

.FJ
.DF\sbar =\thsp |\thsp
where
\mabe  = 2#Ie#N\bra \sab \sbar \vect r#N\sbar \sab \ket
is the electronic dipole expectation value for an electron
pair in the \sab  NLMO
or NBO, and \mabn  is the nuclear contribution of compensating
unit positive charges at the positions of nuclei A and B (or both
on A for a 1-center NBO).  The `deloc' contributions 
below each NBO bond dipole 
show the off-diagonal corrections
to an additive bond dipole approximation (i.e.,
the corrections to localized NBO bond dipoles to get the NLMO bond dipoles)
to account for the delocalization from parent NBO #Ii#N onto
other (primarily, non-Lewis) NBOs #Ij#N; in terms of the expansion
of an NLMO in the set {\sj } of NBOs,

.CJ
\sinlmo  = \cii \si  + \sum <<#Rj#N>>\cji \sj
.FJ

this correction is (for each electron, \alpha  or \beta  spin)
.LM+10
.DF\&m =\bra \sigma #d&1#u\sbar \vect \mu \sbar \sigma #d&2#u\ket
.DF\mideloc =\vect \mu #di#u#<#u#u(deloc)#d#d
.DF\&s =\sum <<#R&1#N>>#+\dprime #-
.DF\term =2\cii \&m <<i//j>> + \&sall <<k>> \cki \&m <<j//k>>
.DF\term2 =\&sall <<j>>\cji \[2 \term \]2

\cji #u2#d[\&m <<j//j>>\minus \&m <<i//i>>] + 2\cii \cji \&m <<i//j>> 
+ \&s <<k>>\cji \cki \&m <<j//k>>
.LM-10

where the primes on the summation denote omission of
terms #Ik#N equal to #Ii#N or #Ij#N.  For example, in the above table the
largest individual contribution to \vect \mu  is from the
nitrogen lone pair, table entry 9, which has an NLMO dipole
of 2.91 Debye or NBO dipole of 3.06.  The latter has also the
largest off-diagonal delocalization correction in the table,
a 0.18 D correction due to the 
#In#N#dN#u \rarr  \sigma *#<#dCH#u delocalization into the
vicinal C(1)-H(3) antibond, NBO 24.  

\np For a post-SCF (correlated) calculation, the dipole table would also
include an additional line for the correction due to non-additivity
of the NLMO bond dipoles.  For an ionic species, there 
would also be an additional
line for the ``residual nuclear charge'' contribution; here, one must
be aware that the dipole moment is calculated with respect
to the origin of the cartesian coordinate system chosen by the ESS
program (since the dipole moment is origin-dependent in
this case).

\np Note that the amount of detail in the
dipole table can be altered by using the ``DIPOLE=thr'' form
of the keyword to alter the threshold dipole (`thr') for printing
[default: 0.02 D].
.BM60
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (Matrix Output)//3//10>>
.RL55
#IB.6.4 Matrix Output Keywords#N

\np Two simple examples will be given to illustrate the 
formatting of output for
operators or basis set transformation matrices using the matrix
output keywords of Section B.2.4.  For the RHF/3-21G methylamine
example of Section A.3, the keyword ``FNHO'' would cause the
Fock matrix in the NHO basis to be printed out.  Shown below is
a reproduction of the first eight columns (out of 28) of this output:
.DF\@seg =
NHO Fock matrix:                                                                

         NHO        1       2       3       4       5       6       7       8
     ---------- ------- ------- ------- ------- ------- ------- ------- -------
  1.  C1 ( N2 ) -0.0208 -0.7203 -0.0571 -0.0665  0.0438  0.0672  0.0438  0.0672
  2.  N2 ( C1 ) -0.7203 -0.3083 -0.0773 -0.0627  0.0835  0.0646  0.0835  0.0646
  3.  C1 ( H3 ) -0.0571 -0.0773 -0.1394 -0.6758  0.0638  0.0746  0.0638  0.0746
  4.  H3 ( C1 ) -0.0665 -0.0627 -0.6758  0.1349  0.0740  0.0672  0.0740  0.0672
  5.  C1 ( H4 )  0.0438  0.0835  0.0638  0.0740 -0.1466 -0.6761 -0.0548 -0.0759
  6.  H4 ( C1 )  0.0672  0.0646  0.0746  0.0672 -0.6761  0.1541 -0.0759 -0.0697
  7.  C1 ( H5 )  0.0438  0.0835  0.0638  0.0740 -0.0548 -0.0759 -0.1466 -0.6761
  8.  H5 ( C1 )  0.0672  0.0646  0.0746  0.0672 -0.0759 -0.0697 -0.6761  0.1541
  9.  N2 ( H6 )  0.0926  0.1499  0.0240 -0.0113  0.0912 -0.0078 -0.0349  0.0134
 10.  H6 ( N2 )  0.1083  0.0826 -0.0010  0.0232 -0.0118 -0.0242  0.0017 -0.0224
 11.  N2 ( H7 )  0.0926  0.1499  0.0240 -0.0113 -0.0349  0.0134  0.0912 -0.0078
 12.  H7 ( N2 )  0.1083  0.0826 -0.0010  0.0232  0.0017 -0.0224 -0.0118 -0.0242
 13.  C1 (cr)    0.3962  0.4168  0.4400  0.3893 -0.4447 -0.3869 -0.4447 -0.3869
 14.  N2 (cr)    0.6147  0.7083  0.0039  0.0249 -0.0130 -0.0251 -0.0130 -0.0251
 15.  N2 (lp)    0.0762  0.0955 -0.1043  0.0254 -0.0386  0.0160 -0.0386  0.0160
 16.  C1 (ry*)  -0.1320  0.0924  0.0705 -0.0815  0.0022 -0.0037  0.0022 -0.0037
 17.  C1 (ry*)   0.0000  0.0000  0.0000  0.0000  0.0719 -0.0910 -0.0719  0.0910
 18.  C1 (ry*)  -0.1023  0.0764 -0.0643  0.0795 -0.0074  0.0105 -0.0074  0.0105
 19.  C1 (ry*)   0.0266 -0.0213  0.0019 -0.0057  0.0667 -0.0788  0.0667 -0.0788
 20.  N2 (ry*)   0.0151 -0.0177 -0.0351 -0.0172 -0.0179 -0.0146 -0.0179 -0.0146
 21.  N2 (ry*)   0.0000  0.0000  0.0000  0.0000 -0.0158 -0.0249  0.0158  0.0249
 22.  N2 (ry*)   0.1799 -0.1440 -0.0064  0.0295  0.0038 -0.0289  0.0038 -0.0289
 23.  N2 (ry*)   0.0183 -0.0136 -0.0051  0.0213  0.0032 -0.0095  0.0032 -0.0095
 24.  H3 (ry*)   0.0253 -0.0038  0.2834 -0.3497 -0.0248  0.0047 -0.0248  0.0047
 25.  H4 (ry*)   0.0223 -0.0071  0.0211 -0.0068 -0.2789  0.3553 -0.0227  0.0069
 26.  H5 (ry*)   0.0223 -0.0071  0.0211 -0.0068 -0.0227  0.0069 -0.2789  0.3553
 27.  H6 (ry*)   0.0124  0.0172 -0.0067  0.0219 -0.0080  0.0097  0.0057 -0.0222
 28.  H7 (ry*)   0.0124  0.0172 -0.0067  0.0219  0.0057 -0.0222 -0.0080  0.0097
.ED

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 #N

\np The NHO labels on each row identify the atom to which the NHO
belongs, and (in parentheses) the atom toward which the hybrid is
pointed, if a bond hybrid, or a 1-center label (cr, lp, lp*, or ry*), if
a non-bonded hybrid.  Thus, ``C 1 (N 2)'' (NHO 1) 
is the bonding hybrid on C(1) directed
toward N(2), ``N 2(lp)'' (NBO 15) is a non-bonded (lone pair) hybrid
on N(2), etc.  This label allows one to find the precise form of 
the NHO in the main listing of NBOs.  The FNHO matrix shows, for
example, that 
the (1,2) Fock matrix element between the directly
interacting NHOs forming the C-N bond NBO is -0.7203 a.u.,
whereas the (1,9) matrix element,
between the C(1) hybrid pointing toward N(2)
and the N(2) hybrid pointing toward H(6), is 0.0926 a.u.

\np As a second example, the keyword ``NBOMO=PVAL'' would print out
the core + valence columns of the NBO \rarr  MO transformation, 
as reproduced below:
.DF\@seg =
MOs in the NBO basis:                                                           

         NBO        1       2       3       4       5       6       7       8
     ---------- ------- ------- ------- ------- ------- ------- ------- -------
  1.  C1 - N2   -0.0661 -0.0574  0.6288 -0.1243  0.0000 -0.3239  0.6816  0.0000
  2.  C1 - H3   -0.0018 -0.0578  0.2061 -0.4716  0.0000  0.7747  0.1386  0.0000
  3.  C1 - H4    0.0023  0.0579 -0.1836  0.4908  0.3813  0.2304  0.3921  0.5940
  4.  C1 - H5    0.0023  0.0579 -0.1836  0.4908 -0.3813  0.2304  0.3921 -0.5940
  5.  N2 - H6    0.0570  0.0000 -0.4742 -0.3567 -0.5937 -0.1954  0.3035  0.3814
  6.  N2 - H7    0.0570  0.0000 -0.4742 -0.3567  0.5937 -0.1954  0.3035 -0.3814
  7.  C1 (cr)   -0.0021  0.9931  0.0692 -0.0920  0.0000  0.0006  0.0019  0.0000
  8.  N2 (cr)    0.9935 -0.0019  0.1048  0.0348  0.0000 -0.0131  0.0022  0.0000
  9.  N2 (lp)    0.0432 -0.0037 -0.1676 -0.1219  0.0000  0.3312  0.1525  0.0000
 10.  C1 (ry*)  -0.0088 -0.0005  0.0114  0.0089  0.0000 -0.0016 -0.0086  0.0000
 11.  C1 (ry*)   0.0000  0.0000  0.0000  0.0000  0.0109  0.0000  0.0000 -0.0070
 12.  C1 (ry*)  -0.0063  0.0001 -0.0050 -0.0035  0.0000 -0.0030  0.0026  0.0000
 13.  C1 (ry*)   0.0020 -0.0002 -0.0003 -0.0003  0.0000 -0.0009  0.0002  0.0000
 14.  N2 (ry*)  -0.0041 -0.0003 -0.0006  0.0016  0.0000  0.0192  0.0107  0.0000
 15.  N2 (ry*)   0.0000  0.0000  0.0000  0.0000  0.0080  0.0000  0.0000  0.0124
 16.  N2 (ry*)   0.0035 -0.0060 -0.0039  0.0102  0.0000 -0.0023  0.0040  0.0000
 17.  N2 (ry*)  -0.0018  0.0023 -0.0007  0.0013  0.0000 -0.0007  0.0005  0.0000
 18.  H3 (ry*)  -0.0008 -0.0094 -0.0103  0.0146  0.0000  0.0017 -0.0021  0.0000
 19.  H4 (ry*)  -0.0008 -0.0100 -0.0061  0.0119  0.0062  0.0004 -0.0054 -0.0098
 20.  H5 (ry*)  -0.0008 -0.0100 -0.0061  0.0119 -0.0062  0.0004 -0.0054  0.0098
 21.  H6 (ry*)  -0.0052 -0.0013 -0.0147 -0.0018 -0.0027 -0.0016 -0.0097 -0.0159
 22.  H7 (ry*)  -0.0052 -0.0013 -0.0147 -0.0018  0.0027 -0.0016 -0.0097  0.0159
 23.  C1 - N2 * -0.0019 -0.0035 -0.0026  0.0025  0.0000  0.0043  0.0049  0.0000
 24.  C1 - H3 * -0.0013 -0.0024  0.0059 -0.0018  0.0000 -0.0349 -0.0139  0.0000
 25.  C1 - H4 *  0.0009  0.0028 -0.0138  0.0033 -0.0408 -0.0188  0.0061  0.0148
 26.  C1 - H5 *  0.0009  0.0028 -0.0138  0.0033  0.0408 -0.0188  0.0061 -0.0148
 27.  N2 - H6 * -0.0010  0.0051 -0.0047  0.0182  0.0179  0.0122  0.0154  0.0322
 28.  N2 - H7 * -0.0010  0.0051 -0.0047  0.0182 -0.0179  0.0122  0.0154 -0.0322

         NBO        9      10      11      12      13      14      15
     ---------- ------- ------- ------- ------- ------- ------- -------
  1.  C1 - N2    0.1062 -0.0143  0.0006  0.0000  0.0049  0.0000 -0.0061
  2.  C1 - H3   -0.3343 -0.0044  0.0015  0.0000  0.0007  0.0000 -0.0080
  3.  C1 - H4   -0.1186 -0.0186  0.0103  0.0258 -0.0048 -0.0272 -0.0104
  4.  C1 - H5   -0.1186 -0.0186  0.0103 -0.0258 -0.0048  0.0272 -0.0104
  5.  N2 - H6   -0.1167 -0.0024 -0.0145 -0.0293 -0.0162 -0.0253  0.0040
  6.  N2 - H7   -0.1167 -0.0024 -0.0145  0.0293 -0.0162  0.0253  0.0040
  7.  C1 (cr)    0.0037 -0.0134 -0.0082  0.0000  0.0008  0.0000 -0.0008
  8.  N2 (cr)   -0.0189 -0.0055  0.0030  0.0000 -0.0026  0.0000  0.0035
  9.  N2 (lp)    0.9007 -0.0144  0.0055  0.0000  0.0925  0.0000  0.0130
 10.  C1 (ry*)  -0.0128 -0.0993  0.0553  0.0000  0.0536  0.0000  0.3301
 11.  C1 (ry*)   0.0000  0.0000  0.0000  0.0836  0.0000  0.1845  0.0000
 12.  C1 (ry*)  -0.0039 -0.0612  0.0748  0.0000 -0.1160  0.0000  0.1213
 13.  C1 (ry*)  -0.0018  0.0936  0.0192  0.0000  0.1022  0.0000 -0.1516
 14.  N2 (ry*)  -0.0086 -0.0232  0.0071  0.0000 -0.0461  0.0000 -0.0178
 15.  N2 (ry*)   0.0000  0.0000  0.0000  0.0176  0.0000 -0.0856  0.0000
 16.  N2 (ry*)   0.0006  0.0395 -0.0836  0.0000  0.0221  0.0000 -0.1565
 17.  N2 (ry*)   0.0003  0.0614 -0.0222  0.0000  0.0114  0.0000  0.0584
 18.  H3 (ry*)  -0.0218 -0.2483 -0.2232  0.0000  0.4827  0.0000  0.0001
 19.  H4 (ry*)   0.0060 -0.1973 -0.3224 -0.3372 -0.2069 -0.2151 -0.0483
 20.  H5 (ry*)   0.0060 -0.1973 -0.3224  0.3372 -0.2069  0.2151 -0.0483
 21.  H6 (ry*)   0.0027 -0.2869  0.2132  0.2297 -0.0372 -0.3543 -0.1737
 22.  H7 (ry*)   0.0027 -0.2869  0.2132 -0.2297 -0.0372  0.3543 -0.1737
 23.  C1 - N2 * -0.0031 -0.2357  0.2598  0.0000 -0.1096  0.0000  0.8051
 24.  C1 - H3 * -0.0799 -0.3214 -0.2654  0.0000  0.6687  0.0000  0.1133
 25.  C1 - H4 * -0.0369  0.2559  0.3890  0.4699  0.2968  0.3193 -0.0477
 26.  C1 - H5 * -0.0369  0.2559  0.3890 -0.4699  0.2968 -0.3193 -0.0477
 27.  N2 - H6 * -0.0031  0.4339 -0.3112 -0.3280  0.0474  0.4519  0.2168
 28.  N2 - H7 * -0.0031  0.4339 -0.3112  0.3280  0.0474 -0.4519  0.2168
.ED

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\np In this transformation matrix, rows correspond to NBOs and
columns to MOs (in the ordering used elesewhere in the program),
and each basis NBO is further identified with 
a row label.  The print parameter
``PVAL'' specified that only 15 MOs (the
number of core + valence orbitals) 
should be printed, corresponding to the nine
occupied MOs 1-9 and the lowest six virtual MOs 10-15.  The matrix
allows one to see the composition of each canonical MO in terms of
localized bond NBOs.  For example, MOs 5 and 8 
can be approximately described as
.CJ
.DF\sch14 =\sigma #dC#d1#uH#d4#u#u
.DF\sch15 =\sigma #dC#d1#uH#d5#u#u
.DF\snh16 =\sigma #dN#d2#uH#d6#u#u
.DF\snh17 =\sigma #dN#d2#uH#d7#u#u
.DF\tc =(\sch14  \minus  \sch15 )
.DF\tn =(\snh16  \minus  \snh17 )

\phi #d5#u \~=  \minus 0.594\tn  + 0.381\tc

\phi #d8#u \~=  0.381\tn  + 0.594\tc

.FJ
whereas \phi #d6#u is primarily the C-H(3) NBO and \phi #d9#u 
the N lone pair NBO.
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (BNDIDX)//3//10>>
.RL55
#IB.6.5 BNDIDX Keyword#N

\np The BNDIDX keyword activates the printing of several types
of `bond order' and valency indices, based on different assumptions
and formulas, but all having some connection to the NAO/NBO/NLMO
formalism.  We illustrate these bond
order tables for the example of RHF/3-21G methylamine (Section A.3).

\np The first segment of BNDIDX output shows the Wiberg bond index (the sum of
squares of off-diagonal density matrix elements between
atoms), as formulated
in terms of the NAO basis set:
.DF\@seg =
Wiberg bond index matrix in the NAO basis:                                      

    Atom    1       2       3       4       5       6       7
    ---- ------  ------  ------  ------  ------  ------  ------
  1.  C  0.0000  0.9964  0.9472  0.9394  0.9394  0.0020  0.0020
  2.  N  0.9964  0.0000  0.0208  0.0052  0.0052  0.8611  0.8611
  3.  H  0.9472  0.0208  0.0000  0.0004  0.0004  0.0002  0.0002
  4.  H  0.9394  0.0052  0.0004  0.0000  0.0009  0.0079  0.0005
  5.  H  0.9394  0.0052  0.0004  0.0009  0.0000  0.0005  0.0079
  6.  H  0.0020  0.8611  0.0002  0.0079  0.0005  0.0000  0.0003
  7.  H  0.0020  0.8611  0.0002  0.0005  0.0079  0.0003  0.0000


Wiberg bond index, Totals by atom:                                              

    Atom    1
    ---- ------
  1.  C  3.8265
  2.  N  2.7499
  3.  H  0.9691
  4.  H  0.9544
  5.  H  0.9544
  6.  H  0.8720
  7.  H  0.8720
.ED

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\np This index is intrinsically a positive quantity, making no
distinction between net bonding
or antibonding character of the density matrix elements.

.RL15
\np The next segment tabulates the ``overlap-weighted
NAO bond order,'' as shown below:
.DF\@seg =
Atom-atom overlap-weighted NAO bond order:                                      

    Atom    1       2       3       4       5       6       7
    ---- ------  ------  ------  ------  ------  ------  ------
  1.  C  0.0000  0.7815  0.7614  0.7633  0.7633 -0.0103 -0.0103
  2.  N  0.7815  0.0000 -0.0225 -0.0097 -0.0097  0.6688  0.6688
  3.  H  0.7614 -0.0225  0.0000 -0.0039 -0.0039 -0.0019 -0.0019
  4.  H  0.7633 -0.0097 -0.0039  0.0000  0.0024  0.0038 -0.0032
  5.  H  0.7633 -0.0097 -0.0039  0.0024  0.0000 -0.0032  0.0038
  6.  H -0.0103  0.6688 -0.0019  0.0038 -0.0032  0.0000 -0.0069
  7.  H -0.0103  0.6688 -0.0019 -0.0032  0.0038 -0.0069  0.0000


Atom-atom overlap-weighted NAO bond order, Totals by atom:                      

    Atom    1
    ---- ------
  1.  C  3.0488
  2.  N  2.0772
  3.  H  0.7273
  4.  H  0.7527
  5.  H  0.7527
  6.  H  0.6503
  7.  H  0.6503
.ED

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\np This index corresponds to a sum of off-diagonal
NAO density matrix elements between atoms,
each multiplied by the corresponding PNAO overlap integral.

\np Another type of BNDIDX output appears if the NLMO
keyword is included, summarizing a formal
``NLMO/NPA bond order'' that can be associated with each NLMO:
.DF\@seg =
Individual LMO bond orders greater than 0.002 in magnitude,
 with the overlap between the hybrids in the NLMO given:

Atom I / Atom J / NLMO / Bond Order / Hybrid Overlap /
   1       2       1     0.8007741       0.7314361
   1       2       5     0.0022694       0.1796696
   1       2       6     0.0022694       0.1796696
   1       2       9     0.0088061       0.3053730
   1       3       2     0.8051647       0.7862263
   1       3       9    -0.0088061      -0.5762575
   1       4       3     0.7772179       0.7874312
   1       4       5    -0.0022694      -0.5396947
   1       5       4     0.7772179       0.7874312
   1       5       6    -0.0022694      -0.5396947
   1       6       3    -0.0031652      -0.0920524
   1       6       5     0.0022694       0.0852070
   1       7       4    -0.0031652      -0.0920524
   1       7       6     0.0022694       0.0852070
   2       3       9    -0.0097841      -0.0930204
   2       4       5    -0.0027437      -0.0701717
   2       5       6    -0.0027437      -0.0701717
   2       6       5     0.6358512       0.7286061
   2       7       6     0.6358512       0.7286061
   4       6       3     0.0031652       0.0429202
   4       6       5     0.0027437       0.0399352
   5       7       4     0.0031652       0.0429202
   5       7       6     0.0027437       0.0399352
.ED

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#NThis NLMO bond order is calculated by the method described by
A. E. Reed and P. v.R. Schleyer [#IInorg. Chem. #B27#N, 3969-3987 (1988);
#IJ. Am. Chem. Soc.#N (to be published)],
based on the shared occupancies and hybrid overlaps (last column)
of NAOs composing the NLMO.  In the above table, for example, NLMO 1
occurs only in the first line,
contributing a bond of formal order 0.801 between C(1) and N(2), whereas
NLMO 9 (the nitrogen lone pair) contributes a slight strengthening
(+0.0088) of the C(1)-N(2) bond, a weakening (-0.0088) of the
vicinal C(1)-H(3) bond, and a slight negative bond order (-0.0098)
between atoms N(2), H(3).

\np The NLMO bond order contributions are then summed for each
atom pair to give the net NLMO/NPA bond orders shown below:
.DF\@seg =
Atom-Atom Net Linear NLMO/NPA Bond Orders:                                      

    Atom    1       2       3       4       5       6       7
    ---- ------  ------  ------  ------  ------  ------  ------
  1.  C  0.0000  0.8174  0.7960  0.7732  0.7732 -0.0013 -0.0013
  2.  N  0.8174  0.0000 -0.0104 -0.0030 -0.0030  0.6337  0.6337
  3.  H  0.7960 -0.0104  0.0000 -0.0020 -0.0020  0.0001  0.0001
  4.  H  0.7732 -0.0030 -0.0020  0.0000  0.0020  0.0062  0.0000
  5.  H  0.7732 -0.0030 -0.0020  0.0020  0.0000  0.0000  0.0062
  6.  H -0.0013  0.6337  0.0001  0.0062  0.0000  0.0000 -0.0001
  7.  H -0.0013  0.6337  0.0001  0.0000  0.0062 -0.0001  0.0000
.ED

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#NFor example, the table attributes a formal bond order of 0.8174 to the
C(1)-N(2) bond of methylamine, the highest bond order in this 
molecule.  (The higher value for C(1)-H(3) than for the other
two CH bonds reflects an unsatisfactory aspect of this
method of assessing bond order.)

\np These bond indices are based on different
assumptions, and each has certain advantages and
disadvantages.  #ICaveat emptor!#N
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (RESONANCE)//3//10>>
.RL55
#IB.6.6 RESONANCE Keyword: Benzene#N

\np When NBO analysis is performed on a wavefunction that cannot
be satisfactorily localized [i.e., in which one or more NBOs of
the natural Lewis structure fail to achieve
the threshold occupancy (1.90) for a satisfactory
`pair'], the NBO program aborts with a message indicating that
the wavefunction is unsuitable for localized analysis.  For example,
when benzene (RHF/STO-3G level, idealized Pople-Gordon geometry)
is treated by the NBO program in default mode, one obtains the output:
.DF\@seg =
NATURAL BOND ORBITAL ANALYSIS:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    1.90    38.87476   3.12524      6  12   0   3     3      3    0.44
  2(2)    1.90    38.87476   3.12524      6  12   0   3     3      3    0.44
-----------------------------------------------------------------------------

Only strongly delocalized resonance structures can be found.
The default procedure is to abort the NBO search.
.ED

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\np #NWhen the RESONANCE keyword is activated for this same example,
one obtains a summary of NBO search cycles as shown below:
.DF\@seg =
NATURAL BOND ORBITAL ANALYSIS:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    1.90    38.87476   3.12524      6  12   0   3     3      3    0.44
  2(2)    1.90    38.87476   3.12524      6  12   0   3     3      3    0.44
  3(1)    1.80    38.87476   3.12524      6  12   0   3     3      3    0.44
  4(2)    1.80    38.87476   3.12524      6  12   0   3     3      3    0.44
  5(1)    1.70    38.87476   3.12524      6  12   0   3     3      3    0.44
  6(2)    1.70    38.87476   3.12524      6  12   0   3     3      3    0.44
  7(1)    1.60    40.87476   1.12524      6  15   0   0     0      3    0.44
  8(2)    1.60    40.87476   1.12524      6  15   0   0     0      3    0.44
  9(1)    1.50    40.87476   1.12524      6  15   0   0     0      3    0.44
 10(2)    1.50    40.87476   1.12524      6  15   0   0     0      3    0.44
 11(1)    1.60    40.87476   1.12524      6  15   0   0     0      3    0.44
-----------------------------------------------------------------------------

Structure accepted: RESONANCE keyword permits strongly delocalized structure
.ED

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\np As this table shows, the occupancy threshold was successively
lowered from 1.90 to 1.50 by 0.1e for each cycle, 
and the NBO search repeated.  In
this case, the `best' Lewis structure (lowest overall non-Lewis
occupancy, 1.12524e) was found in cycle 7, with occupancy
thresh#|old 1.60e.  The NBO program therefore reset the 
thresh#|old to this value and calculated
the set of NBOs corresponding to this
`best' Lewis structure, as shown below:
.DF\@seg =
    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (1.98940) BD ( 1) C 1- C 2      
               ( 50.00%)   0.7071* C 1 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.8109  0.0097  0.0000
               ( 50.00%)   0.7071* C 2 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.8109  0.0097  0.0000
  2. (1.98940) BD ( 1) C 1- C 6      
               ( 50.00%)   0.7071* C 1 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.4138 -0.6974  0.0000
               ( 50.00%)   0.7071* C 6 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.3971  0.7071  0.0000
  3. (1.66667) BD ( 2) C 1- C 6      
               ( 50.00%)   0.7071* C 1 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
               ( 50.00%)   0.7071* C 6 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
  4. (1.98977) BD ( 1) C 1- H 7      
               ( 51.73%)   0.7193* C 1 s( 31.53%)p 2.17( 68.47%)
                                        0.0000  0.5615  0.4137  0.7166  0.0000
               ( 48.27%)   0.6947* H 7 s(100.00%)
                                        1.0000
  5. (1.98940) BD ( 1) C 2- C 3      
               ( 50.00%)   0.7071* C 2 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.4138 -0.6974  0.0000
               ( 50.00%)   0.7071* C 3 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.3971  0.7071  0.0000
  6. (1.66667) BD ( 2) C 2- C 3      
               ( 50.00%)   0.7071* C 2 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
               ( 50.00%)   0.7071* C 3 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
  7. (1.98977) BD ( 1) C 2- H 8      
               ( 51.73%)   0.7193* C 2 s( 31.53%)p 2.17( 68.47%)
                                        0.0000  0.5615 -0.4137  0.7166  0.0000
               ( 48.27%)   0.6947* H 8 s(100.00%)
                                        1.0000
  8. (1.98940) BD ( 1) C 3- C 4      
               ( 50.00%)   0.7071* C 3 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.3971 -0.7071  0.0000
               ( 50.00%)   0.7071* C 4 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.4138  0.6974  0.0000
  9. (1.98977) BD ( 1) C 3- H 9      
               ( 51.73%)   0.7193* C 3 s( 31.53%)p 2.17( 68.47%)
                                        0.0000  0.5615 -0.8275  0.0000  0.0000
               ( 48.27%)   0.6947* H 9 s(100.00%)
                                        1.0000
 10. (1.66667) BD ( 2) C 4- C 5      
               ( 50.00%)   0.7071* C 4 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
               ( 50.00%)   0.7071* C 5 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
 11. (1.98940) BD ( 1) C 4- C 5      
               ( 50.00%)   0.7071* C 4 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.8109 -0.0097  0.0000
               ( 50.00%)   0.7071* C 5 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.8109 -0.0097  0.0000
 12. (1.98977) BD ( 1) C 4- H10      
               ( 51.73%)   0.7193* C 4 s( 31.53%)p 2.17( 68.47%)
                                        0.0000  0.5615 -0.4137 -0.7166  0.0000
               ( 48.27%)   0.6947* H10 s(100.00%)
                                        1.0000
 13. (1.98940) BD ( 1) C 5- C 6      
               ( 50.00%)   0.7071* C 5 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.4138  0.6974  0.0000
               ( 50.00%)   0.7071* C 6 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.3971 -0.7071  0.0000
 14. (1.98977) BD ( 1) C 5- H11      
               ( 51.73%)   0.7193* C 5 s( 31.53%)p 2.17( 68.47%)
                                        0.0000  0.5615  0.4137 -0.7166  0.0000
               ( 48.27%)   0.6947* H11 s(100.00%)
                                        1.0000
 15. (1.98977) BD ( 1) C 6- H12      
               ( 51.73%)   0.7193* C 6 s( 31.53%)p 2.17( 68.47%)
                                        0.0000  0.5615  0.8275  0.0000  0.0000
               ( 48.27%)   0.6947* H12 s(100.00%)
                                        1.0000
 16. (1.99995) CR ( 1) C 1             s(100.00%)
                                        1.0000  0.0000  0.0000  0.0000  0.0000
 17. (1.99995) CR ( 1) C 2             s(100.00%)
                                        1.0000  0.0000  0.0000  0.0000  0.0000
 18. (1.99995) CR ( 1) C 3             s(100.00%)
                                        1.0000  0.0000 -0.0001  0.0000  0.0000
 19. (1.99995) CR ( 1) C 4             s(100.00%)
                                        1.0000  0.0000  0.0000  0.0000  0.0000
 20. (1.99995) CR ( 1) C 5             s(100.00%)
                                        1.0000  0.0000  0.0000  0.0000  0.0000
 21. (1.99995) CR ( 1) C 6             s(100.00%)
                                        1.0000  0.0000  0.0001  0.0000  0.0000
 22. (0.01077) BD*( 1) C 1- C 2      
               ( 50.00%)   0.7071* C 1 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.8109  0.0097  0.0000
               ( 50.00%)  -0.7071* C 2 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.8109  0.0097  0.0000
 23. (0.01077) BD*( 1) C 1- C 6      
               ( 50.00%)   0.7071* C 1 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.4138 -0.6974  0.0000
               ( 50.00%)  -0.7071* C 6 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.3971  0.7071  0.0000
 24. (0.33333) BD*( 2) C 1- C 6      
               ( 50.00%)   0.7071* C 1 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
               ( 50.00%)  -0.7071* C 6 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
 25. (0.01011) BD*( 1) C 1- H 7      
               ( 48.27%)   0.6947* C 1 s( 31.53%)p 2.17( 68.47%)
                                        0.0000 -0.5615 -0.4137 -0.7166  0.0000
               ( 51.73%)  -0.7193* H 7 s(100.00%)
                                       -1.0000
 26. (0.01077) BD*( 1) C 2- C 3      
               ( 50.00%)   0.7071* C 2 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.4138 -0.6974  0.0000
               ( 50.00%)  -0.7071* C 3 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.3971  0.7071  0.0000
 27. (0.33333) BD*( 2) C 2- C 3      
               ( 50.00%)   0.7071* C 2 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
               ( 50.00%)  -0.7071* C 3 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
 28. (0.01011) BD*( 1) C 2- H 8      
               ( 48.27%)   0.6947* C 2 s( 31.53%)p 2.17( 68.47%)
                                        0.0000 -0.5615  0.4137 -0.7166  0.0000
               ( 51.73%)  -0.7193* H 8 s(100.00%)
                                       -1.0000
 29. (0.01077) BD*( 1) C 3- C 4      
               ( 50.00%)   0.7071* C 3 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.3971 -0.7071  0.0000
               ( 50.00%)  -0.7071* C 4 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.4138  0.6974  0.0000
 30. (0.01011) BD*( 1) C 3- H 9      
               ( 48.27%)   0.6947* C 3 s( 31.53%)p 2.17( 68.47%)
                                        0.0000 -0.5615  0.8275  0.0000  0.0000
               ( 51.73%)  -0.7193* H 9 s(100.00%)
                                       -1.0000
 31. (0.33333) BD*( 2) C 4- C 5      
               ( 50.00%)   0.7071* C 4 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
               ( 50.00%)  -0.7071* C 5 s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  1.0000
 32. (0.01077) BD*( 1) C 4- C 5      
               ( 50.00%)   0.7071* C 4 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.8109 -0.0097  0.0000
               ( 50.00%)  -0.7071* C 5 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.8109 -0.0097  0.0000
 33. (0.01011) BD*( 1) C 4- H10      
               ( 48.27%)   0.6947* C 4 s( 31.53%)p 2.17( 68.47%)
                                        0.0000 -0.5615  0.4137  0.7166  0.0000
               ( 51.73%)  -0.7193* H10 s(100.00%)
                                       -1.0000
 34. (0.01077) BD*( 1) C 5- C 6      
               ( 50.00%)   0.7071* C 5 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851  0.4138  0.6974  0.0000
               ( 50.00%)  -0.7071* C 6 s( 34.23%)p 1.92( 65.77%)
                                        0.0000  0.5851 -0.3971 -0.7071  0.0000
 35. (0.01011) BD*( 1) C 5- H11      
               ( 48.27%)   0.6947* C 5 s( 31.53%)p 2.17( 68.47%)
                                        0.0000 -0.5615 -0.4137  0.7166  0.0000
               ( 51.73%)  -0.7193* H11 s(100.00%)
                                       -1.0000
 36. (0.01011) BD*( 1) C 6- H12      
               ( 48.27%)   0.6947* C 6 s( 31.53%)p 2.17( 68.47%)
                                        0.0000 -0.5615 -0.8275  0.0000  0.0000
               ( 51.73%)  -0.7193* H12 s(100.00%)
                                       -1.0000
.ED

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\np As one can see from this table, the set of NBOs 
obtained by the program corresponds
to one of the two equivalent Kekul\acute e structures, with 
reasonably well
localized \sigma #dCC#u and \sigma #dCH#u NBOs (1.98940 and 1.98977
electrons, respectively), but three severely depleted \pi #dCC#u
bonds (1.66667e) and corresponding high occupancy 
\pi *#<#dCC#u antibonds (0.33333e).  Other sections of the NBO
output (not shown) will similarly exhibit the sharp distinctions 
between benzene and more `typical' non-aromatic compounds.

.LM+10
.RM-10
.BX<<3//18//72//+1//+11>>

.CJ
#-#BWARNING#N#+
.FJ

If you attempt to analyze an open-shell wavefunction with an
ESS method that produces only the ``spinless'' (spin-averaged) density
matrix, rather than the separate density matrices for \alpha  
and \beta  spin, the job will likely abort, as in the default
benzene example.  However, you should #Inot#N use the RESONANCE
keyword to bypass this abort!  NBO analysis of an open-shell 
spinless density matrix is a fundamental misuse
of the program.

.LM10
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.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (NOBOND): Hydrogen Fluoride//3//10>>
.RL55
#IB.6.7 NOBOND Keyword#N

\np The NOBOND keyword forces the NBO program to analyze the
wavefunction in terms of 1-center functions only, thus forcing
a description of the bonding in terms of atomic or 
ionic hybrids.  The modifications of NBO output that result
from activating this keyword can be illustrated for the 
HF molecule (RHF/3-21G//RHF/3-21G level).  This molecule
might be described in terms of a polar covalent H-F
bond or in terms of ionic H#u+#d\thsp F#u\minus #d interactions.

\np The default NBO analysis of this example is shown below:
.DF\@seg =
NATURAL BOND ORBITAL ANALYSIS:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    1.90     9.99942   0.00058      1   1   0   3     0      0    0.00
-----------------------------------------------------------------------------

Structure accepted: No low occupancy Lewis orbitals

--------------------------------------------------------
  Core                      1.99994 ( 99.997% of   2)
  Valence Lewis             7.99948 ( 99.994% of   8)
 ==================       ============================
  Total Lewis               9.99942 ( 99.994% of  10)
 -----------------------------------------------------
  Valence non-Lewis         0.00000 (  0.000% of  10)
  Rydberg non-Lewis         0.00058 (  0.006% of  10)
 ==================       ============================
  Total non-Lewis           0.00058 (  0.006% of  10)
--------------------------------------------------------


    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (2.00000) BD ( 1) F 1- H 2      
               ( 75.22%)   0.8673* F 1 s( 16.31%)p 5.13( 83.69%)
                                        0.0000  0.4036  0.0158  0.0000  0.0000
                                        0.0000  0.0000  0.9148  0.0001
               ( 24.78%)   0.4978* H 2 s(100.00%)
                                        1.0000  0.0000
  2. (1.99994) CR ( 1) F 1             s(100.00%)
                                        1.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000
  3. (2.00000) LP ( 1) F 1             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  1.0000 -0.0013
                                        0.0000  0.0000  0.0000  0.0000
  4. (2.00000) LP ( 2) F 1             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        1.0000 -0.0013  0.0000  0.0000
  5. (1.99948) LP ( 3) F 1             s( 83.71%)p 0.19( 16.29%)
                                        0.0000  0.9149 -0.0052  0.0000  0.0000
                                        0.0000  0.0000 -0.4036 -0.0062
  6. (0.00002) RY*( 1) F 1             s(  0.00%)p 1.00(100.00%)
  7. (0.00000) RY*( 2) F 1             s(  0.00%)p 1.00(100.00%)
  8. (0.00000) RY*( 3) F 1             s(  0.00%)p 1.00(100.00%)
  9. (0.00000) RY*( 4) F 1             s( 99.97%)p 0.00(  0.03%)
 10. (0.00056) RY*( 1) H 2             s(100.00%)
                                        0.0000  1.0000
 11. (0.00000) BD*( 1) F 1- H 2      
               ( 24.78%)   0.4978* F 1 s( 16.31%)p 5.13( 83.69%)
               ( 75.22%)  -0.8673* H 2 s(100.00%)
.ED

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.LM10
.RM80
.HR<<3//+1//5//85>>
 #N

As the output shows, default NBO analysis
leads to a polar covalent description of HF.  The
\sigma #dHF#u bond, NBO 1, is formed from a #Ip#N-rich 
(#Isp#N#u5.13#d) hybrid on F and the 1#Is#N AO on H,
strongly polarized (about 75.22%) toward F.  This provides a
satisfactory Lewis structure, describing 99.994% of
the total electron density.

\np When the NOBOND keyword is activated to bypass
the search for 2-center bonds, the NBO output is
modified as shown below:
.DF\@seg =

       /NOBOND / : No two-center NBO search


NATURAL BOND ORBITAL ANALYSIS:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    1.00     9.50378   0.49622      1   0   0   4     0      1    0.75
-----------------------------------------------------------------------------

Structure accepted: Search for bonds prevented by NOBOND keyword

--------------------------------------------------------
  Core                      1.99993 ( 99.997% of   2)
  Valence Lewis             7.50385 ( 93.798% of   8)
 ==================       ============================
  Total Lewis               9.50378 ( 95.038% of  10)
 -----------------------------------------------------
  Valence non-Lewis         0.49564 (  4.956% of  10)
  Rydberg non-Lewis         0.00058 (  0.006% of  10)
 ==================       ============================
  Total non-Lewis           0.49622 (  4.962% of  10)
--------------------------------------------------------


    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (1.99993) CR ( 1) F 1             s(100.00%)p 0.00(  0.00%)
                                        1.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0001  0.0000
  2. (2.00000) LP ( 1) F 1             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  1.0000 -0.0013
                                        0.0000  0.0000  0.0000  0.0000
  3. (2.00000) LP ( 2) F 1             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        1.0000 -0.0013  0.0000  0.0000
  4. (1.99948) LP ( 3) F 1             s( 83.71%)p 0.19( 16.29%)
                                        0.0000  0.9149 -0.0052  0.0000  0.0000
                                        0.0000  0.0000 -0.4036 -0.0062
  5. (1.50436) LP ( 4) F 1             s( 16.31%)p 5.13( 83.69%)
                                       -0.0001  0.4036  0.0158  0.0000  0.0000
                                        0.0000  0.0000  0.9148  0.0001
  6. (0.49564) LP*( 1) H 2             s(100.00%)
                                        1.0000  0.0000
  7. (0.00002) RY*( 1) F 1             s(  0.00%)p 1.00(100.00%)
  8. (0.00000) RY*( 2) F 1             s(  0.00%)p 1.00(100.00%)
  9. (0.00000) RY*( 3) F 1             s(  0.00%)p 1.00(100.00%)
 10. (0.00000) RY*( 4) F 1             s( 99.97%)p 0.00(  0.03%)
 11. (0.00056) RY*( 1) H 2             s(100.00%)
                                        0.0000  1.0000
.ED

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\np In this case, the NBO output indicates a rather poor Lewis
structure (4.962% non-Lewis density), with a severely
depleted F#u\minus #d lone pair (NBO 5, the #Isp#N#u5.13#d hybrid)
and significant occupancy (about 0.496e) in the `empty' H#u+#d
1#Is#N orbital (NBO 6) of the cation.  The NOBOND comparison
would therefore indicate the superiority of a polar
covalent description in this case.
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (3CBOND)//3//10>>
.RL55
#IB.6.8 3CBOND Keyword: Diborane#N

\np When the default NBO analysis is applied to diborane or
related electron-deficient compounds, there is a dramatic
failure to represent the electronic distribution in terms of
1- and 2-center functions only.  For example, for
B#d2#uH#d6#u at the RHF/3-21G//RHF/3-21G level,
the default NBO search (if the RESONANCE keyword is activated
to allow NBO printout) returns
a fractured set of 4 units (two BH#d2#u#u+#d and two H#u\minus #d
fragments), with about 2.13 electrons unaccounted for (~15%
non-Lewis occupancy), symptomatic of general breakdown of the
conventional Lewis structure representation.

\np However, when the NBO search is extended to 3-center bonds
by activating the 3CBOND keyword, one obtains
the NBO output shown below:
.DF\@seg =

       /3CBOND / : Search for 3-center bonds

NATURAL BOND ORBITAL ANALYSIS:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    1.90    15.94335   0.05665      2   4   2   0     0      0    0.15
  2(2)    1.90    15.94335   0.05665      2   4   2   0     0      0    0.15
-----------------------------------------------------------------------------

Structure accepted: No low occupancy Lewis orbitals

WARNING:  1 low occupancy (<1.9990e) core orbital  found on  B 1
          1 low occupancy (<1.9990e) core orbital  found on  B 2

--------------------------------------------------------
  Core                      3.99702 ( 99.925% of   4)
  Valence Lewis            11.94633 ( 99.553% of  12)
 ==================       ============================
  Total Lewis              15.94335 ( 99.646% of  16)
 -----------------------------------------------------
  Valence non-Lewis         0.04565 (  0.285% of  16)
  Rydberg non-Lewis         0.01100 (  0.069% of  16)
 ==================       ============================
  Total non-Lewis           0.05665 (  0.354% of  16)
--------------------------------------------------------


    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (1.98467) 3C ( 1) B 1- B 2- H 3 
               ( 26.43%)   0.5141* B 1 s( 18.00%)p 4.55( 82.00%)
                                        0.0005  0.4241  0.0124 -0.7067 -0.0245
                                        0.0000  0.0000  0.5657 -0.0007
               ( 26.43%)   0.5141* B 2 s( 18.00%)p 4.55( 82.00%)
                                        0.0005  0.4241  0.0124 -0.7067 -0.0245
                                        0.0000  0.0000 -0.5657  0.0007
               ( 47.14%)   0.6866* H 3 s(100.00%)
                                        1.0000  0.0066
  2. (1.98467) 3C ( 1) B 1- B 2- H 4 
               ( 26.43%)   0.5141* B 1 s( 18.00%)p 4.55( 82.00%)
                                        0.0005  0.4241  0.0124  0.7067  0.0245
                                        0.0000  0.0000  0.5657 -0.0007
               ( 26.43%)   0.5141* B 2 s( 18.00%)p 4.55( 82.00%)
                                        0.0005  0.4241  0.0124  0.7067  0.0245
                                        0.0000  0.0000 -0.5657  0.0007
               ( 47.14%)   0.6866* H 4 s(100.00%)
                                        1.0000  0.0066
  3. (1.99425) BD ( 1) B 1- H 6      
               ( 48.80%)   0.6985* B 1 s( 31.98%)p 2.13( 68.02%)
                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
                                        0.7067 -0.0243 -0.4239 -0.0222
               ( 51.20%)   0.7156* H 6 s(100.00%)
                                        1.0000  0.0004
  4. (1.99425) BD ( 1) B 1- H 7      
               ( 48.80%)   0.6985* B 1 s( 31.98%)p 2.13( 68.02%)
                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
                                       -0.7067  0.0243 -0.4239 -0.0222
               ( 51.20%)   0.7156* H 7 s(100.00%)
                                        1.0000  0.0004
  5. (1.99425) BD ( 1) B 2- H 5      
               ( 48.80%)   0.6985* B 2 s( 31.98%)p 2.13( 68.02%)
                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
                                       -0.7067  0.0243  0.4239  0.0222
               ( 51.20%)   0.7156* H 5 s(100.00%)
                                        1.0000  0.0004
  6. (1.99425) BD ( 1) B 2- H 8      
               ( 48.80%)   0.6985* B 2 s( 31.98%)p 2.13( 68.02%)
                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
                                        0.7067 -0.0243  0.4239  0.0222
               ( 51.20%)   0.7156* H 8 s(100.00%)
                                        1.0000  0.0004
  7. (1.99851) CR ( 1) B 1             s(100.00%)p 0.00(  0.00%)
                                        1.0000 -0.0002  0.0000  0.0000  0.0000
                                        0.0000  0.0000 -0.0007  0.0000
  8. (1.99851) CR ( 1) B 2             s(100.00%)p 0.00(  0.00%)
                                        1.0000 -0.0002  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0007  0.0000
  9. (0.00147) RY*( 1) B 1             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0344  0.9994  0.0000  0.0000
 10. (0.00080) RY*( 2) B 1             s(  4.02%)p23.87( 95.98%)
                                        0.0000  0.0245  0.1990  0.0000  0.0000
                                        0.0000  0.0000 -0.0214  0.9795
 11. (0.00002) RY*( 3) B 1             s( 96.01%)p 0.04(  3.99%)
 12. (0.00000) RY*( 4) B 1             s(  0.00%)p 1.00(100.00%)
 13. (0.00147) RY*( 1) B 2             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0344  0.9994  0.0000  0.0000
 14. (0.00080) RY*( 2) B 2             s(  4.02%)p23.87( 95.98%)
                                        0.0000  0.0245  0.1990  0.0000  0.0000
                                        0.0000  0.0000  0.0214 -0.9795
 15. (0.00002) RY*( 3) B 2             s( 96.01%)p 0.04(  3.99%)
 16. (0.00000) RY*( 4) B 2             s(  0.00%)p 1.00(100.00%)
 17. (0.00181) RY*( 1) H 3             s(100.00%)
                                       -0.0066  1.0000
 18. (0.00181) RY*( 1) H 4             s(100.00%)
                                       -0.0066  1.0000
 19. (0.00070) RY*( 1) H 5             s(100.00%)
                                       -0.0004  1.0000
 20. (0.00070) RY*( 1) H 6             s(100.00%)
                                       -0.0004  1.0000
 21. (0.00070) RY*( 1) H 7             s(100.00%)
                                       -0.0004  1.0000
 22. (0.00070) RY*( 1) H 8             s(100.00%)
                                       -0.0004  1.0000
 23. (0.01464) 3C*( 1) B 1- B 2- H 3 
               ( 23.57%)   0.4855* B 1 s( 18.00%)p 4.55( 82.00%)
                                        0.0005  0.4241  0.0124 -0.7067 -0.0245
                                        0.0000  0.0000  0.5657 -0.0007
               ( 23.57%)  -0.4855* B 2 s( 18.00%)p 4.55( 82.00%)
                                       -0.0005 -0.4241 -0.0124  0.7067  0.0245
                                        0.0000  0.0000  0.5657 -0.0007
               ( 52.86%)  -0.7271* H 3 s(100.00%)
                                        1.0000  0.0066
 24. (0.00026) 3C*( 1) B 1- B 2- H 3 
               ( 50.00%)   0.7071* B 1 s( 18.00%)p 4.55( 82.00%)
                                       -0.0005 -0.4241 -0.0124  0.7067  0.0245
                                        0.0000  0.0000 -0.5657  0.0007
               ( 50.00%)  -0.7071* B 2 s( 18.00%)p 4.55( 82.00%)
                                       -0.0005 -0.4241 -0.0124  0.7067  0.0245
                                        0.0000  0.0000  0.5657 -0.0007
               (  0.00%)   0.0000* H 3 s(  0.00%)
                                        0.0000  0.0000
 25. (0.01464) 3C*( 1) B 1- B 2- H 4 
               ( 23.57%)   0.4855* B 1 s( 18.00%)p 4.55( 82.00%)
                                        0.0005  0.4241  0.0124  0.7067  0.0245
                                        0.0000  0.0000  0.5657 -0.0007
               ( 23.57%)  -0.4855* B 2 s( 18.00%)p 4.55( 82.00%)
                                       -0.0005 -0.4241 -0.0124 -0.7067 -0.0245
                                        0.0000  0.0000  0.5657 -0.0007
               ( 52.86%)  -0.7271* H 4 s(100.00%)
                                        1.0000  0.0066
 26. (0.00026) 3C*( 1) B 1- B 2- H 4 
               ( 50.00%)   0.7071* B 1 s( 18.00%)p 4.55( 82.00%)
                                       -0.0005 -0.4241 -0.0124 -0.7067 -0.0245
                                        0.0000  0.0000 -0.5657  0.0007
               ( 50.00%)  -0.7071* B 2 s( 18.00%)p 4.55( 82.00%)
                                       -0.0005 -0.4241 -0.0124 -0.7067 -0.0245
                                        0.0000  0.0000  0.5657 -0.0007
               (  0.00%)   0.0000* H 4 s(  0.00%)
                                        0.0000  0.0000
 27. (0.00396) BD*( 1) B 2- H 5      
               ( 51.20%)   0.7156* B 2 s( 31.98%)p 2.13( 68.02%)
                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
                                       -0.7067  0.0243  0.4239  0.0222
               ( 48.80%)  -0.6985* H 5 s(100.00%)
                                        1.0000  0.0004
 28. (0.00396) BD*( 1) B 2- H 8      
               ( 51.20%)   0.7156* B 2 s( 31.98%)p 2.13( 68.02%)
                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
                                        0.7067 -0.0243  0.4239  0.0222
               ( 48.80%)  -0.6985* H 8 s(100.00%)
                                        1.0000  0.0004
 29. (0.00396) BD*( 1) B 1- H 6      
               ( 51.20%)   0.7156* B 1 s( 31.98%)p 2.13( 68.02%)
                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
                                        0.7067 -0.0243 -0.4239 -0.0222
               ( 48.80%)  -0.6985* H 6 s(100.00%)
                                        1.0000  0.0004
 30. (0.00396) BD*( 1) B 1- H 7      
               ( 51.20%)   0.7156* B 1 s( 31.98%)p 2.13( 68.02%)
                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
                                       -0.7067  0.0243 -0.4239 -0.0222
               ( 48.80%)  -0.6985* H 7 s(100.00%)
                                        1.0000  0.0004
.ED

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.LM10
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.HR<<3//+1//5//85>>
 #N

\np The resulting NBO Lewis structure has improved significantly
[only 0.057e (0.35%) non-Lewis occupancy].  The structure includes
the expected 3-center B-H-B bonds (NBOs 1, 2), each with reasonably
high occupancy (1.9847e).  Each 3-c bond is composed of #Ip#N-rich
(#Isp#N#u4.55#d) boron hybrids and the hydrogen 1#Is#N NAO,
with about 47.14% of the orbital density on the central hydrogen.  Note
that each 3-center bond NBO is associated with #Itwo#N 3-c antibond
NBOs (viz., NBOs 23, 24 for the first 3-c bond, NBO 1), which contribute
in distinct ways to delocalization interactions.  Of course, the 
accuracy of #Iany#N molecular Lewis structure might be improved
slightly by extending the NBO search to 3-center bonds (thus
allowing greater variational flexibility to maximize occupancy),
but this example illustrates the kind of #Iqualitative#N improvement
that indicates when 3-center bonds are needed
in the zeroth-order picture of the bonding.

\np Note that
the NBO 3-c label may frequently have the wrong `connectivity' (as
in the present case, e.g., where ``B 1- B 2- H 3'' is written
instead of the more reasonable ``B 1- H 3- B 2'').  This is a
consequence of the fact that the NBO algorithms have no inkling
of the positions of the atoms in space, and thus of which
label is more `reasonable.'
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS ($CHOOSE)//3//10>>
.RL55
#IB.6.9 NBO Directed Search ($CHOOSE Keylist)#N

\np To illustrate the $CHOOSE keylist for a directed NBO search, we
again make use of the methylamine example (Section A.3).  The vicinal
#In#N#dN#u \rarr  \sigma *#<#dCH#u delocalization, to which attention
has been repeatedly called in the examples,
may be associated, in resonance theory terms,
with the ``double-bond, no-bond'' resonance structure shown below:
.DF\:nobond =<<0B3'C#d1#u'//0B7R'\umlaut H#d3#u#+\minus #-'//
W10R'#-\nthsp H#d4#u#+\thsp '//
D11R'H#d5#u'//BD3'N#d2#u#<#+#++#-#-'//W5R'H#d6#u'//D4R'H#d7#u'>>
.CJ


\:nobond



.FJ
To investigate the suitability of this resonance structure
for describing the methylamine wavefunction, we would
specify the $CHOOSE keylist (Section B.4) as follows:
 #T
     $CHOOSE            !double-bond, no-bond resonance
        LONE  3  1  END
        BOND  S 1 4  S 1 5  D 1 2  S 2 6  S 2 7  END
     $END

#NWhen this is included in the input file, the NBO program produces
the output shown below:
.DF\@seg =
NATURAL BOND ORBITAL ANALYSIS:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    1.90    16.66741   1.33259      2   6   0   1     1      2    0.95
-----------------------------------------------------------------------------

Structure accepted: NBOs selected via the $CHOOSE keylist

WARNING:  1 low occupancy (<1.9990e) core orbital  found on  C 1

--------------------------------------------------------
  Core                      3.99853 ( 99.963% of   4)
  Valence Lewis            12.66888 ( 90.492% of  14)
 ==================       ============================
  Total Lewis              16.66741 ( 92.597% of  18)
 -----------------------------------------------------
  Valence non-Lewis         1.30491 (  7.249% of  18)
  Rydberg non-Lewis         0.02768 (  0.154% of  18)
 ==================       ============================
  Total non-Lewis           1.33259 (  7.403% of  18)
--------------------------------------------------------


    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (1.95945) BD ( 1) C 1- N 2      
               (  7.66%)   0.2768* C 1 s(  0.63%)p99.99( 99.37%)
                                       -0.0001 -0.0770 -0.0186  0.5107 -0.0551
                                        0.8520 -0.0632  0.0000  0.0000
               ( 92.34%)   0.9609* N 2 s( 19.31%)p 4.18( 80.69%)
                                        0.0000  0.4395 -0.0001 -0.1175 -0.0067
                                        0.8905 -0.0110  0.0000  0.0000
  2. (1.93778) BD ( 2) C 1- N 2      
               ( 39.14%)   0.6256* C 1 s( 36.80%)p 1.72( 63.20%)
                                       -0.0004 -0.6055 -0.0371 -0.7047 -0.0632
                                        0.3594 -0.0471  0.0000  0.0000
               ( 60.86%)   0.7801* N 2 s( 19.33%)p 4.17( 80.67%)
                                       -0.0001 -0.4396  0.0011  0.8364 -0.0016
                                        0.3271 -0.0137  0.0000  0.0000
  3. (1.98365) BD ( 1) C 1- H 4      
               ( 61.02%)   0.7811* C 1 s( 31.10%)p 2.22( 68.90%)
                                        0.0001  0.5577  0.0006 -0.3480  0.0095
                                        0.2603  0.0094  0.7070 -0.0103
               ( 38.98%)   0.6244* H 4 s(100.00%)
                                        1.0000  0.0008
  4. (1.98365) BD ( 1) C 1- H 5      
               ( 61.02%)   0.7811* C 1 s( 31.10%)p 2.22( 68.90%)
                                        0.0001  0.5577  0.0006 -0.3480  0.0095
                                        0.2603  0.0094 -0.7070  0.0103
               ( 38.98%)   0.6244* H 5 s(100.00%)
                                        1.0000  0.0008
  5. (1.99491) BD ( 1) N 2- H 6      
               ( 68.46%)   0.8274* N 2 s( 30.67%)p 2.26( 69.33%)
                                        0.0000  0.5538  0.0005  0.3785  0.0165
                                       -0.2232  0.0044 -0.7070 -0.0093
               ( 31.54%)   0.5616* H 6 s(100.00%)
                                        1.0000  0.0031
  6. (1.99491) BD ( 1) N 2- H 7      
               ( 68.46%)   0.8274* N 2 s( 30.67%)p 2.26( 69.33%)
                                        0.0000  0.5538  0.0005  0.3785  0.0165
                                       -0.2232  0.0044  0.7070  0.0093
               ( 31.54%)   0.5616* H 7 s(100.00%)
                                        1.0000  0.0031
  7. (1.99900) CR ( 1) C 1             s(100.00%)p 0.00(  0.00%)
                                        1.0000 -0.0003  0.0000 -0.0001  0.0000
                                        0.0002  0.0000  0.0000  0.0000
  8. (1.99953) CR ( 1) N 2             s(100.00%)p 0.00(  0.00%)
                                        1.0000 -0.0001  0.0000  0.0001  0.0000
                                        0.0000  0.0000  0.0000  0.0000
  9. (0.81453) LP ( 1) H 3             s(100.00%)
                                        1.0000  0.0000
 10. (0.01893) RY*( 1) C 1             s( 10.61%)p 8.42( 89.39%)
                                        0.0000 -0.0737  0.3173 -0.0090  0.7223
                                        0.0971  0.6021  0.0000  0.0000
 11. (0.00034) RY*( 2) C 1             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0146  0.9999
 12. (0.00025) RY*( 3) C 1             s( 57.37%)p 0.74( 42.63%)
                                        0.0000 -0.0012  0.7575 -0.0176  0.1886
                                       -0.0071 -0.6248  0.0000  0.0000
 13. (0.00002) RY*( 4) C 1             s( 32.38%)p 2.09( 67.62%)
 14. (0.00117) RY*( 1) N 2             s(  1.48%)p66.74( 98.52%)
                                        0.0000 -0.0067  0.1213  0.0062  0.0380
                                        0.0166  0.9917  0.0000  0.0000
 15. (0.00044) RY*( 2) N 2             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000 -0.0132  0.9999
 16. (0.00038) RY*( 3) N 2             s( 33.41%)p 1.99( 66.59%)
                                        0.0000  0.0133  0.5779  0.0087 -0.8150
                                       -0.0120 -0.0392  0.0000  0.0000
 17. (0.00002) RY*( 4) N 2             s( 65.14%)p 0.54( 34.86%)
 18. (0.00177) RY*( 1) H 3             s(100.00%)
                                        0.0000  1.0000
 19. (0.00096) RY*( 1) H 4             s(100.00%)
                                       -0.0008  1.0000
 20. (0.00096) RY*( 1) H 5             s(100.00%)
                                       -0.0008  1.0000
 21. (0.00122) RY*( 1) H 6             s(100.00%)
                                       -0.0031  1.0000
 22. (0.00122) RY*( 1) H 7             s(100.00%)
                                       -0.0031  1.0000
 23. (1.02290) BD*( 1) C 1- N 2      
               ( 92.34%)   0.9609* C 1 s(  0.63%)p99.99( 99.37%)
                                       -0.0001 -0.0770 -0.0186  0.5107 -0.0551
                                        0.8520 -0.0632  0.0000  0.0000
               (  7.66%)  -0.2768* N 2 s( 19.31%)p 4.18( 80.69%)
                                        0.0000  0.4395 -0.0001 -0.1175 -0.0067
                                        0.8905 -0.0110  0.0000  0.0000
 24. (0.22583) BD*( 2) C 1- N 2      
               ( 60.86%)   0.7801* C 1 s( 36.80%)p 1.72( 63.20%)
                                       -0.0004 -0.6055 -0.0371 -0.7047 -0.0632
                                        0.3594 -0.0471  0.0000  0.0000
               ( 39.14%)  -0.6256* N 2 s( 19.33%)p 4.17( 80.67%)
                                       -0.0001 -0.4396  0.0011  0.8364 -0.0016
                                        0.3271 -0.0137  0.0000  0.0000
 25. (0.01415) BD*( 1) C 1- H 4      
               ( 38.98%)   0.6244* C 1 s( 31.10%)p 2.22( 68.90%)
                                       -0.0001 -0.5577 -0.0006  0.3480 -0.0095
                                       -0.2603 -0.0094 -0.7070  0.0103
               ( 61.02%)  -0.7811* H 4 s(100.00%)
                                       -1.0000 -0.0008
 26. (0.01415) BD*( 1) C 1- H 5      
               ( 38.98%)   0.6244* C 1 s( 31.10%)p 2.22( 68.90%)
                                       -0.0001 -0.5577 -0.0006  0.3480 -0.0095
                                       -0.2603 -0.0094  0.7070 -0.0103
               ( 61.02%)  -0.7811* H 5 s(100.00%)
                                       -1.0000 -0.0008
 27. (0.01394) BD*( 1) N 2- H 6      
               ( 31.54%)   0.5616* N 2 s( 30.67%)p 2.26( 69.33%)
                                        0.0000 -0.5538 -0.0005 -0.3785 -0.0165
                                        0.2232 -0.0044  0.7070  0.0093
               ( 68.46%)  -0.8274* H 6 s(100.00%)
                                       -1.0000 -0.0031
 28. (0.01394) BD*( 1) N 2- H 7      
               ( 31.54%)   0.5616* N 2 s( 30.67%)p 2.26( 69.33%)
                                        0.0000 -0.5538 -0.0005 -0.3785 -0.0165
                                        0.2232 -0.0044 -0.7070 -0.0093
               ( 68.46%)  -0.8274* H 7 s(100.00%)
                                       -1.0000 -0.0031
.ED

.HR<<3//+1//5//85>>
 #T
.LM5
.RM85

.LJ
\@seg
.FJ
 
.LM10
.RM80
.HR<<3//+1//5//85>>
 #N

\np One can see that the $CHOOSE resonance structure is significantly
inferior to the principal resonance structure 
found by the default NBO search in 
Section A.3.  About 1.333e, or 7.4% of the electron density,
is found in non-Lewis NBOs of 
the $CHOOSE structure (compared to 0.05e, or 0.3%, for
the principal structure).  Particularly defective is the hydride
`lone pair' (NBO 9), which has less than half the 
expected occupancy (0.81453e).  The C-N \pi  bond (NBO 1) is seen
to be more than 92% polarized toward N, indicative of essential
lone pair character.  

\np Note that structural elements shared by the two resonance
structures (e.g., the two N-H bonds, which are common to
both structures) need not have identical
forms, since each detail of the NBOs 
is optimized with respect to the overall structure.
.CM-----------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS ($DEL)//3//10>>
.RL55
#IB.6.10 NBO Energetic Analysis ($DEL Keylist)#N

\np The NBO energetic analysis with deletions ($DEL keylist) will be
illustrated with two simple examples for RHF/3-21G methylamine
(Section A.3).

\np The first example is the ``NOSTAR'' option (type 4,
Section B.5), requesting deletion
of all non-Lewis orbitals, and hence leading to the energy of the
idealized natural Lewis structure.  The $DEL keylist in this case is
 #T
     $DEL  NOSTAR  $END

#NThis leads to the output shown below:
.DF\@seg =
NOSTAR: Delete all Rydberg/antibond NBOs
Deletion of the following orbitals from the NBO Fock matrix:
  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28

Occupations of bond orbitals:

      Orbital                   No deletions   This deletion   Change
------------------------------------------------------------------------------
  1. BD ( 1) C 1- N 2               1.99858        2.00000    0.00142
  2. BD ( 1) C 1- H 3               1.99860        2.00000    0.00140
  3. BD ( 1) C 1- H 4               1.99399        2.00000    0.00601
  4. BD ( 1) C 1- H 5               1.99399        2.00000    0.00601
  5. BD ( 1) N 2- H 6               1.99442        2.00000    0.00558
  6. BD ( 1) N 2- H 7               1.99442        2.00000    0.00558
  7. CR ( 1) C 1                    1.99900        2.00000    0.00100
  8. CR ( 1) N 2                    1.99953        2.00000    0.00047
  9. LP ( 1) N 2                    1.97795        2.00000    0.02205
 10. RY*( 1) C 1                    0.00105        0.00000   -0.00105
 11. RY*( 2) C 1                    0.00034        0.00000   -0.00034
 12. RY*( 3) C 1                    0.00022        0.00000   -0.00022
 13. RY*( 4) C 1                    0.00002        0.00000   -0.00002
 14. RY*( 1) N 2                    0.00116        0.00000   -0.00116
 15. RY*( 2) N 2                    0.00044        0.00000   -0.00044
 16. RY*( 3) N 2                    0.00038        0.00000   -0.00038
 17. RY*( 4) N 2                    0.00002        0.00000   -0.00002
 18. RY*( 1) H 3                    0.00178        0.00000   -0.00178
 19. RY*( 1) H 4                    0.00096        0.00000   -0.00096
 20. RY*( 1) H 5                    0.00096        0.00000   -0.00096
 21. RY*( 1) H 6                    0.00122        0.00000   -0.00122
 22. RY*( 1) H 7                    0.00122        0.00000   -0.00122
 23. BD*( 1) C 1- N 2               0.00016        0.00000   -0.00016
 24. BD*( 1) C 1- H 3               0.01569        0.00000   -0.01569
 25. BD*( 1) C 1- H 4               0.00769        0.00000   -0.00769
 26. BD*( 1) C 1- H 5               0.00769        0.00000   -0.00769
 27. BD*( 1) N 2- H 6               0.00426        0.00000   -0.00426
 28. BD*( 1) N 2- H 7               0.00426        0.00000   -0.00426

NEXT STEP:  Evaluate the energy of the new density matrix
            that has been constructed from the deleted NBO
            Fock matrix by doing one SCF cycle.

------------------------------------------------------------------------------
  Energy of deletion :        -94.618081014
    Total SCF energy :        -94.679444944
                         -------------------
       Energy change :          0.061364 a.u.,          38.506 kcal/mol
.ED

.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

.LJ
\@seg
.FJ

.HR<<3//+1//5//85>>
.LM10
.RM80
 #N

\np In the output above, the NBO program first enumerates the 19 NBOs
to be deleted by the ``NOSTAR'' request, then gives the complete list
of NBOs with their occupancies before (``no deletions'') and after 
(``this deletion'') deletions, with the
net change for each.  For this NOSTAR deletion, each of the
nine Lewis NBOs (1-9) necessarily gets 2.0000 electrons, and each
of the non-Lewis NBOs (10-28) gets occupancy 0.0000.  The program
than reports the energy (\minus 94.618081 a.u.) obtained from a single
pass through the SCF evaluator with the modified density matrix.  In
this case, deletion of the 19 non-Lewis orbitals led to an energy
change of only 0.061364 a.u. (38.5 kcal/mol), less than 0.07% of the
total energy.

\np The next example is a more selective set of deletions between
`chemical fragments' (type 9), selected by the $DEL keylist input
shown below:
 #T
     $DEL 
        ZERO  2  ATOM BLOCKS
                 4  BY  3
                    1  3  4  5
                    2  6  7
                 3  BY  4
                    2  6  7
                    1  3  4  5
     $END

#NThis specifies removal of all delocalizing interactions from
Lewis NBOs of the methyl fragment (atoms 1,3,4,5) into non-Lewis
NBOs of the amine fragment (atoms 2,6,7), or vice versa.  The
NBO output for this example is shown below:
.DF\@seg =
Zero delocalization from NBOs localized on atoms:
   1   3   4   5
to NBOs localized on atoms:
   2   6   7
    (NBOs in common to the two groups of atoms left out)
Zero delocalization from NBOs localized on atoms:
   2   6   7
to NBOs localized on atoms:
   1   3   4   5
    (NBOs in common to the two groups of atoms left out)
Deletion of the NBO Fock matrix elements between orbitals:
   2   3   4   7
and orbitals:
  14  15  16  17  21  22  27  28
Deletion of the NBO Fock matrix elements between orbitals:
   5   6   8   9
and orbitals:
  10  11  12  13  18  19  20  24  25  26

Occupations of bond orbitals:

      Orbital                   No deletions   This deletion   Change
------------------------------------------------------------------------------
  1. BD ( 1) C 1- N 2               1.99858        1.99860    0.00002
  2. BD ( 1) C 1- H 3               1.99860        1.99937    0.00077
  3. BD ( 1) C 1- H 4               1.99399        1.99911    0.00512
  4. BD ( 1) C 1- H 5               1.99399        1.99911    0.00512
  5. BD ( 1) N 2- H 6               1.99442        1.99979    0.00537
  6. BD ( 1) N 2- H 7               1.99442        1.99979    0.00537
  7. CR ( 1) C 1                    1.99900        1.99919    0.00019
  8. CR ( 1) N 2                    1.99953        1.99974    0.00021
  9. LP ( 1) N 2                    1.97795        1.99996    0.02201
 10. RY*( 1) C 1                    0.00105        0.00016   -0.00090
 11. RY*( 2) C 1                    0.00034        0.00000   -0.00033
 12. RY*( 3) C 1                    0.00022        0.00002   -0.00020
 13. RY*( 4) C 1                    0.00002        0.00002    0.00000
 14. RY*( 1) N 2                    0.00116        0.00004   -0.00112
 15. RY*( 2) N 2                    0.00044        0.00000   -0.00044
 16. RY*( 3) N 2                    0.00038        0.00003   -0.00035
 17. RY*( 4) N 2                    0.00002        0.00001   -0.00001
 18. RY*( 1) H 3                    0.00178        0.00088   -0.00090
 19. RY*( 1) H 4                    0.00096        0.00057   -0.00038
 20. RY*( 1) H 5                    0.00096        0.00057   -0.00038
 21. RY*( 1) H 6                    0.00122        0.00057   -0.00065
 22. RY*( 1) H 7                    0.00122        0.00057   -0.00065
 23. BD*( 1) C 1- N 2               0.00016        0.00034    0.00018
 24. BD*( 1) C 1- H 3               0.01569        0.00027   -0.01542
 25. BD*( 1) C 1- H 4               0.00769        0.00055   -0.00714
 26. BD*( 1) C 1- H 5               0.00769        0.00055   -0.00714
 27. BD*( 1) N 2- H 6               0.00426        0.00009   -0.00417
 28. BD*( 1) N 2- H 7               0.00426        0.00009   -0.00417

NEXT STEP:  Evaluate the energy of the new density matrix
            that has been constructed from the deleted NBO
            Fock matrix by doing one SCF cycle.

------------------------------------------------------------------------------
  Energy of deletion :        -94.635029232
    Total SCF energy :        -94.679444944
                         -------------------
       Energy change :          0.044416 a.u.,          27.871 kcal/mol
.ED

.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

.LJ
\@seg
.FJ

.HR<<3//+1//5//85>>
.LM10
.RM80
 #N

\np The output first lists the various orbitals and Fock matrix
elements affected by this deletion, then the `before' and `after'
occupancies and net changes for each NBO.  In this case, one can
see that the principal effect of the deletion was increased occupancy
(+0.022) of the nitrogen lone pair, NBO 9, and depleted occupancy
(\minus 0.015) of the antiperiplanar \sigma *#<#dC#d1#uH#d3#u#u
antibond, NBO 24, with somewhat lesser depletion (\minus 0.007)
of the other two C-H antibonds.  The total energy change (loss of
delocalization energy) associated with this deletion 
was 27.9 kcal/mol.

\np To further pinpoint the source of this delocalization, one could
do more selective deletions of individual orbitals or Fock
matrix elements.  For example, if one uses 
deletion type 2 (deletion of a single
Fock matrix element, Section B.5.2) to delete the 
(9,24) element associated with the
#In#N#dN#u \rarr  \sigma *#<#dC#d1#uH#d3#u#u interaction, one finds
a deletion energy of 7.06 kcal/mol associated with this 
interaction alone.  [This value may be compared with the simple second-order
perturbative estimate (8.13 kcal/mol) of the
#In#N#dN#u \rarr  \sigma *#<#dC#d1#uH#d3#u#u (9\rarr 24) interaction
that was noted in Section A.3.5.]
.CM------------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (Open-Shell)//3//10>>
.RL55
#IB.6.11 Open-Shell UHF Output: Methyl Radical#N

\np Open-shell NBO output will be illustrated with the simple
example of the planar methyl radical (CH#d3#u), treated at the UHF/6-31G*
level (#IR#N#dCH#u = 1.0736\thsp \angstrom ).  In 
the open-shell case, one obtains
two separate NPA and NBO listings, one for the \alpha  and one for 
the \beta  spin set, corresponding to the ``different Lewis structures
for different spins'' description.  A portion of the NBO output for
the \alpha  spin manifold is reproduced below:
.DF\@seg =
NATURAL BOND ORBITAL ANALYSIS, alpha spin orbitals:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    0.90     4.99903   0.00097      1   3   0   1     0      0    0.00
-----------------------------------------------------------------------------

Structure accepted: No low occupancy Lewis orbitals

--------------------------------------------------------
  Core                      0.99984 ( 99.984% of   1)
  Valence Lewis             3.99919 ( 99.980% of   4)
 ==================       ============================
  Total Lewis               4.99903 ( 99.981% of   5)
 -----------------------------------------------------
  Valence non-Lewis         0.00081 (  0.016% of   5)
  Rydberg non-Lewis         0.00016 (  0.003% of   5)
 ==================       ============================
  Total non-Lewis           0.00097 (  0.019% of   5)
--------------------------------------------------------


    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (0.99973) BD ( 1) C 1- H 2      
               ( 61.14%)   0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
                                        0.0000  0.5772 -0.0070  0.0000 -0.4076
                                       -0.0110  0.7060  0.0191  0.0000  0.0000
                                       -0.0338  0.0000  0.0000 -0.0195 -0.0090
               ( 38.86%)   0.6233* H 2 s(100.00%)
                                        1.0000  0.0080
  2. (0.99973) BD ( 1) C 1- H 3      
               ( 61.14%)   0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
                                        0.0000  0.5772 -0.0070  0.0000 -0.4076
                                       -0.0110 -0.7060 -0.0191  0.0000  0.0000
                                        0.0338  0.0000  0.0000 -0.0195 -0.0090
               ( 38.86%)   0.6233* H 3 s(100.00%)
                                        1.0000  0.0080
  3. (0.99973) BD ( 1) C 1- H 4      
               ( 61.14%)   0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
                                        0.0000  0.5772 -0.0070  0.0000  0.8153
                                        0.0221  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0391 -0.0090
               ( 38.86%)   0.6233* H 4 s(100.00%)
                                        1.0000  0.0080
  4. (0.99984) CR ( 1) C 1             s(100.00%)
                                        1.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
  5. (1.00000) LP ( 1) C 1             s(  0.00%)p 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.9978 -0.0668
                                        0.0000  0.0000  0.0000  0.0000  0.0000
  6. (0.00000) RY*( 1) C 1             s(100.00%)p 0.00(  0.00%)d 0.00(  0.00%)
  7. (0.00000) RY*( 2) C 1             s(100.00%)
  8. (0.00000) RY*( 3) C 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
  9. (0.00000) RY*( 4) C 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
 10. (0.00000) RY*( 5) C 1             s(  0.00%)p 1.00(100.00%)
 11. (0.00000) RY*( 6) C 1             s(  0.00%)p 1.00(  0.23%)d99.99( 99.77%)
 12. (0.00000) RY*( 7) C 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 13. (0.00000) RY*( 8) C 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 14. (0.00000) RY*( 9) C 1             s(  0.00%)p 1.00(  0.23%)d99.99( 99.77%)
 15. (0.00000) RY*(10) C 1             s(  0.02%)p 0.00(  0.00%)d99.99( 99.98%)
 16. (0.00005) RY*( 1) H 2             s(100.00%)
 17. (0.00005) RY*( 1) H 3             s(100.00%)
 18. (0.00005) RY*( 1) H 4             s(100.00%)
 19. (0.00027) BD*( 1) C 1- H 2      
               ( 38.86%)   0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
                                        0.0000 -0.5772  0.0070  0.0000  0.4076
                                        0.0110 -0.7060 -0.0191  0.0000  0.0000
                                        0.0338  0.0000  0.0000  0.0195  0.0090
               ( 61.14%)  -0.7819* H 2 s(100.00%)
                                       -1.0000 -0.0080
 20. (0.00027) BD*( 1) C 1- H 3      
               ( 38.86%)   0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
                                        0.0000 -0.5772  0.0070  0.0000  0.4076
                                        0.0110  0.7060  0.0191  0.0000  0.0000
                                       -0.0338  0.0000  0.0000  0.0195  0.0090
               ( 61.14%)  -0.7819* H 3 s(100.00%)
                                       -1.0000 -0.0080
 21. (0.00027) BD*( 1) C 1- H 4      
               ( 38.86%)   0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
                                        0.0000 -0.5772  0.0070  0.0000 -0.8153
                                       -0.0221  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000 -0.0391  0.0090
               ( 61.14%)  -0.7819* H 4 s(100.00%)
                                       -1.0000 -0.0080
.ED

.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

.LJ
\@seg
.FJ

.HR<<3//+1//5//85>>
.LM10
.RM80
 #N

\np As can be seen in the output, the NBO spin-orbital 
occupancy threshold was set at 0.90 (rather than 1.90), and the
occupancies of \alpha  Lewis spin-NBOs (1-5) are about 1.0000, but
other aspects of the output are familiar.  Note the slight admixture
of #Id#N-character (0.16%) in the \sigma #dCH#u bond hybrids 
(NBOs 1-3), whereas the out-of-plane radical non-bonded orbital (NBO 5) has
pure #Ip#N-character.

\np The NBO output for the \beta  (`ionized') spin set then follows:
.DF\@seg =
NATURAL BOND ORBITAL ANALYSIS, beta spin orbitals:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    0.90     3.99981   0.00019      1   3   0   0     0      0    0.00
-----------------------------------------------------------------------------

Structure accepted: No low occupancy Lewis orbitals

--------------------------------------------------------
  Core                      0.99985 ( 99.985% of   1)
  Valence Lewis             2.99996 ( 99.999% of   3)
 ==================       ============================
  Total Lewis               3.99981 ( 99.995% of   4)
 -----------------------------------------------------
  Valence non-Lewis         0.00002 (  0.000% of   4)
  Rydberg non-Lewis         0.00017 (  0.004% of   4)
 ==================       ============================
  Total non-Lewis           0.00019 (  0.005% of   4)
--------------------------------------------------------


    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (0.99999) BD ( 1) C 1- H 2      
               ( 55.80%)   0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
                                        0.0000  0.5762  0.0080  0.0000 -0.4076
                                       -0.0125  0.7059  0.0217  0.0000  0.0000
                                       -0.0345  0.0000  0.0000 -0.0199 -0.0350
               ( 44.20%)   0.6649* H 2 s(100.00%)
                                        1.0000 -0.0069
  2. (0.99999) BD ( 1) C 1- H 3      
               ( 55.80%)   0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
                                        0.0000  0.5762  0.0080  0.0000 -0.4076
                                       -0.0125 -0.7059 -0.0217  0.0000  0.0000
                                        0.0345  0.0000  0.0000 -0.0199 -0.0350
               ( 44.20%)   0.6649* H 3 s(100.00%)
                                        1.0000 -0.0069
  3. (0.99999) BD ( 1) C 1- H 4      
               ( 55.80%)   0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
                                        0.0000  0.5762  0.0080  0.0000  0.8151
                                        0.0251  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0399 -0.0350
               ( 44.20%)   0.6649* H 4 s(100.00%)
                                        1.0000 -0.0069
  4. (0.99985) CR ( 1) C 1             s(100.00%)
                                        1.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
  5. (0.00002) LP*( 1) C 1             s( 10.35%)p 0.00(  0.00%)d 8.66( 89.65%)
  6. (0.00000) RY*( 1) C 1             s( 98.99%)p 0.00(  0.00%)d 0.01(  1.01%)
  7. (0.00000) RY*( 2) C 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
  8. (0.00000) RY*( 3) C 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
  9. (0.00000) RY*( 4) C 1             s(  0.00%)p 1.00(100.00%)
 10. (0.00000) RY*( 5) C 1             s(  0.00%)p 1.00(100.00%)
 11. (0.00000) RY*( 6) C 1             s(  0.00%)p 1.00(  0.24%)d99.99( 99.76%)
 12. (0.00000) RY*( 7) C 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 13. (0.00000) RY*( 8) C 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 14. (0.00000) RY*( 9) C 1             s(  0.00%)p 1.00(  0.24%)d99.99( 99.76%)
 15. (0.00000) RY*(10) C 1             s( 91.02%)p 0.00(  0.00%)d 0.10(  8.98%)
 16. (0.00006) RY*( 1) H 2             s(100.00%)
 17. (0.00006) RY*( 1) H 3             s(100.00%)
 18. (0.00006) RY*( 1) H 4             s(100.00%)
 19. (0.00000) BD*( 1) C 1- H 2      
               ( 44.20%)   0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
               ( 55.80%)  -0.7470* H 2 s(100.00%)
 20. (0.00000) BD*( 1) C 1- H 3      
               ( 44.20%)   0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
               ( 55.80%)  -0.7470* H 3 s(100.00%)
 21. (0.00000) BD*( 1) C 1- H 4      
               ( 44.20%)   0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
               ( 55.80%)  -0.7470* H 4 s(100.00%)
.ED

.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

.LJ
\@seg
.FJ

.HR<<3//+1//5//85>>
.LM10
.RM80
 #N

\np The principal difference to be seen is that the radical
orbital (NBO 5) is essentially empty in this spin set, and
the polarization of the \sigma #dCH#u bonds is somewhat altered
(about 55.8% on the C atom in the \beta  set set, 
#Ivs.#N 61.1% in the \alpha  set).  [In other cases, the
\alpha  and \beta  NBO Lewis structures might differ even
in the number and location of 1-c (non-bonding) and 2-c (bond)
structural elements.]  Note that the overall quality of the open-shell
natural Lewis structure description (> 99.9%) is
comparable to that of ordinary closed-shell molecules, and the
interpretation of the NBO output follows
familiar lines.

.LM+10
.RM-10
.BX<<3//18//72//+1//+11>>

.CJ
#-#BWARNING#N#+
.FJ

You should not attempt to analyze an open-shell wavefunction with an
ESS method that produces only the ``spinless'' (spin-averaged) density
matrix, rather than the separate density matrices for \alpha  
and \beta  spin.  Although NAOs and their total populations are
calculated correctly from the spinless density matrix, NBOs
and NLMOs are not.  NBO analysis of an open-shell 
spinless density matrix is a fundamental misuse
of the program.
.LM10
.RM80
.CM------------------------------------------------------------------
.HF<<B.6 NBO KEYLIST ILLUSTRATIONS (Effective Core Potential)//3//10>>
.RL55
#IB.6.12 Effective Core Potential: Cu#d2#u Dimer#N

\np To illustrate some of the variations of NBO output associated
with use of effective core potentials (ECP) and inclusion of
#Id#N orbitals, we use the example of the copper dimer Cu#d2#u
(#IR#N = 2.2195\thsp \angstrom ),
treated at the RHF level with a Hay-Wadt ECP and valence DZ
basis (RHF/LANL1DZ), carried out with
the GAUSSIAN-88 system.  (The wavefunction returned by GAUSSIAN-88
in this case corresponds
to an excited state configuration of Cu#d2#u.)  Since the 
NBO program communicates directly with
the ESS program for details
about the ECP, no special keywords are necessary.

\np Use of an ECP shows up most directly in the NPA portion
of the output, shown below:
.DF\@seg =
NATURAL POPULATIONS:  Natural atomic orbital occupancies 
                                                         
 NAO Atom #  lang   Type(AO)    Occupancy      Energy    
---------------------------------------------------------
  1   Cu  1  s      Val( 4s)     0.94240      -0.26321
  2   Cu  1  s      Ryd( 5s)     0.00019       0.92165
  3   Cu  1  px     Ryd( 4p)     0.99604      -0.06989
  4   Cu  1  px     Ryd( 5p)     0.00001       0.09916
  5   Cu  1  py     Ryd( 4p)     0.99604      -0.06989
  6   Cu  1  py     Ryd( 5p)     0.00001       0.09916
  7   Cu  1  pz     Ryd( 5p)     0.05481       1.09062
  8   Cu  1  pz     Ryd( 4p)     0.00062       0.52821
  9   Cu  1  dxy    Val( 3d)     0.00000      -0.36077
 10   Cu  1  dxy    Ryd( 4d)     0.00000       0.72280
 11   Cu  1  dxz    Val( 3d)     1.99997      -1.29316
 12   Cu  1  dxz    Ryd( 4d)     0.00398       0.75681
 13   Cu  1  dyz    Val( 3d)     1.99997      -1.29316
 14   Cu  1  dyz    Ryd( 4d)     0.00398       0.75681
 15   Cu  1  dx2y2  Val( 3d)     1.99939      -1.38791
 16   Cu  1  dx2y2  Ryd( 4d)     0.00061       0.67825
 17   Cu  1  dz2    Val( 3d)     1.99890      -1.26114
 18   Cu  1  dz2    Ryd( 4d)     0.00308       1.16392

 19   Cu  2  s      Val( 4s)     0.94240      -0.26321
 20   Cu  2  s      Ryd( 5s)     0.00019       0.92165
 21   Cu  2  px     Ryd( 4p)     0.99604      -0.06989
 22   Cu  2  px     Ryd( 5p)     0.00001       0.09916
 23   Cu  2  py     Ryd( 4p)     0.99604      -0.06989
 24   Cu  2  py     Ryd( 5p)     0.00001       0.09916
 25   Cu  2  pz     Ryd( 5p)     0.05481       1.09062
 26   Cu  2  pz     Ryd( 4p)     0.00062       0.52821
 27   Cu  2  dxy    Val( 3d)     0.00000      -0.36077
 28   Cu  2  dxy    Ryd( 4d)     0.00000       0.72280
 29   Cu  2  dxz    Val( 3d)     1.99997      -1.29316
 30   Cu  2  dxz    Ryd( 4d)     0.00398       0.75681
 31   Cu  2  dyz    Val( 3d)     1.99997      -1.29316
 32   Cu  2  dyz    Ryd( 4d)     0.00398       0.75681
 33   Cu  2  dx2y2  Val( 3d)     1.99939      -1.38791
 34   Cu  2  dx2y2  Ryd( 4d)     0.00061       0.67825
 35   Cu  2  dz2    Val( 3d)     1.99890      -1.26114
 36   Cu  2  dz2    Ryd( 4d)     0.00308       1.16392

[ 36 electrons found in the effective core potential]

WARNING:  Population inversion found on atom Cu 1
          Population inversion found on atom Cu 2


Summary of Natural Population Analysis:                  
                                                         
                                      Natural Population 
              Natural   -----------------------------------------------
   Atom #     Charge        Core      Valence    Rydberg      Total
-----------------------------------------------------------------------
    Cu  1    0.00000     18.00000     8.94064    2.05936    29.00000
    Cu  2    0.00000     18.00000     8.94064    2.05936    29.00000
=======================================================================
  * Total *  0.00000     36.00000    17.88127    4.11873    58.00000

                                Natural Population      
--------------------------------------------------------
  Effective Core            36.00000
  Valence                   17.88127 ( 81.2785% of  22)
  Natural Minimal Basis     53.88127 ( 92.8987% of  58)
  Natural Rydberg Basis      4.11873 (  7.1013% of  58)
--------------------------------------------------------

   Atom #          Natural Electron Configuration
----------------------------------------------------------------------------
    Cu  1      [core]4s( 0.94)3d( 8.00)4p( 1.99)4d( 0.01)5p( 0.05)
    Cu  2      [core]4s( 0.94)3d( 8.00)4p( 1.99)4d( 0.01)5p( 0.05)
.ED

.HR<<3//+1//5//85>>
 #T
.LM5
.RM85

.RS#~
.LJ
\@seg
.FJ
.RS~#
 
.LM10
.RM80
.HR<<3//+1//5//85>>
 #N

\np As noted below the first NPA table, 36 electrons were found
in the ECP, so the labels for NAOs in the table begin with the
designations 4#Is#N, 5#Is#N, etc. of the presumed extra-core
electrons.  The ECP electrons are duly entered in the NPA tables
(labelled as ``effective core'' in the NPA summary table)
as part of the total Lewis occupancy,
and are taken into proper account in assigning atomic charges.  The
NPA output in this case includes a ``population inversion'' message to
warn that one or more NAO occupancies are not ordered in accordance
with the energy order [e.g., the 3#Id#N#dxy#u orbital (NAO 9)
is unoccupied in this excited configuration, although
its energy lies below the occupied 4#Is#N, 4#Ip#N#dy#u, 4#Ip#N#dz#u
levels.]

.RL20
\np The main ECP effect in the NBO portion of the output is the
omission of core NBOs, as illustrated below:
.DF\@seg =
NATURAL BOND ORBITAL ANALYSIS:

                      Occupancies       Lewis Structure    Low   High
          Occ.    -------------------  -----------------   occ   occ
 Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
=============================================================================
  1(1)    1.90    57.99970   0.00030      0   3   0   8     0      0    0.00
-----------------------------------------------------------------------------

Structure accepted: No low occupancy Lewis orbitals

--------------------------------------------------------
  Effective Core           36.00000
  Valence Lewis            21.99970 ( 99.999% of  22)
 ==================       ============================
  Total Lewis              57.99970 ( 99.999% of  58)
 -----------------------------------------------------
  Valence non-Lewis         0.00000 (  0.000% of  58)
  Rydberg non-Lewis         0.00030 (  0.001% of  58)
 ==================       ============================
  Total non-Lewis           0.00030 (  0.001% of  58)
--------------------------------------------------------


    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
-------------------------------------------------------------------------------
  1. (2.00000) BD ( 1)Cu 1-Cu 2      
               ( 50.00%)   0.7071*Cu 1 s( 94.13%)p 0.06(  5.54%)d 0.00(  0.33%)
                                        0.9702 -0.0003  0.0000  0.0000  0.0000
                                        0.0000 -0.2340  0.0245  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0225  0.0530
               ( 50.00%)   0.7071*Cu 2 s( 94.13%)p 0.06(  5.54%)d 0.00(  0.33%)
                                        0.9702 -0.0003  0.0000  0.0000  0.0000
                                        0.0000  0.2340 -0.0245  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0225  0.0530
  2. (2.00000) BD ( 2)Cu 1-Cu 2      
               ( 50.00%)   0.7071*Cu 1 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
                                        0.0000  0.0000  0.9980  0.0029  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                       -0.0035 -0.0630  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000
               ( 50.00%)   0.7071*Cu 2 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
                                        0.0000  0.0000  0.9980  0.0029  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0035  0.0630  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000
  3. (2.00000) BD ( 3)Cu 1-Cu 2      
               ( 50.00%)   0.7071*Cu 1 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
                                        0.0000  0.0000  0.0000  0.0000  0.9980
                                        0.0029  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000 -0.0035 -0.0630  0.0000
                                        0.0000  0.0000  0.0000
               ( 50.00%)   0.7071*Cu 2 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
                                        0.0000  0.0000  0.0000  0.0000  0.9980
                                        0.0029  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0035  0.0630  0.0000
                                        0.0000  0.0000  0.0000
  4. (2.00000) LP ( 1)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.9998
                                       -0.0175  0.0000  0.0000
  5. (2.00000) LP ( 2)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0037
                                       -0.0010  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  1.0000  0.0026  0.0000
                                        0.0000  0.0000  0.0000
  6. (2.00000) LP ( 3)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
                                        0.0000  0.0000  0.0037 -0.0010  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        1.0000  0.0026  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000
  7. (1.99985) LP ( 4)Cu 1             s(  0.06%)p 0.02(  0.00%)d99.99( 99.94%)
                                        0.0231  0.0070  0.0000  0.0000  0.0000
                                        0.0000 -0.0030 -0.0008  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000 -0.9996 -0.0115
  8. (2.00000) LP ( 1)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.9998
                                       -0.0175  0.0000  0.0000
  9. (2.00000) LP ( 2)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
                                        0.0000  0.0000  0.0000  0.0000 -0.0037
                                        0.0010  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0000  1.0000  0.0026  0.0000
                                        0.0000  0.0000  0.0000
 10. (2.00000) LP ( 3)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
                                        0.0000  0.0000 -0.0037  0.0010  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        1.0000  0.0026  0.0000  0.0000  0.0000
                                        0.0000  0.0000  0.0000
 11. (1.99985) LP ( 4)Cu 2             s(  0.06%)p 0.02(  0.00%)d99.99( 99.94%)
                                        0.0231  0.0070  0.0000  0.0000  0.0000
                                        0.0000  0.0030  0.0008  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000 -0.9996 -0.0115
 12. (0.00015) RY*( 1)Cu 1             s( 63.84%)p 0.51( 32.31%)d 0.06(  3.85%)
                                       -0.1106  0.7913  0.0000  0.0000  0.0000
                                        0.0000 -0.4699  0.3199  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0064 -0.1962
 13. (0.00000) RY*( 2)Cu 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
 14. (0.00000) RY*( 3)Cu 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
 15. (0.00000) RY*( 4)Cu 1             s( 31.12%)p 2.21( 68.87%)d 0.00(  0.00%)
 16. (0.00000) RY*( 5)Cu 1             s(  7.79%)p11.84( 92.21%)d 0.00(  0.00%)
 17. (0.00000) RY*( 6)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 18. (0.00000) RY*( 7)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 19. (0.00000) RY*( 8)Cu 1             s(  0.00%)p 1.00(  0.40%)d99.99( 99.60%)
 20. (0.00000) RY*( 9)Cu 1             s(  0.00%)p 1.00(  0.40%)d99.99( 99.60%)
 21. (0.00000) RY*(10)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 22. (0.00000) RY*(11)Cu 1             s(  3.06%)p 0.35(  1.07%)d31.35( 95.87%)
 23. (0.00015) RY*( 1)Cu 2             s( 63.84%)p 0.51( 32.31%)d 0.06(  3.85%)
                                       -0.1106  0.7913  0.0000  0.0000  0.0000
                                        0.0000  0.4699 -0.3199  0.0000  0.0000
                                        0.0000  0.0000  0.0000  0.0000  0.0000
                                        0.0000  0.0064 -0.1962
 24. (0.00000) RY*( 2)Cu 2             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
 25. (0.00000) RY*( 3)Cu 2             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
 26. (0.00000) RY*( 4)Cu 2             s( 31.12%)p 2.21( 68.87%)d 0.00(  0.00%)
 27. (0.00000) RY*( 5)Cu 2             s(  7.79%)p11.84( 92.21%)d 0.00(  0.00%)
 28. (0.00000) RY*( 6)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 29. (0.00000) RY*( 7)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 30. (0.00000) RY*( 8)Cu 2             s(  0.00%)p 1.00(  0.40%)d99.99( 99.60%)
 31. (0.00000) RY*( 9)Cu 2             s(  0.00%)p 1.00(  0.40%)d99.99( 99.60%)
 32. (0.00000) RY*(10)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
 33. (0.00000) RY*(11)Cu 2             s(  3.06%)p 0.35(  1.07%)d31.35( 95.87%)
 34. (0.00000) BD*( 1)Cu 1-Cu 2      
               ( 50.00%)   0.7071*Cu 1 s( 94.13%)p 0.06(  5.54%)d 0.00(  0.33%)
               ( 50.00%)  -0.7071*Cu 2 s( 94.13%)p 0.06(  5.54%)d 0.00(  0.33%)
 35. (0.00000) BD*( 2)Cu 1-Cu 2      
               ( 50.00%)   0.7071*Cu 1 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
               ( 50.00%)  -0.7071*Cu 2 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
 36. (0.00000) BD*( 3)Cu 1-Cu 2      
               ( 50.00%)   0.7071*Cu 1 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
               ( 50.00%)  -0.7071*Cu 2 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)




Natural Bond Orbitals (Summary):

                                                    Principal Delocalizations
          NBO              Occupancy    Energy      (geminal,vicinal,remote)
===============================================================================
Molecular unit  1  (Cu2)
  1. BD ( 1)Cu 1-Cu 2       2.00000    -0.53276
  2. BD ( 2)Cu 1-Cu 2       2.00000    -0.21503
  3. BD ( 3)Cu 1-Cu 2       2.00000    -0.21503
  4. LP ( 1)Cu 1            2.00000    -1.38854
  5. LP ( 2)Cu 1            2.00000    -1.29317
  6. LP ( 3)Cu 1            2.00000    -1.29317
  7. LP ( 4)Cu 1            1.99985    -1.26133
  8. LP ( 1)Cu 2            2.00000    -1.38854
  9. LP ( 2)Cu 2            2.00000    -1.29317
 10. LP ( 3)Cu 2            2.00000    -1.29317
 11. LP ( 4)Cu 2            1.99985    -1.26133
 12. RY*( 1)Cu 1            0.00015     0.70166
 13. RY*( 2)Cu 1            0.00000     0.09932
 14. RY*( 3)Cu 1            0.00000     0.09932
 15. RY*( 4)Cu 1            0.00000     1.09217
 16. RY*( 5)Cu 1            0.00000     0.44430
 17. RY*( 6)Cu 1            0.00000    -0.36077
 18. RY*( 7)Cu 1            0.00000     0.72280
 19. RY*( 8)Cu 1            0.00000     0.75266
 20. RY*( 9)Cu 1            0.00000     0.75266
 21. RY*(10)Cu 1            0.00000     0.67888
 22. RY*(11)Cu 1            0.00000     1.26372
 23. RY*( 1)Cu 2            0.00015     0.70166
 24. RY*( 2)Cu 2            0.00000     0.09932
 25. RY*( 3)Cu 2            0.00000     0.09932
 26. RY*( 4)Cu 2            0.00000     1.09217
 27. RY*( 5)Cu 2            0.00000     0.44430
 28. RY*( 6)Cu 2            0.00000    -0.36077
 29. RY*( 7)Cu 2            0.00000     0.72280
 30. RY*( 8)Cu 2            0.00000     0.75266
 31. RY*( 9)Cu 2            0.00000     0.75266
 32. RY*(10)Cu 2            0.00000     0.67888
 33. RY*(11)Cu 2            0.00000     1.26372
 34. BD*( 1)Cu 1-Cu 2       0.00000     0.41179
 35. BD*( 2)Cu 1-Cu 2       0.00000     0.08327
 36. BD*( 3)Cu 1-Cu 2       0.00000     0.08327
      -------------------------------
             Total Lewis   57.99970  ( 99.9995%)
       Valence non-Lewis    0.00000  (  0.0000%)
       Rydberg non-Lewis    0.00030  (  0.0005%)
      -------------------------------
           Total unit  1   58.00000  (100.0000%)
          Charge unit  1    0.00000
.ED

.HR<<3//+1//5//85>>
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.LM5
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.LM10
.RM80
.HR<<3//+1//5//85>>
 #N

\np As the output shows, the NBO tables include reference 
to only 11 occupied NBOs, rather than
the 29 that would appear in a full calculation.  Semi-empirical 
methods that neglect core electrons (AMPAC, etc.) are
handled similarly.

\np The output for the Cu#d2#u
example also illustrates some aspects of the inclusion of #Id#N orbitals
in the basis set.  NBOs 4-7 and 8-11 represent the 3#Id#N#u8#d
subshells on each atom, essentially of pure atomic #Id#N
character (except for a small admixture
of #Ip#N character in NBOs 7, 11).  Both
the \sigma #dCuCu#u bond (NBO 1) and the two \pi #dCuCu#u bonds 
(NBOs 2, 3) have very slight admixtures (< 0.4%) of #Id#N 
character.  The remaining orbitals of predominant #Id#N 
character (NBOs 17-22 and 28-33) are of negligible occupancy.  Note
that the abbreviated ``#Isp#u\lambda #dd#u\mu #d#N'' designations
can lead to strange variations among hybrids
of essentially similar character; thus, NBO 20 (#Ip#u1.0#dd#u99.9#d#N),
NBO 21 (#Id#N#u1.0#d), and NBO 22 (#Is#u3.1#dp#u0.4#dd#u31.4#d#N)
are all of nearly pure (> 95%) #Id#N character, the difference in
labelling stemming from 
whether there is sufficient
#Is#N or #Ip#N character (in numerical terms) to express the
hybrid ratios in #Isp#u\lambda #dd#u\mu #d#N form.  Consult 
the percentages of #Is#N-.
#Ip#N-, and #Id#N-character whenever there is doubt about how to
interpret a particular #Isp#u\lambda #dd#u\mu #d#N designation.
.CM------------------------------------------------------------------
.DF\ss =#Is#N
.DF\px =#Ip#N#dx#u
.DF\py =#Ip#N#dy#u
.DF\pz =#Ip#N#dz#u
.HF<<B.7  FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM//3//10>>
.RL55
#BB.7  FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM#N

#IB.7.1  Introduction#N

\np The general NBO program, GENNBO, is a stand-alone program which is not
directly attached to an ESS program.  Rather, information about the
wavefunction is provided to the core NBO routines by a sequential input
file, FILE47, described in this section.

\np Some knowledge of FILE47 is useful even if your NBO program is attached
to an ESS package.  If requested (see the ARCHIVE option, Section B.2.5),
the NBO program writes out FILE47 which summarizes all information pertaining
to the computed electronic wavefunction.  This file can be subsequently
used as input to the GENNBO program (reassigned as LFN 5)
to repeat the analysis of this
wavefunction; simply include the $NBO, $CORE, and $CHOOSE keylists in
FILE47 and execute GENNBO.  You need never recompute the wavefunction to
vary its NBO analysis!  In fact, generating the FILE47 input file is a
useful way to archive a wavefunction for future use or reference.  [Note:
the GENNBO program can not perform the NBO energetic analysis ($DEL keylist)
since this would require access to the formatted one- and two-electron
integrals of the parent ESS package.]

\np If you intend to use the NBO program in conjunction with an ESS package
not supported in this distribution (i.e. for which no custom drivers are
provided), you might consider attaching a routine to your ESS program which
would write the proper form of FILE47 for input into the GENNBO program.
Thus, a two-step process would be required to obtain the NBO analysis of
a wavefunction: (i) the initial calculation of the wavefunction with the
ESS package, writing FILE47; (ii) the NBO analysis using the GENNBO program
with FILE47 as input.  Alternatively, you may decide to attach the NBO program
directly to your ESS package by writing your own driver routines.  See
the Programmer's Guide, Section C.13, for direction.

\np Section B.7.2 describes and illustrates the overall
format of FILE47.  Sections B.7.3-B.7.7 detail the entries of the
keylists and datalists that compose this file.
.RL55
#IB.7.2  Format of the FILE47 Input File#N

\np The FILE47 input file is composed of a set of keylists and datalists, each
list beginning with a ``$'' identifier (e.g. ``$BASIS'') and ending with
``$END'',

#T     $BASIS   entries  $END#N

Individual lists are used to specify basis set information ($BASIS),
density matrix elements ($DENSITY), and so forth.  The order of the
lists within FILE47 is immaterial.  Entries within each datalist are generally
free format, and may be continued on as many lines as desired.  An
exclamation point (!) on any line terminates input from the line, and may
be followed by arbitrary comments.  The $GENNBO keylist and
the $COORD, $BASIS, $DENSITY, and $OVERLAP datalists 
are required, but the other
datalists ($FOCK, $LCAOMO, $CONTRACT, $DIPOLE) or the standard
NBO keylists ($NBO, $CORE, $CHOOSE) are optional, depending on the requested
application.  If the $NBO keylist is not present in FILE47, the default
NBO analysis is performed.

\np The entries of each keylist or datalist may be keywords, numerical matrix
elements, or other parameters of prescribed form.  A sample FILE47 input
file (for the RHF/3-21G methyl#|amine example of Section A.3) is shown below:
.DF\@seg =
 $GENNBO  NATOMS=7  NBAS=28  UPPER  BODM $END
 $NBO  NAOMO=PVAL  $END
 $COORD
 Methylamine...Pople-Gordon standard geometry...RHF/3-21G                
  6   6   -0.74464  -0.03926   0.00000    ! Carbon
  7   7    0.71885   0.09893   0.00000    ! Nitrogen
  1   1   -1.00976  -1.09653   0.00000    ! Hydrogen
  1   1   -1.15467   0.43814   0.88998    ! Hydrogen
  1   1   -1.15467   0.43814  -0.88998    ! Hydrogen
  1   1    1.09878  -0.34343  -0.82466    ! Hydrogen
  1   1    1.09878  -0.34343   0.82466    ! Hydrogen
 $END
 $BASIS
   CENTER = 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,6,6,7,7
    LABEL = 1,1,101,102,103,1,101,102,103,1,1,101,102,103,1,101,102,103,
            1,1,1,1,1,1,1,1,1,1
 $END
 $CONTRACT
  NSHELL =  16
    NEXP =  21
   NCOMP =   1,  4,  4,  1,  4,  4,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1 
   NPRIM =   3,  2,  1,  3,  2,  1,  2,  1,  2,  1,  2,  1,  2,  1,  2,  1 
    NPTR =   1,  4,  6,  7, 10, 12, 13, 15, 16, 18, 16, 18, 19, 21, 19, 21 
     EXP =   0.1722560E+03,  0.2591090E+02,  0.5533350E+01,  0.3664980E+01,
             0.7705450E+00,  0.1958570E+00,  0.2427660E+03,  0.3648510E+02,
             0.7814490E+01,  0.5425220E+01,  0.1149150E+01,  0.2832050E+00,
             0.5447178E+01,  0.8245472E+00,  0.1831916E+00,  0.5447178E+01,
             0.8245472E+00,  0.1831916E+00,  0.5447178E+01,  0.8245472E+00,
             0.1831916E+00 
      CS =   0.2093132E+01,  0.2936751E+01,  0.1801737E+01, -0.7473843E+00,
             0.7126610E+00,  0.2098285E+00,  0.2624092E+01,  0.3734359E+01,
             0.2353454E+01, -0.1047101E+01,  0.9685501E+00,  0.2766851E+00,
             0.3971513E+00,  0.5579200E+00,  0.1995672E+00,  0.3971513E+00,
             0.5579200E+00,  0.1995672E+00,  0.3971513E+00,  0.5579200E+00,
             0.1995672E+00 
      CP =   0.0000000E+00,  0.0000000E+00,  0.0000000E+00,  0.1709178E+01,
             0.8856221E+00,  0.1857223E+00,  0.0000000E+00,  0.0000000E+00,
             0.0000000E+00,  0.2808586E+01,  0.1456735E+01,  0.2944871E+00,
             0.0000000E+00,  0.0000000E+00,  0.0000000E+00,  0.0000000E+00,
             0.0000000E+00,  0.0000000E+00,  0.0000000E+00,  0.0000000E+00,
             0.0000000E+00 
 $END
 $OVERLAP   ! Overlap matrix elements in the AO basis
  0.10000000E+01  0.19144744E+00  0.10000000E+01  . . .
 $END
 $DENSITY   ! Bond-order matrix elements in the AO basis
  0.20363224E+01  0.11085239E+00  0.10393086E+00  . . .
 $END
 $FOCK      ! Fock matrix elements in the AO basis
 -0.11127777E+02 -0.28589754E+01 -0.89570272E+00  . . .
 $END
 $LCAOMO    ! AO to MO transformation matrix
 -0.57428375E-03 -0.23835711E-02  0.17741799E-02  . . .
 $END
 $DIPOLE    ! dipole matrix elements in the AO basis
 -0.14071733E+01 -0.26939974E+00 -0.14071733E+01  . . .
 $END
.ED
.HR<<3//+1//5//85>>
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.HR<<3//+1//5//85>>
.LM10
.RM80
 #N

The nine lists of FILE47 are described in turn in
the following sections, making use of this
example for illustration.
.RL55
#IB.7.3 $GENNBO Keylist#N

\np The $GENNBO keylist (required) contains keywords 
essential to the proper execution
of the NBO program.  The following is the list of keywords recognized
by this keylist:

.LM+12
.OS<<12//#IKEYWORD#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//22//80>>


.OS<<12//REUSE>>
Instructs GENNBO to reuse an old NBO direct-access file, FILE48,
rather than create a new FILE48 from the wavefunction information
contained in the FILE47 data#|lists.  Therefore, if the REUSE keyword
is specified, all data#|lists in FILE47 will be ignored, but the
$NBO, $CORE, and $CHOOSE keylists will still be recognized.  This keyword
preempts all other keywords of the $GENNBO keylist.

.OS<<12//NATOMS>>
Number of atoms in the molecule (required).

.OS<<12//NBAS>>
Number of basis functions (required).

.OS<<12//OPEN>>
Designates an open shell wavefunction.  GENNBO will subsequently
read in alpha and beta density, Fock, and MO coefficient matrices.

.OS<<12//ORTHO>>
Indicates that the AO basis set is orthogonal (basis
functions are always assumed normalized).  If this keyword is
specified, GENNBO will not read the $OVERLAP datalist.  This keyword
is incompatible with $NBO keywords for `pre-orthogonal'
basis sets (SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, AOPNHO, AOPNBO,
AOPNLMO).

.OS<<12//UPPER>>
Indicates that only the upper triangular portions of the overlap,
density, Fock, and dipole matrices are listed in the their respective
datalists.  By default, GENNBO assumes that the full matrices are
given.

.OS<<12//BODM>>
Indicates that the $DENSITY datalist contains the
bond-order matrix (``Fock-Dirac density matrix'') rather
than the density matrix (i.e., matrix elements of the
density operator).  (In orthogonal AO basis sets, the bond-order matrix
and density matrix are identical, but in nonorthogonal basis sets they
must be distinguished.)  By default, GENNBO assumes this data#|list contains
the density matrix elements.  If ``BODM'' is included, the datalist
elements are transformed with the AO overlap matrix to produce the
true density matrix.

.OS<<12//BOHR>>
Indicates that the atomic coordinates ($COORD) and the dipole
integrals ($DIPOLE) are in atomic units, rather than the default
angstroms.

.OS<<12//EV>>
Indicates that the Fock matrix elements ($FOCK) have units of
electron volts (eV), rather than the default atomic units (Hartrees).

.OS<<12//CUBICF>>
Instructs GENNBO to use the set of seven cubic #If#N-type functions
rather than the ten Cartesian or seven pure #If#N functions
(cf. Section B.7.5).

.HR<<1//+1//10//80>>


.LM10
The methylamine sample $GENNBO keylist 
specifies 7 atoms, 28 basis
functions, upper triangular matrix input, and $DENSITY datalist containing
the bond-order matrix.
.RL55
#IB.7.4 $COORD Datalist#N

\np The $COORD datalist (required, unless REUSE is
specified in $GENNBO) contains the job title and information indicating
the identity and coordinates of each atom, including missing core electrons
or effective core potentials.

\np The first line following the $COORD identifier is an arbitrary
job title, up to 80 characters.

\np Subsequent lines are used to specify the
atomic number, the nuclear charge, and the (x,y,z) coordinates of each
atom.
[For example, atom 1 in the methylamine sample input is a carbon
atom (atomic number 6) with nuclear charge 6 and coordinates 
x = \minus 0.74464,
y = \minus 0.03926, z = 0.00000, in angstroms.]
Coordinates are assumed to be in angstroms unless the BOHR keyword
appears in the $GENNBO keylist, specifying atomic units.  The 
atomic number and nuclear charge
are generally identical, but if core electrons are neglected (as in most
semi-empirical treatments) or if effective core potentials (ECP) are employed,
the nuclear charge will be less than the atomic number by the number of
electrons neglected on that particular atom.  Thus, for an AMPAC calculation,
in which the two 1#Is#N core electron of a carbon atom are neglected, the line
following the job title in the methylamine example would read

#T   6    4    -0.74464   -0.03926    0.00000   ! Carbon#N

where ``4'' is the effective (valence) nuclear charge of the atom.
.RL55
#IB.7.5 $BASIS Datalist#N

\np The $BASIS datalist (required, unless REUSE is specified
in $GENNBO) provides essential information about the AO basis
functions,
specifying the atomic center and the angular symmetry (\ss , \px ,
\py , \pz ,
etc.) of each AO.  This information is contained 
in two arrays in this datalist called CENTER and LABEL.

\np The atomic center for each AO is 
specified by entering ``CENTER='' followed
by the serial number of the atom for each AO, separated by commas or spaces.
[For example, the entry

#T   CENTER = 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,6,6,7,7#N

of the methylamine sample file indicates that the first 9 AOs (1-9) are
centered on atom 1 (the carbon atom), the next nine AOs (10-18) on center 2,
and so forth.]

\np The angular symmetry for each AO is specified by entering ``LABEL=''
followed by a symmetry label for each AO, separated by commas or 
spaces.  The NBO program handles #Is#N, #Ip#N, #Id#N,
or #If#N (\l  = 0-3) basis AOs, of either cartesian or pure angular 
symmetry types.  The label for each AO is a 3-digit integer of the
form \l *100 + #Ik#N + #Im#N, where #Ik#N is 0 (cartesian) or 50 (pure),
and #Im#N is a particular component of the \l -type symmetry (see
table below).  For
#Is#N or #Ip#N AOs,
the cartesian and pure \l -symmetry sets are identical, so each AO can be
labelled in two distinct ways, but
the six cartesian #Id#N functions can be transformed to the five pure #Id#N
functions plus an additional #Is#N function, and the ten cartesian #If#N
functions can be transformed to the seven
pure #If#N functions plus three additional #Ip#N 
functions.  Two distinct sets of pure #If#N
functions are recognized, the ``standard'' [default] set and
the ``cubic'' set, the latter being used whenever the ``CUBICF''
keyword is included in the $GENNBO keylist.
 
\np The labels associated
with each allowed AO function type are tabulated below, 
where #Ix, y, z#N refer to the
specified cartesian axis system:

.RL32 
.VS160
.TB
.FM<<1C6//2L14//1C6//2L14//1C6//2L14>>
.RW-
.RW<<#Ilabel#N//#IAO type#N//#Ilabel#N//#IAO type#N//#Ilabel#N//#IAO type#N>>
.RW=
.FM<<0L23//0L23//0L23>>
.RW<<#_Pure #Is, p#N sets:#/ //#_Cartesian #If#N set:#/ //
#_Pure #If#N ``cubic'' set:#/>>
.FM<<1C6//2L14//1C6//2L14//1C6//2L14>>
.RW<<1 (51)//#Is#N//301//#If#N#dxxx#u//
351//#If#N(D1): x(5x#u2#d\minus 3r#u2#d)>>
.RW<<101 (151)//#Ip#N#dx#u//302//#If#N#dxxy#u//
352//#If#N(D2): y(5y#u2#d\minus 3r#u2#d)>>
.RW<<102 (152)//#Ip#N#dy#u//303//#If#N#dxxz#u//
353//#If#N(D3): z(5z#u2#d\minus 3r#u2#d)>>
.RW<<103 (153)//#Ip#dz#u#N//304//#If#N#dxyy#u//
354//#If#N(B):  xyz>>
.RW<< // //305//#If#N#dxyz#u//
355//#If#N(E1): x(z#u2#d\minus y#u2#d)>>
.FM<<0L23//1C6//2L14//1C6//2L14>>
.RW<<#_Cartesian #Id#N set:#/ //306//#If#N#dxzz#u//
356//#If#N(E2): y(z#u2#d\minus x#u2#d)>>
.FM<<1C6//2L14//1C6//2L14//1C6//2L14>>
.RW<<201//#Id#N#dxx#u//307//#If#N#dyyy#u//
357//#If#N(E3): z(x#u2#d\minus y#u2#d)>>
.FM<<1C6//2L14//1C6//2L14>>
.RW<<202//#Id#N#dxy#u//308//#If#N#dyyz#u>>
.RW<<203//#Id#N#dxz#u//309//#If#N#dyzz#u>>
.RW<<204//#Id#N#dyy#u//310//#If#N#dzzz#u>>
.RW<<205//#Id#N#dyz#u// // >>
.FM<<1C6//2L14//0L23>>
.RW<<206//#Id#N#dzz#u//#_Pure #If#N ``standard'' set:#/>>
.FM<<1C6//2L14//1C6//2L14>>
.RW<< // //351//#If#N(0):  z(5z#u2#d\minus 3r#u2#d)>>
.FM<<0L23//1C6//2L14>>
.RW<<#_Pure #Id#N set:#/ //352//#If#N(c1): x(5z#u2#d\minus r#u2#d)>>
.FM<<1C6//2L14//1C6//2L14>>
.RW<<251//#Id#N#dxy#u//353//#If#N(s1): y(5z#u2#d\minus r#u2#d)>>
.RW<<252//#Id#N#dxz#u//354//#If#N(c2): z(x#u2#d\minus y#u2#d)>>
.RW<<253//#Id#N#dyz#u//355//#If#N(s2): xyz>>
.RW<<254//#Id#R#dx#u2#d\minus y#u2#N//
356//#If#N(c3): x(x#u2#d\minus 3y#u2#d)>>
.RW<<255//#Id#R#dz#u2#N = #Id#R#d3z#u2#d\minus r#u2#N//
357//#If#N(s3): y(3x#u2#d\minus y#u2#d)>>
.FM<<0L69>>
.RW-
.ET
.VS120
 
[For example, in the methylamine sample input,
the first nine entries of the LABEL array,

#T    LABEL = 1,1,101,102,103,1,101,102,103,. . .#N

identify the first 9 AOs (of carbon) as being of \ss , \ss , \px , \py , \pz ,
\ss , \px , \py , \pz  type, respectively.]
.RL55
#IB.7.6 $CONTRACT Datalist#N

\np The $CONTRACT datalist (optional)
contains additional information about the contraction coefficients
and orbital exponents of AO basis functions.  This information is
not used in the NBO analysis of a wavefunction.  However, if the
AOINFO or PLOT keyword is specified in the $NBO keylist (See Section B.2.5),
the GENNBO driver routines write out this information to
an external file (LFN 31) in the proper format for orbital plotting with
the ORBPLOT program.  Omit the $CONTRACT datalist if you do not
intend to make orbital plots.

\np Two integers must be initially given: NSHELL (the number of shells of
basis functions) and NEXP (the number of orbital exponents).
[In the methylamine example, there are 16 shells of basis functions and 27
orbital exponents.]  These integers should precede 
the remainder of the basis set information
of this datalist.

\np The number of components (basis functions) in each shell is specified in
the NCOMP array.  The sum of the components for each shell should equal
the total number of basis functions.  This list of components is a
partitioning of the basis function centers and labels (in the $BASIS
datalist) into shells.  [For example, in the methylamine sample, the NCOMP array

#T    NCOMP = 1,4,4,. . .#N

indicates that the first three shells have a total of 9 (i.e. 1+4+4) basis 
functions.  These are the 9 AOs (1-9) discussed previously in the $BASIS
datalist.]

\np The NPRIM array gives the number of primitive gaussian functions of each
shell.  [For the methylamine example, the first three shells of the AO
basis are contractions of

#T    NPRIM = 3,2,1,. . .#N

three, two, and one primitives, respectively, corresponding to
the conventional ``3-21G'' basis set designation.]

\np Pointers for each shell are listed in the NPTR array.  These pointers
specify the location of the orbital exponents (EXP) and contraction
coefficients (CS, CP, CD, CF) for each shell.  [In the sample input file,

#T     NPTR = 1,4,6,. . .#N

the orbital exponents and contraction coefficients for the first three
shells begin at elements 1, 4, and 6, respectively.]

\np EXP, CS, CP, CD, and CF are free format, real arrays containing the orbital
exponents, and the s, p, d, and f contraction coefficients of the AO basis set.
NEXP elements should appear in each array, and the arrays of contraction
coefficients need only appear if there are basis functions of that particular
symmetry in the basis set.  [For example, the 3-21G basis of the sample
methylamine input only has #Is#N and #Ip#N basis functions.  Therefore, the
CD and CF arrays are not necessary.]

\np The information in the $CONTRACT datalist along with that in the $BASIS
datalist is enough to completely determine the AO basis set.  [For example,
the second shell on the methylamine sample contains 4 basis functions
(NCOMP). These are #Is#N, #Ip#N#dx#u, #Ip#N#dy#u, and #Ip#N#dz#u
orbitals (LABEL), all centered on atom 1 (CENTER), and each basis function
is a contraction of two primitive gaussians (NPRIM).  From NPTR, EXP, CS,
and CP, we find the explicit form of these functions:

.CJ
.DF\s1 =\minus 0.747\thsp e#u#u\minus 3.66\thsp r#u2#d#d#d
.DF\s2 =0.713\thsp e#u#u\minus 0.77\thsp r#u2#d#d#d
.DF\p1 =1.709\thsp x\thsp e#u#u\minus 3.66\thsp r#u2#d#d#d
.DF\p2 =0.886\thsp x\thsp e#u#u\minus 0.77\thsp r#u2#d#d#d
.DF\p3 =1.709\thsp y\thsp e#u#u\minus 3.66\thsp r#u2#d#d#d
.DF\p4 =0.886\thsp y\thsp e#u#u\minus 0.77\thsp r#u2#d#d#d
.DF\p5 =1.709\thsp z\thsp e#u#u\minus 3.66\thsp r#u2#d#d#d
.DF\p6 =0.886\thsp z\thsp e#u#u\minus 0.77\thsp r#u2#d#d#d
\phi #ds#u(#Br#N)   \thsp =  \s1    \thsp +  \s2

\phi #dp#dx#u#u(#Br#N)  =   \p1   +  \p2

\phi #dp#dy#u#u(#Br#N)  =   \p3   +  \p4

\phi #dp#dz#u#u(#Br#N)  =   \p5   +  \p6

.FJ
where #Br#N=(x,y,z) is measured in bohr units relative to the cartesian
coordinates of atom 1.]
.RL55
#IB.7.7 Matrix Datalists#N

\np The remaining datalists ($OVERLAP, $DENSITY, $FOCK, $LCAOMO, $DIPOLE)
specify various matrix elements possibly used by the NBO analysis.  All 
entries in these datalists are free format, with entries separated
by commas or spaces.  Only the upper triangular portions of each symmetric
matrix (overlap, density, Fock, dipole) should be provided if the
UPPER keyword is specified in the $GENNBO keylist.  The numbering of the
matrix rows and columns must correspond to the ordering of the AOs in 
the $BASIS datalist.  All three matrices of dipole integrals should appear
in the $DIPOLE datalist, all #Ix#N integrals before #Iy#N before #Iz#N.

\np Of the matrix datalists, the $DENSITY datalist is 
always required, and
the $OVERLAP data#|list is required for all non-orthogonal 
AO basis sets, but other data#|lists are optional (unless implicitly
required by specified keyword options).  Nevertheless, it is good practice 
to include as many of these datalists
in FILE47 as possible for later use with keyword options which require
them.  The following table lists the $NBO keywords that require
each datalist to be included in FILE47:

.LM+5
.LM+12
.OS<<12//#IDatalist#N>>
#I$NBO Keywords Requiring the Datalist#N
.HR<<1//+1//15//25>>
.HR<<1//+1//27//75>>

.OS<<12//$OVERLAP>>
SAO, SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, 
.LM+0
AOPNHO, AOPNBO, AOPNLMO

.OS<<12//$FOCK>>
E2PERT, FAO, FNAO, FNHO, FNBO, FNLMO

.OS<<12//$LCAOMO>>
AOMO, NAOMO, NHOMO, NBOMO, NLMOMO

.OS<<12//$DIPOLE>>
DIAO, DINAO, DINHO, DINBO, DINLMO, DIPOLE

.OS<<12//$CONTRACT>>
AOINFO, PLOT
.HR<<1//+1//15//75>>


.LM10
\np For example, in the methylamine sample input, the keyword ``NAOMO=PVAL''
of the $NBO keylist requires that the $LCAOMO data#|list be present (in
addition to the $OVERLAP, $DENSITY, and $FOCK data#|lists used for default
PRINT=2 analysis), but the $DIPOLE data#|list might have been omitted in
this case.  Inclusion of the $LCAOMO data#|list (in addition to the $FOCK
datalist) insures that degenerate MOs will be chosen in a prescribed way
for decomposition in terms of other functions.
.CM-------------------------END OF NBOB.MAN------------------------------
.CM-----------------------------NBOC.MAN---------------------------
.TP2
.DF\np =\thsp \nthsp
.HF<<C.1 INTRODUCTION//3//10>>
.NF<<C-// >>
.PN1
.CM----------------------------------------------------------------





.CJ
#HSection C: NBO PROGRAMMER'S GUIDE#N
.FJ


#BC.1 INTRODUCTION#N

\np Section C constitutes the
programmer's guide to the NBO.SRC program.  It
assumes that the user has a thorough familiarity with Fortran
programming and the operations of the NBO program (Sections
A and B) as well as some familiarity with
published algorithms for NAO/NBO/NLMO
determination.  This section is intended for the accomplished
programmer who wishes to inquire into the details of the
NBO numerical methods and find the specific source
code associated with individual steps of the published 
NAO/NBO/NLMO algorithms or segments of NBO output.

\np The NBO.SRC program consists of about 20000 lines, of which
more than 6000 are comment lines (approximately the length of
this manual!).  These comment statements provide the principal
documentation of the steps within each subroutine
or function, and should be consulted on questions pertaining
to individual subprograms.  

\np In this Programmer's Guide, 
we focus on global aspects of program organization 
and data structure.  Individual subprograms
(about 180 in number) are described in capsule form, in the
order in which they appear in the source listing, to
indicate the relationship to 
program tasks and the association with specific segments
of NBO output.  The capsule descriptions include mention [in
brackets] of numerical thresholds
or possible dependencies on machine precision that are of particular
concern to the programmer.  Throughout the Programmer's Guide,
in referring to individual subprograms, we
use the abbreviation ``SR'' for ``subroutine'' and ``FN'' for 
``function''.

\np Sections C.2-C.4 describe the overall NBO.SRC source layout,
labelled COMMON blocks, and I/O structures (including the
FILE48 direct access file).  Sections C.5-C.11 then
follow the layout of the source code in describing the principal
groupings of subprograms, with a brief description of each
subprogram.  Section C.12 similarly describes subprograms of
the GENNBO stand-alone program.  The final section C.13 provides
guidance on attaching the NBO program to a new ESS package not
supported by this distribution.

.CM------------------------------------------------------------------
.HF<<C.2 OVERVIEW OF NBO SOURCE PROGRAM GROUPS//3//10>>
.RL55
#BC.2 OVERVIEW OF NBO SOURCE PROGRAM GROUPS#N

\np The NBO.SRC program is organized into seven principal groups
of routines (I-VII), described in Sections C.5-C.11, respectively,
as shown below:


.LM+5
.TB
.FM<<0R5//3L27//0C6//0C6>>
.RW-
.RW<<Group//description//no.//Section>>
.RW=
.RW<<I.//NAO/NBO/NLMO routines//61//C.5>>
.RW<<II.//Energy analysis routines//6//C.6>>
.RW<<III.//Direct access file (DAF) routines//41//C.7>>
.RW<<IV.//Free format input routines//7//C.8>>
.RW<<V.//Other I/O routines//27//C.9>>
.RW<<VI.//General utility routines//31//C.10>>
.RW<<VII.//System-dependent routines//(3)//C.11>>
.RW-
.ET
.LM10

The routines of Groups I, II are associated with the two
main tasks of the NBO program: (1) NAO/NBO/NLMO formation, 
and (2) NBO energetic analysis.  Group II routines generally
require Fock matrix information, and thus are restricted to
RHF and UHF wavefunctions, whereas Group I are 
applicable to general wavefunctions.  Each of these
groups is controlled by a master subroutine
(NBO and NBOEAN, respectively) of highest precedence, which in turn 
calls routines of secondary precedence (such 
as NAODRV, NBODRV, etc.) to control the
task.  Routines are generally clustered together under the
subroutine of next higher precedence, and within each cluster, the order
of routines generally corresponds to the chronological
sequence in which the routines are called in execution.  

\np The remaining Groups III-VI `serve' various routines of Groups
I-II, and are ordered more loosely by function, 
or alphabetically.  Groups I-VI 
are system-independent, whereas Group VII contains the special
drivers (RUNNBO, FEAOIN, DELSCF) for individual ESS programs, whose
generic function is described in Section C.11.  Further information
on the ESS-specific forms of the Group VII driver routines is given
in the Appendix.  

\np A general overview of the subprograms of Groups I and II
is shown in the accompanying flow chart, 
indicating the logical relationship of the routines to
be discussed in Sections C.5, C.6.  The sequence of execution
is generally from top to bottom and from left to right, 
with subprograms of equal precedence shown at an equal vertical level.

.RL55
.CM------------------------------------------------------------------
.LM10
.RM80
 
 
 
.CJ
#HNBO Flow Chart for Group I, II Subprograms#N
.LJ
.LM15
.DF\!hs =4
.DF\!w =3
.DF\!wl =1
.BX<<3//10//80//+2//+42>>
#T
 
 
.BX<<\!w //\!hs +38//\!hs +47//+1//+3>>
.CM-------runnbo to nbo-------------------
.VR<<\!wl //\!hs +41//+3//+5>>
.HR<<\!wl //+5//\!hs +20//\!hs +41>>
.VR<<\!wl //\!hs +20//+5//+6>>
.CM-------runnbo to nboean----------------
.VR<<\!wl //\!hs +44//+3//+5>>
.HR<<\!wl //+5//\!hs +44//\!hs +65>>
.VR<<\!wl //\!hs +65//+5//+6>>
 
                            RUNNBO
 
                   I                   II
 
.BX<<\!w //\!hs +17//\!hs +23//+1//+3>>
.BX<<\!w //\!hs +61//\!hs +70//+1//+3>>
.VR<<\!wl //\!hs +65//+3//+6>>
.CM------nbo to startup-----------------
.VR<<\!wl //\!hs +19//+3//+5>>
.HR<<\!wl //+5//\!hs +15//\!hs +19>>
.VR<<\!wl //\!hs +15//+5//+6>>
.CM------nbo to naodrv------------------
.VR<<\!wl //\!hs +20//+3//+5>>
.HR<<\!wl //+5//\!hs +20//\!hs +30>>
.VR<<\!wl //\!hs +30//+5//+6>>
.CM------nbo to nbodrv------------------
.VR<<\!wl //\!hs +21//+3//+4>>
.HR<<\!wl //+4//\!hs +21//\!hs +47>>
.VR<<\!wl //\!hs +47//+4//+6>>
 
       NBO                                        NBOEAN
 
 
 
.BX<<\!w //\!hs +11//\!hs +20//+1//+6>>
.BX<<\!w //\!hs +22//\!hs +38//+1//+4>>
.BX<<\!w //\!hs +43//\!hs +51//+1//+3>>
.BX<<\!w //\!hs +57//\!hs +73//+1//+5>>
.CM------naodrv to prepare---------------
.VR<<\!wl //\!hs +28//+4//+7>>
.HR<<\!wl //+7//\!hs +15//\!hs +28>>
.VR<<\!wl //\!hs +15//+7//+9>>
.CM------naodrv to nao-------------------
.VR<<\!wl //\!hs +30//+4//+8>>
.HR<<\!wl //+8//\!hs +27//\!hs +30>>
.VR<<\!wl //\!hs +27//+8//+9>>
.CM------naodrv to naoanl----------------
.VR<<\!wl //\!hs +32//+4//+8>>
.HR<<\!wl //+8//\!hs +32//\!hs +36>>
.VR<<\!wl //\!hs +36//+8//+9>>
.CM------nbodrv to nathyb----------------
.VR<<\!wl //\!hs +47//+3//+9>>
.CM------nbodrv to nlmo------------------
.VR<<\!wl //\!hs +48//+3//+8>>
.HR<<\!wl //+8//\!hs +48//\!hs +59>>
.VR<<\!wl //\!hs +59//+8//+9>>
.CM------nbodrv to dipanl----------------
.VR<<\!wl //\!hs +49//+3//+7>>
.HR<<\!wl //+7//\!hs +49//\!hs +69>>
.VR<<\!wl //\!hs +69//+7//+9>>
 
 (init.)        NAODRV          NBODRV        NBODEL,DELETE,  
 NBOSET     (& simulation)                    NEWDM,RNKEIG,
 JOBOPT                                          SIMTRN
 NBODIM
 
 
 
.BX<<\!w //\!hs +10//\!hs +21//+1//+6>>
.BX<<\!w //\!hs +24//\!hs +30//+1//+3>>
.BX<<\!w //\!hs +32//\!hs +40//+1//+3>>
.BX<<\!w //\!hs +42//\!hs +52//+1//+5>>
.BX<<\!w //\!hs +55//\!hs +62//+1//+3>>
.BX<<\!w //\!hs +65//\!hs +73//+1//+3>>
.CM---nao to nao formation----------------
.VR<<\!wl //\!hs +27//+3//+7>>
.HR<<\!wl //+7//\!hs +18//\!hs +27>>
.VR<<\!wl //\!hs +18//+7//+8>>
.CM---nathyb to nbo formation-------------
.VR<<\!wl //\!hs +47//+5//+7>>
.HR<<\!wl //+7//\!hs +42//\!hs +47>>
.VR<<\!wl //\!hs +42//+7//+8>>
.CM----nlmo to lmoanl---------------------
.VR<<\!wl //\!hs +59//+3//+8>>
.CM----dipanl to dipele-------------------
.VR<<\!wl //\!hs +69//+3//+8>>
 
(prepare)     NAO    NAOANL     NATHYB      NLMO     DIPANL 
 SIMTRM                        (CHSDRV,                   
 MULANA                         CHOOSE)
 DFGORB                                 
                                        
 
.BX<<\!w //\!hs +10//\!hs +27//+1//+9>> 
.BX<<\!w //\!hs +29//\!hs +53//+1//+12>>
.BX<<\!w //\!hs +55//\!hs +63//+1//+5>>
.BX<<\!w //\!hs +65//\!hs +73//+1//+4>>
 
(NAO formation)      (NBO formation)       LMOANL    DIPELE 
LOADAV,ATDIAG,     SRTNBO,XCITED,ANLYZE,   SYMUNI    DIPNUC
SETBAS,NEWWTS,     HTYPE,FRMHYB,HYBDIR,    SYMORT
WORTH,SCHMDT,      HYBCMP,FNDMOL,NBOCLA,       
NEWRYD,RYDIAG,     FNBOAN,NBOSUM,GETDEL, 
RYDSEL,REDIAG,     BLDSTR,CORE,IWPRJ,    
   REDBLK          DEPLET,LOAD,PRJEXP,  
                   STASH,ORTHYB,FRMPRJ,
                   ANGMNT,REPOL,FORMT,
                          CYCLES
 
.LM10
.RM80
.FJ
.CM----------------------------------------------------------------------

.HF<<C.3 LABELLED COMMON BLOCKS//3//10>>
.RL55
#BC.3 LABELLED COMMON BLOCKS#N

\np The NBO programs contain eighteen
labelled COMMON blocks 
to control information flow between subprograms
(other than through explicit argument
lists).  Each COMMON 
block name begins with ``NB'' to minimize
possible conflicts with a linked ESS program.  

The eighteen COMMON blocks can be divided into six `primary'
and twelve `secondary' blocks, with regard to claim on the
programmer's attention.  The `primary'
COMMON blocks 1-6 (/NBINFO/, /NBFLAG/, /NBOPT/,
/NBAO/, /NBATOM/, and /NBIO/)
contain variables that must be set by the
ESS-specific driver routine FEAOIN, or by an equivalent interface
provided by the programmer.  The remaining `secondary'
blocks 7-18 are for internal communication
only, and are ordinarily of lesser concern.

The dimensions of COMMON block arrays are 
fixed by PARAMETER declarations of the form
 #T
     PARAMETER(MAXATM = 99,MAXBAS = 500)

#Nwhere MAXATM and MAXBAS are, respectively,
the maximum allowed numbers of atoms and basis 
functions.  These program limits can therefore be simply 
altered.  There is no difficulty in #Idecreasing#N either of these values,
or in increasing MAXBAS (up to 999).  However, the program cannot
readily adapt to MAXATM > 99, since this 
would result in format overflows in orbital labels throughout the output.

All entries of a given COMMON block are generally of the same
numeric type (INTEGER, LOGICAL, etc.), as specified below.  The names (dummy),
and meaning of variables in each primary COMMON block 1-6 are 
described briefly, with an asterisk (*) marking the items
that must be passed from the external ESS program via driver routines:

.LM+3
.OS<<3//#_1. COMMON/NBINFO/#/>>


The INTEGER variables of this block store general information
related to basis set dimensionality, spin manifold, number of atoms,
and energy units:

.RL12
.TB
.FM<<0L1//0L12//2L50>>
.RW-
.RW<< //variable//meaning>>
.RW=
.FM<<0L1//0L12//2L50>>
.RW<< //ISPIN//+2 for \alpha  spin, \minus 2 for \beta  spin>>
.RW<<*//NATOMS//number of atoms (\le  MAXATM)>>
.RW<<*//NDIM//declared dimensionality of matrices (overlap, density, etc.)>>
.RW<<*//NBAS//number of basis AOs (\le  NDIM \le  MAXBAS)>>
.RW<< //MXBO//maximum number of AOs per 2-c or 3-c NBO>>
.RW<< //MXAO//maximum AOs per atom>>
.RW<< //MXAOLM//maximum AOs of the same symmetry per atom>>
.RW<<*//MUNIT//0 for Hartree energy units, 1 for eV units, 2 for kcal/mol.>>
.RW-
.ET

.RL20
.OS<<3//#_2. COMMON/NBFLAG/#/>>


The LOGICAL variables of this block are set .TRUE. or .FALSE.
depending on whether the ``condition'' (type of wavefunction, spin
set, etc.) is satisfied:

.TB
.FM<<0L1//0C14//2L50>>
.RW-
.RW<< //variable (FLAG)//condition that FLAG=.TRUE.>>
.RW=
.FM<<0L1//0L12//2L50>>
.RW<<*//ROHF//Restricted open-shell Hartree-Fock wavefunction>>
.RW<<*//UHF//Unrestricted Hartree-Fock wavefunction>>
.RW<<*//CI//Configuration Interaction wavefunction>>
.RW<<*//OPEN//open-shell calculation>>
.RW<<*//COMPLX//complex-valued wavefunction (not currently implemented)>>
.RW<< //ALPHA//\alpha  spin set>>
.RW<< //BETA//\beta  spin set>>
.RW<<*//MCSCF//Multi-Configuration Self-Consistent-Field wavefunction>>
.RW<<*//AUHF//Spin-Annihilated UHF wavefunction>>
.RW<<*//ORTHO//basis set is orthonormal>>
.RW-
.ET

Note (Section B.6.11) that both \alpha  and \beta  spin density matrices
should be available if OPEN is set `.TRUE.' for the open-shell case.



.RL30
.OS<<3//#_3. COMMON/NBOPT/#/>>


The INTEGER variables (flags) of this block are used for storing the keyword
options selected by the user in the $NBO keylist.  In many cases, a variable
of the form IWOPT (``IW'' stands for ``I Want'') is set to one or zero
(or to some Hollerith content; see below) depending on whether 
the ``requested option'' has been specified or not.  The table also 
lists the keyword (if any) that requests the option:

.LJ
.RL22
.TB
.FM<<0L1//0L10//2L10//2L42>>
.RW-
.RW<< //variable//keyword//requested option>>
.RW=
.FM<<0L1//0L10//2L10//2L40>>
.RW<<*//IWDM//BODM//1 to transform input bond-order matrix, 0 otherwise>>
.RW<< //IW3C//3CBOND//3-center bonds>>
.RW<< //IWAPOL// //`apolar' bonds, #Ic#N#dA#u = #Ic#N#dB#u (not used)>>
.RW<< //IWHYBS//$NBO//set equal to JPRINT(5)>>
.RW<< //IWPNAO//(PAOPNAO)//PAO\rarr PNAO transformation>>
.RW<< //IWTNAO//AONAO//AO\rarr NAO transformation>>
.RW<< //IWTNAB//NAONBO//NAO\rarr NBO transformation>>
.RW<< //IWTNBO//AONBO//AO\rarr NBO transformation>>
.RW<< //IWFOCK// //+1 if Fock matrix available on DAF, 0 otherwise>>
.RW<<*//IWCUBF//CUBICF//cubic #If#N functions>>
.RW<<*//IPSEUD// //effective core potential>>
.RW<< //KOPT// //(not used)>>
.RW<< //IPRINT//PRINT=n//print level>>
.RW<< //IWDETL//DETAIL//detailed output>>
.RW<< //IWMULP//MULAT//Mulliken population analysis>>
.RW<< //ICHOOS//$CHOOSE//directed NBO ($CHOOSE) search>>
.RW<< //JCORE//$CORE//user-specified core list>>
.RW<< //JPRINT(60)//various//printing option flags>>
.RW-
.ET
.FJ

.RL22
.BM60
The keyword associated with each element I=1-54 
of the JPRINT array is shown below (55-60 are not currently used):

.LJ
.TB
.FM<<0L68>>
.RW<<JPRINT(I) #Iassociated keywords:#N>>
.FM<<2C3//2L12//2C3//2L10//2C3//2L10//2C3//2L10>>
.RW-
.RW<<I//keyword//I//keyword//I//keyword//I//keyword>>
.RW=
.RW<<1//SKIPBO//15//FNLMO//29//FNHO//43//PLOT>>
.RW<<2//version//16//DMNBO//30//AOPNHO//44//AOPNAO>>
.RW<<3//E2PERT//17//DMNLMO//31//FNAO//45//NBOMO>>
.RW<<4//NPA//18//NAONLMO//32//(reserved)//46//DIPOLE>>
.RW<<5//NBO//19//SPNAO//33//NAONHO//47//NBONLMO>>
.RW<<6//NBOSUM//20//SPNHO//34//DMNHO//48//SPNLMO>>
.RW<<7//ARCHIVE//21//SPNBO//35//DMNAO//49//AOPNLMO>>
.RW<<8//NLMO//22//AOINFO//36//BEND//50//DIAO>>
.RW<<9//NAOMO//23//AONLMO//37//FNBO//51//DINAO>>
.RW<<10//NOBOND//24//NHONLMO//38//NHOMO//52//DINHO>>
.RW<<11//RPNAO//25//AOPNBO//39//SAO//53//DINBO>>
.RW<<12//BNDIDX//26//AOMO//40//FAO//54//DINLMO>>
.FM<<2C3//2L12//2C3//2L10//2C3//2L10//0C5//2L10>>
.RW<<13//NLMOMO//27//DMAO//41//NHONBO//55-60//(not used)>>
.RW<<14//RESONANCE//28//AONHO//42//BOAO// // >>
.RW-
.ET
.FJ

In general, if the flag is
set to zero, its associated keyword option has not been specified.  However, 
if an option is requested, its flag can be set to a variety of
positive, negative, or Hollerith values, depending on the parameters
specified with the keyword option.  In particular, the option flags associated
with the matrix output keywords, described in Section B.2.4, are set
according to the following scheme:

.LJ
.LM+8
.RL10
.TB
.FM<<0C12//2L35>>
.RW-
.RW<<value//effect>>
.RW=
.RW<<0//Do nothing>>
.RW<<0 < #In#N//Print #In#N columns of the matrix>>
.RW<<-1000 < #In#N < 0//Write matrix to external file |#In#N|>>
.RW<<n < -999//Read matrix from external file |#In#N/1000|>>
.RW<<`FULL'//Print the full matrix to the output file>>
.RW<<`VAL'//Print only core plus valence orbitals>>
.RW<<`LEW'//Print only the occupied (Lewis) orbitals>>
.RW-
.ET
.FJ
.LM-8


.RL12
.OS<<3//#_4. COMMON/NBAO/#/>>


The INTEGER arrays of this block store information on the
atomic centers and angular symmetry of each AO:

.TB
.FM<<0L1//0L20//2L40>>
.RW-
.RW<< //variable//meaning>>
.RW=
.FM<<0L1//0L20//2L40>>
.RW<<*//LCTR(MAXBAS)//list of atomic centers of the basis AOs>>
.RW<< // //(LCTR(3)=2 if AO 3 is on atom 2)>>
.RW<<*//LANG(MAXBAS)//angular symmetry labels (Sec. B.7.5) of the basis AOs>>
.RW-
.ET


.RL16
.OS<<3//#_5. COMMON/NBATOM/#/>>


The INTEGER arrays of this block store information about the
orbitals on each atomic center:

.TB
.FM<<0L1//0L20//2L40>>
.RW-
.RW<< //variable//meaning>>
.RW=
.FM<<0L1//0L20//2L40>>
.RW<<*//IATNO(MAXATM)//atomic number for each atom>>
.RW<< //INO(MAXATM)//number of atomic hybrids on each atom>>
.RW<< //NORBS(MAXATM)//number of AOs on each atom>>
.RW<< //LL(MAXATM)//number of the first NAO on each atom>>
.RW<< //LU(MAXATM)//number of the last NAO on each atom>>
.RW<<*//IZNUC(MAXATM)//nuclear charge on each atom (\le  IATNO)>>
.RW<< //IATCR(MAXATM)//atomic core list for modified $CORE table>>
.RW-
.ET


.RL27
.OS<<3//#_6. COMMON/NBIO/#/>>


The INTEGER variables of this block are the
stored default logical file
numbers for I/O operations.  The table below identifies
the value (default file assignment) and the
contents of the file associated with each LFN (cf. Section B.2.4):

.TB
.FM<<0L1//0L8//0C8//2L40>>
.RW-
.RW<< //LFN//value//file contents>>
.RW=
.RW<<*//LFNIN// //standard ESS input file>>
.RW<<*//LFNPR// //standard ESS output (print) file>>
.RW<< //LFNAO//31//AO info file>>
.RW<< //LFNPNA//32//AO\rarr PNAO transformation>>
.RW<< //LFNNAO//33//AO\rarr NAO transformation>>
.RW<< //LFNPNH//34//AO\rarr PNHO transformation>>
.RW<< //LFNNHO//35//AO\rarr NHO transformation>>
.RW<< //LFNPNB//36//AO\rarr PNBO transformation>>
.RW<< //LFNNBO//37//AO\rarr NBO transformation>>
.RW<< //LFNPNL//38//AO\rarr PNLMO transformation>>
.RW<< //LFNNLM//39//AO\rarr NLMO transformation>>
.RW<< //LFNMO//40//AO\rarr MO transformation (LCAO-MO coeffs.)>>
.RW<< //LFNDM//41//density matrix in AO basis>>
.RW<< //LFNNAB//42//NAO\rarr NBO transformation>>
.RW<< //LFNPPA//43//PAO\rarr PNAO transformation>>
.RW<< //LFNGEN//47//`archive' file>>
.RW<< //LFNDAF//48//direct access file (DAF)>>
.RW<< //LFNDEF//49//`default' for other file output>>
.RW-
.ET


.RL35
.LM-3
The remaining `secondary' COMMON blocks 7-18 contain variables that
remain wholly within the system-independent code, and thus can be
ignored with respect to interfacing to a new ESS.  Blocks 7-13
involve communication with the Group I, II subprograms, whereas
blocks 14-18 are wholly within the `support' routines of
Groups III-VII.

.LM+3
.RL16
.OS<<3//#_7. COMMON/NBBAS/#/>>


The INTEGER arrays of this block generally store information about
the atomic, bond, and molecular units with which the NBOs or NAOs are 
associated.  The meaning of all entries in COMMON/NBBAS/ #Ichanges#N
between the NAO and NBO segments of the program, so this block
functions virtually as `scratch storage,' and its entries must be
approached with extreme caution!  The following table indicates the meaning
of COMMON/NBBAS/ entries during NBO segments (only!):

.TB
.FM<<0L18//2L45>>
.RW-
.RW<<variable//meaning>>
.RW=
.FM<<0L18//2L45>>
.RW<<LABEL(MAXBAS,6)//NBO label information (lbl; *; bond no.; at1; at2; at3)>>
.RW<<NBOUNI(MAXBAS)//molecular unit of each NBO>>
.RW<<NBOTYP(MAXBAS)//no. centers + 10 (if low-occ LP) + 20 (if BD* or RY*)>>
.RW<<LSTOCC(MAXBAS)//1 (NMB) or 0 (NRB) NAO labels>>
.RW<<IBXM(MAXBAS)//NBO label permutation list>>
.RW<<LARC(MAXBAS)//re-ordering list>>
.RW<<LBL(MAXBAS)//atomic center of AO>>
.RW<<LORBC(MAXBAS)//angular momentum label of AO>>
.RW<<LORB(MAXBAS)//(variable)>>
.RW-
.ET

.RL16
.OS<<3//#_8. COMMON/NBTHR/#/>>


The DOUBLE PRECISION variables of this block store the 
default values of various
numerical thresh#|olds that can be set by the user:

.TB
.FM<<0L8//2L45>>
.RW-
.RW<<variable//meaning>>
.RW=
.FM<<0L8//2L45>>
.RW<<THRSET//NBO occupancy threshold>>
.RW<<PRJSET//projection threshold>>
.RW<<ACCTHR//threshold [0.1] for assigning acceptor orbital NBOTYP>>
.RW<<CRTSET//threshold for core-occupancy warning>>
.RW<<E2THR//minimum E for 2nd-order energy analysis printing>>
.RW<<ATHR//minimum bend angle for BEND printing>>
.RW<<PTHR//minimum % #Ip#N-character for BEND printing>>
.RW<<ETHR//minimum NBO occupancy for BEND printing>>
.RW<<DTHR//minimum dipole moment for DIPOLE printing>>
.RW-
.ET

.RL16
.OS<<3//#_9. COMMON/NBLBL/#/>>


The INTEGER variables of this block store the number of
orbitals associated with the ``LEW'' and ``VAL'' print parameters
(Section B.2.4) and the 10 Hollerith fragments required to compose each of
the 4 possible types of localized orbital labels (AO, NAO, NHO, NBO):

.TB
.FM<<0L18//2L45>>
.RW-
.RW<<variable//meaning>>
.RW=
.FM<<0L18//2L45>>
.RW<<NLEW//number of Lewis NBOs (= number of occupied MOs)>>
.RW<<NVAL//number of minimal basis (NMB) NAOs>>
.RW<<LBL(10,MAXBAS,4)//label fragments (AO; NAO; NHO; NBO)>>
.RW-
.ET

.RL16
.OS<<3//#_10. COMMON/NBNAO/#/>>


The INTEGER arrays of this block store information pertaining
to the labelling of NAOs in the NPA output:

.TB
.FM<<0L18//2L45>>
.RW-
.RW<<variable//meaning>>
.RW=
.FM<<0L18//2L45>>
.RW<<NAOC(MAXBAS)//atomic center of each NAO>>
.RW<<NAOA(MAXBAS)//angular symmetry label (Sec. B.7.5) of each NAO>>
.RW<<LTYP(MAXBAS)//`Cor', `Val', or `Ryd' label for each NAO>>
.RW<<IPRIN(MAXBAS)//principal quantum number (#In#N) of each NAO>>
.RW-
.ET

.RL16
.OS<<3//#_11. COMMON/NBMOL/#/>>


The INTEGER scalars, vectors, and arrays of this block 
store information pertaining to ``molecular units'':

.TB
.FM<<0L26//2L40>>
.RW-
.RW<<variable//meaning>>
.RW=
.FM<<0L25//2L40>>
.RW<<NMOLEC//number of molecular units>>
.RW<<MOLAT(MAXATM)//molecular unit of each atom>>
.RW<<MOLEC(MAXATM,MAXATM)//list of atoms (J) in each molecular unit (I)>>
.RW<<NMOLA//scratch storage for open-shell case>>
.RW<<MOLATA(MAXATM)//scratch storage for open-shell case>>
.RW<<MOLECA(MAXATM,MAXATM)//scratch storage for open-shell case>>
.RW-
.ET

.RL16
.OS<<3//#_12. COMMON/NBTOPO/#/>>


The INTEGER variables of this block contain atom search lists to direct
the search for NBOs and information pertaining
to the `topology' (bond connectivity) of the molecule: 

.TB
.FM<<0L25//2L40>>
.RW-
.RW<<variable//meaning>>
.RW=
.FM<<0L25//2L40>>
.RW<<IORDER(MAXATM)//permuted atom order for NBO search>>
.RW<<JORDER(MAXATM)//atom ordering for `best' resonance structure>>
.RW<<NTOPO(MAXATM,MAXATM)//number of bonds between atoms I,J>>
.RW<< //(or number of lone pairs on I, if I = J)>>
.RW<<N3CTR//number of 3-center bonds (\le  10)>>
.RW<<IC3TR(10,3)//the 3 atoms of each 3-c bond>>
.RW-
.ET

.RL16
.OS<<3//#_13. COMMON/NBDXYZ/#/>>


The DOUBLE PRECISION variables of this block store 
information pertaining to the molecular dipole moment and charge
distribution:

.TB
.FM<<0L18//2L45>>
.RW-
.RW<<variable//meaning>>
.RW=
.FM<<0L18//2L45>>
.RW<<XDIP//#Ix#N-component of molecular dipole moment (\alpha  spin)>>
.RW<<YDIP//#Iy#N-component of molecular dipole moment (\alpha  spin)>>
.RW<<ZDIP//#Iz#N-component of molecular dipole moment (\alpha  spin)>>
.RW<<CHARGE(MAXATM)//list of `uncompensated' nuclear charges (dipole loops)>>
.RW-
.ET


.RL12
.OS<<3//#_14. COMMON/NBCRD1/#/>>


The INTEGER variables of this block store general information
related to the `card image' (line) being processed
by the free-format input routines:

.TB
.FM<<0L12//2L50>>
.RW-
.RW<<variable//meaning>>
.RW=
.RW<<ICD(80)//array of Hollerith characters (\le  80) of the input line>>
.RW<<LOOK(80)//scratch buffer for card image>>
.RW<<LENGTH//length of the non-blank string in LOOK>>
.RW<<IPT//pointer to current location in ICD>>
.RW<<LFN//input file assignment>>
.RW<<NEXP//exponent of a number in exponential format>>
.RW-
.ET


.RL13
.OS<<3//#_15. COMMON/NBCRD2/#/>>


The LOGICAL variables of this block store information
related to the current line being read
by the free-format input routines.  In each case, the
variable is set .TRUE. if the specified condition is met:

.TB
.FM<<0L12//2L50>>
.RW-
.RW<<variable//condition that variable is .TRUE.>>
.RW=
.RW<<POINT//a number containing a decimal point is present>>
.RW<<END//word `END' or EOF has been encountered>>
.RW<<NEXT//ready for reading next word in line (ICD)>>
.RW<<EXP//a number in exponential notation is present>>
.RW-
.ET


.RL13
.OS<<3//#_16. COMMON/NBODAF/#/>>


The INTEGER variables of this block store information
related to the NBO direct access file (FILE48).  The PARAMETER statement
 #T
     PARAMETER (NBDAR = 100)

#Nsets the maximum number of logical records accessible in FILE48:

.TB
.FM<<0L15//2L50>>
.RW-
.RW<<variable//meaning>>
.RW=
.RW<<INBO//logical file number [48] for DAF>>
.RW<<NAV//last-accessed physical record of DAF>>
.RW<<IONBO(NBDAR)//mapping of physical and logical record numbers>>
.RW-
.ET


.RL13
.OS<<3//#_17. COMMON/NBONAV/#/>>


The INTEGER variables of this block provide scratch storage
for writing to the NBO direct access file (FILE48).  The PARAMETER statement
 #T
     PARAMETER (ISINGL = 2, LENGTH = 256)

#Nsets the FILE48 physical record LENGTH to 256 longwords 
(1024 bytes):

.TB
.FM<<0L16//2L50>>
.RW-
.RW<<variable//meaning>>
.RW=
.RW<<IXDNBO(LENGTH)//scratch array for DAF writes>>
.RW<<NBNAV//number of physical records in IXDNBO>>
.RW-
.ET


.RL13
.OS<<3//#_18. COMMON/NBGEN/#/>>


The LOGICAL variables of this block store information related
to running the GENNBO program in stand-alone mode.  In each case, the
variable is set .TRUE. if the specified condition is met:

.TB
.FM<<0L12//2L50>>
.RW-
.RW<<variable//condition that variable is .TRUE.>>
.RW=
.RW<<REUSE//``REUSE'' keyword requests use of an existing DAF>>
.RW<<UPPER//``UPPER'' keyword specifies upper-triangular matrices>>
.RW<<BOHR//``BOHR'' keyword specifies atomic units of length>>
.RW<<DENOP//density matrix is provided (i.e., ``BODM'' not set)>>
.RW-
.ET


.LM10
.HF<<C.4 DIRECT ACCESS FILE AND OTHER I/O//3//10>>
.RL55
#BC.4 DIRECT ACCESS FILE AND OTHER I/O#N

\np The principal I/O routines of Groups III-V are described in
Sections C.7-C.9.  The #Iinput#N to the NBO programs is primarily
from the standard ESS input file (LFN 5), 
and the #Ioutput#N is primarily to the
standard ESS output file (LFN 6).  Other ``matrix output'' 
(read/write) I/O is by default assigned to LFNs 31-49 (see
Table of Section B.2.4), or to a user-selectable LFN, based
on keyword entries in the $NBO keylist. 

\np The remaining two files that are routinely created or modified
by the NBO programs are the FILE48 direct access file (LFN 48)
and the FILE47 `archive' file
(LFN 47, described in Section B.7).  The latter file can also serve 
as the main input file (reassigned as LFN 5) when the NBO program is run in
stand-alone GENNBO mode.

\np From the programmer's viewpoint, the most important information
concerns the organization of the FILE48 direct access file.  The
records of this file are assigned as shown in the following 
table.  The items marked with an asterisk (*) must be provided
from the ESS program (e.g., through the FEAOIN driver), and hence
are of particular importance to the programmer:

.LM+5
.TB
.FM<<0C6//0C2//0L41>>
.RW-
.RW<<record// //content>>
.RW=
.RW<<   1 // //NBODAF common block>>
.RW<<   2 //*//Job title>>
.RW<<   3 //*//NATOMS,NDIM,NBAS,MUNIT,wavefunction flags>>
.RW<<   4 //*//IATNO,IZNUC,LCTR,LANG>>
.RW<<   5 //*//AO basis set info>>
.RW<<   8 //*//Deletion energy, total energy>>
.RW<<   9 //*//Atomic coordinates>>
.RW<<  10 //*//AO overlap matrix>>
.RW<<  11 // //PNAO overlap matrix>>
.RW<<  20 //*//AO density matrix (alpha)>>
.RW<<  21 //*//AO density matrix (beta)>>
.RW<<  22 // //Pure AO density matrix>>
.RW<<  23 // //NAO density matrix (alpha)>>
.RW<<  24 // //NAO density matrix (beta)>>
.RW<<  25 // //AO density matrix with NBO deletions (alpha)>>
.RW<<  26 // //AO density matrix with NBO deletions (beta)>>
.RW<<  27 // //NBO occupancies (alpha)>>
.RW<<  28 // //NBO occupancies (beta)>>
.RW<<  30 //*//AO Fock matrix (alpha)>>
.RW<<  31 //*//AO Fock matrix (beta)>>
.RW<<  32 // //NAO Fock matrix (alpha)>>
.RW<<  33 // //NAO Fock matrix (beta)>>
.RW<<  34 // //NBO Fock matrix (alpha)>>
.RW<<  35 // //NBO Fock matrix (beta)>>
.RW<<  40 //*//AO to MO transformation matrix (alpha)>>
.RW<<  41 //*//AO to MO transformation matrix (beta)>>
.RW<<  42 // //AO to PNAO transformation matrix>>
.RW<<  43 // //AO to NAO transformation matrix>>
.RW<<  44 // //AO to NBO transformation matrix  (alpha)>>
.RW<<  45 // //AO to NBO transformation matrix  (beta)>>
.RW<<  46 // //AO to NLMO transformation matrix>>
.RW<<  47 // //NAO to NHO transformation matrix>>
.RW<<  48 // //NAO to NBO transformation matrix>>
.RW<<  49 // //NBO to NLMO transformation matrix>>
.RW<<  50 //*//X dipole integrals>>
.RW<<  51 //*//Y dipole integrals>>
.RW<<  52 //*//Z dipole integrals>>
.RW<<  60 // //NBO labels (alpha)>>
.RW<<  61 // //NBO labels (beta)>>
.RW-
.ET
.LM10

[Cartesian coordinates (record 9) and dipole integrals
(records 50-52) should be in angstrom units.]

\np The direct access file serves as 
a principal medium of communication between
all segments of the NBO program.  Input received from the ESS
program (Section C.11) is immediately saved in the direct access file
and subsequently fetched by other subprograms, using
the fetch/save I/O routines of Section C.7.  Further information on
the structure of the direct access file is specified in COMMON
blocks 16, 17 of Section C.3.


.HF<<C.5 NAO/NBO/NLMO ROUTINES//3//10>>
.RL55
#BC.5 NAO/NBO/NLMO ROUTINES (GROUP I)#N

#IC.5.1 SR NBO Master Subroutine#N

\np The subroutine of highest precedence in the core NBO program is
SR NBO.  This routine initially requests that the input file be searched for
the $NBO keylist (See NBOINP, Section C.9).  If found, SR NBO continues by
calling three main clusters of programs, as shown below:

.LJ
.BX<<3//27//63//+1//+5>>
.BX<<3//10//30//+8//+14>>
.BX<<3//35//55//+8//+14>>
.BX<<3//60//80//+8//+14>>
.HR<<1//+3//20//27>>
.HR<<1//+3//63//70>>
.VR<<1//20//+3//+8>>
.VR<<1//45//+5//+8>>
.VR<<1//70//+3//+8>>


#T\V+30                    SR NBO(CORE,MEMORY,NBOOPT)#N






.TB
.FM<<0C20//5C20//5C20>>
.RW<<Job Initialization//NAO Formation//NBO/NLMO Formation>>
.RW<<Routines//Routines//Routines>>
.RW<<(Sec. C.5.2)//(Sec. C.5.3)//(Sec. C.5.4)>>
.ET



.FJ
In addition, SR NBO creates a new NBO direct access file (DAF) each time
it is called, and closes this file upon completion (See NBOPEN and NBCLOS,
Section C.9).

\np SR NBO is provided a memory vector, CORE, which is
`MEMORY' double precision words in length.  For modest-sized calculations
(e.g. 10 heavy atoms with a double-zeta basis set), a vector
of 50,000 words should be adequate.  Although SR NBO performs an initial
partitioning of this memory vector, the majority of the dynamic memory
allocation occurs in the NAO and NBO/NLMO formation routines, described
in Sections C.5.3 and C.5.4.

\np An array of job options, NBOOPT(10), is also passed to SR NBO.
These job options identify the current version of the NBO program
(i.e., the identity of the ESS calling program),
control program input and execution,
and determine several of the default options of the NBO analysis, as
summarized in the following table.  [Entries marked with an asterisk (*)
contain information pertaining to the identity or job options of the
calling ESS program, and thus are of special concern to the
programmer.]

.RL37
.LJ
.LM+20
.OS<<20//#IOPTION#N>>
.OS<<8//#IENTRY#N>>
#IDESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//22//28>>
.HR<<1//+1//30//80>>


.OS<<21//*>>
.OS<<20//NBOOPT(1)>>
.OS<<6//\minus 2>>
Do nothing (return control to calling program)
.OS<<6//\minus 1>>
Perform Natural Population Analysis (NPA) only
.OS<<5//0>>
Perform NPA/NBO/NLMO analyses, normal program run
.OS<<5//1>>
Perform NPA/NBO/NLMO analyses, don't read $NBO keylist
.OS<<5//2>>
Initiate energetic analysis, read one deletion from $DEL
.OS<<5//3>>
Complete energetic analysis, print the energy change

.OS<<21//*>>
.OS<<20//NBOOPT(2)>>
.OS<<5//0>>
SCF density
.OS<<5//1>>
MP first order density
.OS<<5//3>>
MP2 density
.OS<<5//4>>
MP3 density
.OS<<5//5>>
MP4 density
.OS<<5//6>>
CI one-particle density
.OS<<5//7>>
CI density
.OS<<5//8>>
QCI/CC density
.OS<<5//9>>
Density correct to second order

.OS<<20//NBOOPT(3)>>
.OS<<5//1>>
Perform the NBO/NLMO dipole analysis
(force the DIPOLE keyword)

.OS<<20//NBOOPT(4)>>
.OS<<5//1>>
Allow strongly delocalized Lewis structures
(force the RESONANCE keyword)

.OS<<20//NBOOPT(5)>>
.OS<<5//1>>
Spin-annihilated UHF (AUHF) wavefunction (unused)

.OS<<20//NBOOPT(6-9)>>
(unused)

.OS<<21//*>>
.OS<<20//NBOOPT(10)>>
.OS<<5//0>>
General version of the NBO program (GENNBO)
.OS<<5//1>>
AMPAC version
.OS<<5//6>>
GAMESS version
.OS<<5//7>>
HONDO version
.OS<<6//8x>>
GAUSSIAN-8x version

.HR<<1//+1//10//80>>
.LM10


.FJ
These options are read by job
initialization routines (Section C.5.2) and stored in COMMON/NBOPT/,
where they control events throughout the program.  [Note that NBOOPT(2)
is only used by the Gaussian versions.]


.RL35
#IC.5.2 Job Initialization Routines#N

\np The routines of this section initialize the default options
and parameters, read and store the user's $NBO keyword options:

.LM+3
.RL4
.OS<<3//#_#TSR NBOSET(NBOOPT)#N#/>>  

This routine sets default option flags
(COMMON/NBOPT/), default logical file numbers (COMMON/NBIO/), and
default thresholds (COMMON/NBTHR/) for the NBO program.  In addition,
SR NBOSET interprets the NBOOPT array, setting
option flags appropriately.

.RL8
.OS<<3//#_#TSR JOBOPT(NBOOPT)#N#/>>  

This routine is primarily responsible for reading and setting
option flags (COMMON/NBOPT/)
according to the keywords specified in the $NBO keylist.  It reads
the $NBO keywords using the free format routines described in Section C.8,
continuing until the word ``$END'' terminates the keylist.  Options which
are incompatible with the chosen wavefunction or program version are `shut
off', and other options are `turned on' in accord with the requested print
level ($NBO keyword PRINT).  All keywords which are selected in the $NBO
keylist are echoed in the output file.

.RL4
.OS<<3//#_#TSR NBODIM(MEMORY)#N#/>>  
 
Determines the scratch memory
requirements of the NBO program, as determined by the options selected
in the $NBO keylist.  Program execution halts if the memory requirements
exceed the available memory.
.LM10
.CM--------------------------------------------------------------


.RL55
#IC.5.3 NAO Formation Routines#N

\np The principal task of this cluster of routines is to control the formation
of the NAOs from the input AO basis.  In addition, these routines
are responsible for the writing (to an external file) or printing (to the
output file) of a variety of matrices in the AO, PNAO, and NAO basis sets,
according to job options requested in the $NBO keylist.  The first set of
routines are called by SR NBO:

.LM+3
.RL4
.OS<<3//#_#TSR NAODRV(DM,T,A)#/#N>>
 
This is the principal controller routine for non-orthogonal basis sets.
The scratch vector A is partitioned within this routine according to the
memory requirements of the NAO subprograms.

.RL4
.OS<<3//#_#TSR NAOSIM(DM,T,A)#/#N>>
 
This routine `simulates' SR NAODRV in the case of a semi-empirical
calculation, where the (orthonormal) basis AOs are the presumed
effective valence shell atomic orbitals, and no NAO transformation is
needed.

.RL3
.OS<<3//#_#TSR DMNAO(DM,T,A)#/#N>>
 
Performs the transformation and analysis of the open-shell AO density
matrix (alpha or beta spin) to the NAO basis.  This routine employs the
AO to NAO transformation, T, determined by SR NAODRV:

.RL2
.OS<<3//#_#TSR DMSIM(DM,T,A)#/#N>>
 
Simulates SR DMNAO for the open-shell semi-empirical case, when no
transformation is required.

.RL2
.OS<<3//#_#TSR NBODRV(DM,T,A)#N#/>>

Principal driver program for NBO formation; Section C.5.4.
.LM10
.RM80

The next set of routines are called by the main NAO driver,
SR NAODRV.  They include the principal subroutine, SR NAO,
which generates the NAOs:

.LM+3
.RL3
.OS<<3//#_#TSR SIMTRM(A,S,V,NDIM,N,IWMULP,IWCUBF)#N#/>>#N#/>>
 
Performs the similarity transformation S#ut#d*A*S leading to
Mulliken populations, with S = overlap matrix, A = bond-order matrix.

.RL2
.OS<<3//#_#TSR MULANA(BS,VMAYER,BMAYER,IWMULP,IWCUBF)#N#/>>
 
Evaluates Mulliken gross populations and performs Mayer-Mulliken
bond-order analysis (requires bond order matrix).

.RL3
.OS<<3//#_#TSR DFGORB(RENORM,DM,T,ITRAN,IWCUBF,ITOPT,LFNPR)#N#/>>
 
Performs the decomposition of `raw' cartesian #Id#N, #If#N, or #Ig#N
AO sets to pure angular symmetry AOs (e.g., 6 cartesian #Id#N \rarr
5 pure #Id#N + 1 #Is#N); cf. Section B.7.5.

.RL4
.OS<<3//#_#TSR NAO(T,S,OCC,BLK,SBLK,EVAL,C,EVECT,EVAL2,LISTAO,NBLOCK)#N#/>>
 
This is the principal routine for formation of NAOs, following
closely the algorithm described by A. E. Reed, R. B. Weinstock, and
F. Weinhold, #IJ. Chem. Phys. #B83#N, 735-746 (1985).

.RL6
.OS<<3//#_#TSR NAOANL(DM,SPNAO,BINDEX,BINDT,OVPOP,F,ENAO)#N#/>>
 
This is the principal routine for performing and printing out natural
population analysis (NPA).  The routine assigns orbital labels
and energies and writes out the NPA, natural electron configuration (NEC),
NAO-Wiberg bond index and overlap-weighted bond population tables.
[Thresholds TEST, TEST2, ALLOW, ALLOW2 test for numerical conservation of
an integer number of electrons.]

.RL3
.OS<<3//#_#TSR FRMTMO(T,TMO,C,SCR,INDEX,NCOL)#N#/>>

Forms and outputs NCOL columns of the transformation matrix to MOs
from a chosen localized set, specified by INDEX = 2 (NAO), 3 (NHO),
4 (NBO), or 5 (NLMO). Input matrix T is the transformation from AOs
to the basis set specified by INDEX, and matrices TMO, C, and SCR are
scratch arrays employed by this routine.

.LM10
.FJ
#NThe remaining routines of this section are auxiliary subroutines
called by SR NAO to perform individual steps of the NAO algorithm:
.LM+3

.RL4
.OS<<3//#_#TSR LOADAV(LISTAO,NL,M,S,NDIM,A,B,MXAOLM)#N#/>>
 
Averages the AO density matrix elements over the 2\l  + 1 components
of \l  for a particular atom, and loads the density matrix and
overlap integrals for the orbitals of LISTAO into 
matrices A, B, respectively.

.RL3
.OS<<3//#_#TSR ATDIAG(N,A,B,EVAL,C)#N#/>>
 
Solves the generalized eigenvalue problem (A \minus  EVAL*B)*C = 0
to diagonalize an atomic block.

.RL4
.OS<<3//#_#TSR SETBAS(LSTOCC,LSTEMT,NOCC,NEMT,IAT,L,NL,NF,NDIM)#N#/>>
 
Selects the `occupied' NAOs to be included in the natural minimal basis
set for a particular atom (up to Z = 105) and angular
momentum symmetry type (L), and stores them in LSTOCC.

.RL3
.OS<<3//#_#TSR NEWWTS(S,T,WT)#N#/>>

Recomputes symmetry-averaged occupancy weights for PNAOs.  This routine is
only used in conjunction with the `PAOPNAO=R' keyword.

.RL6
.OS<<3//#_#TSR WORTH(S,T,BLK,LIST,NDIM,NBAS,N,OCC,EVAL,BIGBLK)#N#/>>
 
This subroutine implements the occupancy-weighted symmetric
orthogonalization (OWSO), a key feature of the NAO algorithm.  [Note
that BLK and BIGBLK share the same storage area, though they
are dimensioned differently.  The routine includes three
numerical thresholds, WTTHR (10#u\minus 3#d) for occupancy weight,
DIAGTH (10#u\minus 12#d) for Jacobi diagonalization, and DANGER (10#u3#d)
for linear dependence difficulties.]

.RL2
.OS<<3//#_#TSR SHMDT(T,S,NDIM,NBAS,NOCC,LSTOCC,NEMT,LSTEMT,SBLK)#N#/>>
 
Schmidt orthogonalization of column vectors of T.

.RL3
.OS<<3//#_#TSR NEWRYD(T,S,TPNAO,DMBLK,SBLK,EVECT,OCC,EVAL,EVAL2,LIST,IRPNAO)#/>>

#NComputes new Rydberg NAOs after Schmidt orthogonalization of
the Rydberg space to the NMB set.

.RL3
.OS<<3//#_#TSR RYDIAG(T,S,TPNAO,DMBLK,SBLK,OCC,EVAL,EVECT,EVAL2,>>

.OS<<3//IORB,NC,NM,NSTART,NRYDC,LARC,LIST,IRPNAO)#/>>
 
#NDiagonalizes an atomic Rydberg block and updates the PNAO
transformation matrix.

.RL7
.OS<<3//#_#TSR RYDSEL(LSTEMT,NEMT,NSEL1,LIST1,NSEL2,LIST2,WT)#N#/>>
 
Partitions Rydbergs into `significantly occupied' (> WTTHR)
and `negligibly occupied' (\le  WTTHR) sets, assigning the
latter to have equal (non-zero) occupancy weighting.  This
avoids numerical singularities associated with the OWSO occupancy
weighting for orbitals of negligible occupancy, effectively
replacing OWSO by ordinary L\umlaut owdin-orthog#|onalization
of these `residual' Rydbergs among themselves.  [Threshold 
WTTHR (10#u\minus 4#d) controls singularities of the inverse
square-root weighting matrix.]

.RL2
.OS<<3//#_#TSR REDIAG(DM,T,TPNAO,EVAL,BLK,C,IRANK,IRPNAO)#N#/>>
 
Rediagonalizes the atomic density matrix blocks after symmetry
averaging.

.RL2
.OS<<3//#_#TSR REDBLK(T,TPNAO,IL,DM,BLK,EVAL,C,NF,IORB,NC,IRANK,IRPNAO)#N#/>>
 
Finds the rediagonalization transformation for a specific
\l -symmetry atomic subblock of the density matrix.


.RL55
.LM10
.RM80
#IC.5.4 NBO/NLMO Formation Routines#N

.FJ
\np The master routine of this cluster is
SR\thsp \thsp NBODRV(DM,T,A), which partitions the scratch storage
vector (A) according to the memory requirements of the NBO formation
and analysis subprograms and controls the calculation of the
transformation (T) from NAOs to NBOs using the NAO density matrix (DM).
SR NBODRV calls either SR NATHYB (for the default NBO search) or SR CHSDRV
(for the $CHOOSE directed NBO search) to form the NBOs.  It
also calls the NLMO
formation routine (SR NLMO) and dipole analysis routine (SR DIPANL).
According to job options selected in the $NBO keylist, SR NBODRV also
transforms and outputs a variety of matrices in the PNHO, NHO, PNBO, NBO,
PNLMO, and NLMO basis sets.  [Note that the first NATOMS*NATOMS
elements of the A vector store the Wiberg bond index elements
determined in the NAO routines; these should not be destroyed until
calculation of NBOs is complete.]

.RL21
\np The following routines are called by SR NBODRV:

.LM+3
.OS<<3//#_#TSR NATHYB(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,>>

.OS<<3//P,TA,HYB,VA,VB,TOPO)#/>>
 
#NThis routine performs the basic NBO search, the central task of
NBO analysis, closely following the description given by
J. P. Foster and F. Weinhold, #IJ. Am. Chem. Soc. #B102#N, 
7211-7218 (1980).  The routine constructs the 
orthogonal matrix (T) for the NAO to NBO
transformation from the input NAO density matrix (DM).  The efficiency
of the search procedure is enhanced by using the 
NAO-Wiberg bond index as a `GUIDE' to order the NBO search.

[Beware the IBXM bond orbital permutation list (!), which reorders the
LABEL array of COMMON/NBBAS/.  The occupancy threshold, THRESH, determines
whether an NBO is accepted during the search for bond orbitals (cf. SR CYCLES).
Two numerical thresholds
(PRJTHR, PRJINC) control possible linear dependencies:  In
the main loops over 1-c, 2-c (and 3-c) functions, each prospective
NBO is checked for possible redundancy with previous NHOs by
the PRJEXP (projection operator expectation value) test.  The
threshold PRJTHR for a `new' hybrid is initially set
conservatively low (0.20),
but will be auto-incremented by PRJINC (0.05) as needed to prevent
linear dependency; any numerical singularity triggers IALARM and
causes PRJTHR to be incremented and the entire NBO search repeated.]

.RL5
.OS<<3//#_#TSR CHSDRV(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,>>

.OS<<3//P,TA,HYB,VA,VB,TOPO)#/>>
 
#NThis routine, the ``$CHOOSE driver,'' reads the $CHOOSE keylist,
setting up the arrays NTOPO and I3CTR of COMMON/NBTOPO/ which will
control the directed NBO search of SR CHOOSE.

.RL4
.OS<<3//#_#TSR CHOOSE(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,>>

.OS<<3//P,TA,HYB,VA,VB,TOPO,IFLG)#/>>
 
#NThis routine is essentially similar to SR NATHYB, but the search
loops are directed by the $CHOOSE specification.

.RL3
.OS<<3//#_#TSR SRTNBO(T,BNDOCC)#N#/>>
 
Reorders (dangerous!) the NBOs according to bond type and constituent atomic
centers.  NBOs are ordered BD (and 3C), CR, LP, LP*, RY*, BD* (and 3C*).
Note that this step is not required for the proper execution of any of the
NBO analysis or NLMO formation routines, but it leads to more readable
output.

.RL7
.OS<<3//#_#TSR XCITED(DM,T,HYB,THYB,S,OCC,SCR,ISCR)#N#/>>
 
Examines PNHO overlaps to determine whether NBOs were properly labelled
as `bonds' (unstarred, Lewis) or `antibonds' (starred, non-Lewis)
in the NBO formation routines (SR NATHYB and SR CHOOSE).  If incorrect
nodal character is recognized in a bond or antibond (generally indicative
of an excited state), a warning is printed
and the orbital is relabelled.  Note that this will probably mix the
NBO ordering set by SR SRTNBO.

.RL3
.OS<<3//#_#TSR ANLYZE(T,BNDOCC,HYB,HYCOEF,THYB)#N#/>>
 
Prints out the principal table (Section A.3.3) 
of NBO analysis [using the IBXM ordering!],
expressing each NHO in #Isp#u\lambda #d#N form.
 
.RL3
.OS<<3//#_#TSR HTYPE(HYB,LTYP,MXAO,NH,COEF,PCT,NL,ISGN)#N#/>>

Analyzes input hybrid for polarization coefficient and percentages
of each angular momentum component (accepts up to #Ig#N orbitals).

.RL3
.OS<<3//#_#TSR FRMHYB(HYB,THYB,COEFF,HYCLEF,KL,KU,NHYB)#N#/>>

Forms the NAO to NHO transformation (THYB) and saves it on the DAF.

.RL5
.OS<<3//#_#TSR HYBDIR(BNDOCC,ATCOOR,THYB,TBND,SCR)#N#/>>
 
Computes hybrid directionality and bond bending angles as determined from
percentage #Ip#N-character for selected
NBOs, and prints the BEND table 
(Section A.3.4).  [Keyword-selectable thresh#|olds
ATHR (angular deviation), PTHR (% #Ip#N-character), and ETHR (occupancy)
control printing.]

.RL2
.OS<<3//#_#TSR HYBCMP(XYZ,PCENT,IHYB,JCTR,HYB)#N#/>>
 
Finds direction and percentage #Ip#N-character of a given hybrid.

.RL2
.OS<<3//#_#TSR FNDMOL(IATOMS)#N#/>>
 
Finds `molecular units' from NBO connectivity.

.RL3
.OS<<3//#_#TSR NBOCLA(BNDOCC,ACCTHR)#N#/>>
 
Classifies NBOs according to donor/acceptor type, number of atomic centers,
and parent molecular unit.

.RL4
.OS<<3//#_#TSR FNBOAN(BNDOCC,F,MOLNBO)#N#/>>
 
Performs the 2nd-order perturbation theory energy analysis of
the NBO Fock matrix and prints the table (Section A.3.5).  [Thresholds ETHR1
(intramolecular) and ETHR2 (intermolecular) control printing.]

.RL2
.OS<<3//#_#TSR NBOSUM(F,BNDOCC,LIST,LISTA,SCR)#N#/>>
 
Prepares and prints the NBO summary table (Section A.3.6).

.RL4
.OS<<3//#_#TSR GETDEL(IBO,OCC,THR1,THR2,NL,LIST,DEL,DELOC,IFLG)#N#/>>

Assembles the delocalization list, LIST(NL), for the IBO#uth#d 
NBO.  Only intramolecular and intermolecular delocalizations which are
stronger than THR1 and THR2 (in kcal\thsp mol#u\minus 1#d), respectively,
are included in the list.

.RL3
.OS<<3//#_#TSR BLDSTR(IBO,IL,NL,LIST,ML,ISTR)#N#/>>
 
Builds a character string containing delocalization information for the
NBO summary table.

.RL5
.OS<<3//#_#TSR NLMO(N,A,EVAL,EVEC,TSYM,RESON,NOCC,IALARM)#N#/>>

This is the main routine for determination of the NLMOs, following
closely the description given by A. E. Reed and F. Weinhold,
#IJ. Chem. Phys. #B83#N, 1736-1740 (1985).  [Numerical thresholds
DIFFER (10#u\minus 5#d), DONE (10#u\minus 10#d), and EPS (10#u\minus 11#d)
control the modified Jacobi diagonalizations.]

.RL3
.OS<<3//#_#TSR LMOANL(T,S,RESON,OCC,TS,BORDER,OWBORD,ATLMO,SIAB,NOCC,NAB)#/>>

#NPrints out details of the NAO\rarr NLMO transformation and
the NAO/NLMO bond order table (Section B.6.2).

.RL2
.OS<<3//#_#TSR DIPANL(DM,T,C,TNBO,DX,DY,DZ,SCR,INDEX)#N#/>>
 
Calculates and prints out the DIPOLE analysis table (Section B.6.3).

.RL3
.OS<<3//#_#TSR DIPELE(DXYZ,C,T,SCR,ETA,TOANG,NOCC,INDEX)#N#/>>
 
Evaluates the #Ix,y,z#N (INDEX = 1,2,3) electronic dipole moment
contributions, including delocalization contributions, for each
occupied NBO.

.RL2
.OS<<3//#_#TSR DIPNUC(DX,DY,DZ,ATCOOR,ETA,NOCC)#N#/>>

Evaluates the nuclear contributions (DX, DY, DZ) to the molecular
dipole moment.

.LM10
.RL15
The following routines are called by SR NATHYB and SR CHOOSE 
in calculating the NBOs.  Overall supervision
of this set of routines is exercised by SR CYCLES.  Other routines
are associated with specific steps of the NBO algorithm:

.LM+3
.RL3
.OS<<3//#_#TSR CORE(DM,T,BORB,POL,Q,HYB,BNDOCC,IBD,DETAIL,LFNPR)#N#/>>

Performs the first step in the search for NBOs.  This routine identifies
core orbitals and depletes the NAO density matrix of their contributions.

.RL3
.OS<<3//#_#TFN IWPRJ(NCTR)#N#/>>
 
This function returns zero (no projection wanted)
if still on the same atomic center, or one (projection operator should
be formed) if this is a new center.

.RL4
.OS<<3//#_#TSR DEPLET(DM,T,Q,POL,BORB,BNDOCC,NBD)#N#/>>
 
`Depletes' density matrix of contribution from bond orbital (BORB), by
subtracting its diagonal contribution from the spectral expansion of
the density operator.  This insures that the same electron pair will
not be found twice in the NBO loops.

.RL3
.OS<<3//#_#TSR LOAD(DM,IAT1,IAT2,IAT3,BLK,NB)#N#/>>
 
Loads the appropriate atomic blocks of the density matrix
into the local (2-c, 3-c) density matrix subblock (BLK), in
preparation for diagonalization.

.RL4
.OS<<3//#_#TSR PRJEXP(BORB,IAT1,IAT2,IAT3,Q,P,PK,HYB,VA,VB,HYBEXP)#N#/>>

Determines how much of a prospective bond orbital (BORB) is composed
of hybrids already used.  The projection operator onto the space of
previously accepted hybrids is used to evaluate the expectation
value of each hybrid component of BORB.

.RL3
.OS<<3//#_#TSR STASH(BORB,IBD,IAT1,IAT2,IAT3,POL,Q,HYB)#N#/>>

Decomposes bond orbital (BORB) into constituent normalized hybrids
and stores them in the hybrid array (Q).

.RL4
.OS<<3//#_#TSR ORTHYB(Q,S,TA,EVAL,C,IALARM,IFLG)#N#/>>

Performs symmetric (L\umlaut owdin) orthogonalization on occupied
atomic hybrids (PNHOs) to give final NHOs.  [Threshold TOOSML
(10#u\minus 4#d) turns on the alarm (IALARM) to warn of numerical
instabilities due to linear dependence.]

.RL3
.OS<<3//#_#TSR FRMPRJ(P,IA,Q,NK,PK,VK,PI)#N#/>>

Forms projection matrix to annihilate components of the occupied
atomic hybrids on a given center.

.RL4
.OS<<3//#_#TSR AUGMNT(P,BLK,C,EVAL,DM,TA,BORB,V,LARC,IA,NOCC,NORB)#N#/>>

This routine augments the set of occupied atomic hybrids on a center
with a sufficient number of Rydberg AOs (in order of occupancy) to
complete the span of the basis set on that atom. 

.RL3
.OS<<3//#_#TSR REPOL(DM,Q,POL,BLK,EVAL,C,NBD)#N#/>>

Diagonalizes each 2x2 block of the density matrix in the basis of
final NHOs to get the optimal polarization coefficients for each NBO. 

.RL3
.OS<<3//#_#TSR FORMT(T,Q,POL)#N#/>>
 
Constructs the final NAO to NBO transformation matrix (T) from
the final array of NHOs (Q) and polarization coefficients (POL).

.RL6
.OS<<3//#_#TSR CYCLES(ITER,THRESH,GUIDE,BNDOCC,TOPO,ICONT)#N#/>>

Controls the overall search for an acceptable resonance structure,
including the lowering of the occupancy threshold (THRESH) for the
RESONANCE keyword.  Decides whether a structure is acceptable,
initiates reordered searches over atoms for alternative resonance structures,
and returns with the best overall structure.  Prints the 
initial table (Section A.3.3) of the NBO output.

.LM10

The final routines of this group are auxiliary to the formation
of NLMOs, called by SR NLMO:

.LM+3
.RL5
.OS<<3//#_#TSR SYMUNI(TSYM,A,COS,SIN,OVLP,BLK,EVAL,NROT,NIUNIQ,NJUNIQ,ILIST,>>

.OS<<3//JLIST,NOFF,IOFF,JOFF,NDIM)#/>>

#NSymmetrizes the unitary transformation matrix (TSYM) to preserve
symmetries inherent in the density matrix, using symmetric
orthogonalization of columns (if necessary) to preserve unitarity.

.RL5
.OS<<3//#_#TSR SYMORT(S,T,BLK,NDIM,N,EVAL)#N#/>>
 
Symmetric orthogonalization of a set of column vectors (T).  [Thresholds
DIAGTH (10#u\minus 12#d) for off-diagonal Jacobi diagonalization
and DANGER (10#u3#d) to detect singularities of the overlap matrix;
all eigenvalues of S must be less than DIAGTH*DANGER.]
.LM10
.RM80
.CM------------------------------------------------------------------
.HF<<C.6 ENERGY ANALYSIS ROUTINES//3//10>>
.RL55
#BC.6 ENERGY ANALYSIS ROUTINES (GROUP II)#N

.FJ
The small set of routines in this group carry out the second main
task of NBO analysis, the NBO Energetic Analysis (``deletions,''
associated with inclusion of a $DEL keylist; Section B.5).  These routines
depend on the presence of a Fock matrix, and are bypassed in
any non-SCF calculation.

Overall control of Group II routines is with SR NBOEAN, which in turn
calls the remaining programs of this group:

.LM+3
.OS<<3//#_#TSR NBOEAN(A,MEMORY,NBOOPT,IDONE)#N#/>>

The task performed by this subroutine is dependent of the value of
NBOOPT(1).  If set to 2, this routine initiates (by calling SR NBODEL)
the calculation of the next NBO deletion of the $DEL keylist.  If set
to 3, this routine completes the NBO deletion by computing the energy
for the deletion.  INTEGER variable IDONE is set to 1 if no additional
deletions are found in the $DEL keylist.

.RL5
.OS<<3//#_#TSR NBODEL(A,MEMORY,IDONE)#N#/>>
 
Controls the calculation of the new AO density matrix from the requested
deletion in the $DEL keylist.  A modified NBO Fock matrix is created
(SR DELETE) and diagonalized (SR JACOBI), leading to a new AO density
matrix (SR NEWDM).  This routine also prints the NBO deletions table
(Section B.6.10).

.RL3
.OS<<3//#_#TSR DELETE(F,TRF,NDIM,IDEL,LEN,ITYPE,NDEL,NTRUNC,DONE,ISPIN)#N#/>>

Reads the $DEL list for the next deletion, deletes (sets 
to zero) the appropriate
elements from the Fock matrix, and prints out the deletion specification
Section B.6.10).

.RL2
.OS<<3//#_#TSR NEWDM(DM,U,EIG,NDIM,IDEL,LEN,NDEL,ITYPE,NMOOCC,ISPIN)#N#/>>
 
Constructs a new density matrix corresponding to the deleted Fock matrix.

.RL3
.OS<<3//#_#TSR RNKEIG(RANK,EIG,N,NDIM,ARCRNK)#N#/>>

Ranks the eigenvalues found in vector EIG (lowest eigenvalue having
first rank).  I = ARCRNK(N) is the entry whose rank is N.

.RL2
.OS<<3//#_#TSR SIMLTR(N,NDIM,F,U,R,S,KNTROL)#N#/>>

Performs the similarity transform U#ut#d*F*U on a packed
upper-triangular matrix F.
.LM10
.RM80
.HF<<C.7 DIRECT ACCESS FILE ROUTINES//3//10>>
.RL55
#BC.7 DIRECT ACCESS FILE ROUTINES (GROUP III)#N

.FJ
\np The routines of Group III are involved in communication between
the NBO programs and the FILE48
direct access file (DAF), whose contents
are described in Section C.4.  Two levels of I/O routines are employed.

\np The higher-level `fetch/save' routines are called directly by the NBO
subroutines.
In most cases, the
function of the fetch/save routines can be recognized by its name or argument
list; e.g., ``FETITL(TITLE)'' fetches
the job title line, ``FEFAO(F,IWFOCK)'' fetches 
the AO Fock matrix (FAO),
and so forth.  Each routine can also be associated with a
logical record number (IDAR) of the direct access file (Section C.4),
where the I/O item is stored.  We list these 
routines in order of appearance, together with the associated
direct access file record number(s) IDAR, without further description:

.LJ
.TB
.FM<<0L28//0C5//5L28//0C5>>
.RW-
.RW<<routine//IDAR//routine//IDAR>>
.RW=
.RW<<SR FETITL(TITLE)//2//SR SVTLMO(T)//49>>
.RW<<SR FEE0(EDEL,ETOT)//8//SR FETLMO//49>>
.RW<<SR SVE0(EDEL)//8//SR SVTNHO//47>>
.RW<<SR FECOOR(ATCOOR)//9//SR FETNHO//47>>
.RW<<SR FESRAW(S)//10//SR SVPPAO(DM)//22>>
.RW<<SR FEDRAW(DM,SCR)//20,21//SR FEPPAO(DM)//22>>
.RW<<SR FEFAO(F,IWFOCK)//30,31//SR SVTNAO(T)//43>>
.RW<<SR FEAOMO(T,IT)//40,41//SR FETNAO(T)//43>>
.RW<<SR FEDXYZ(DXYZ,I)//50-52//SR SVNLMO(T)//46>>
.RW<<SR SVNBO(T,OCC,ISCR)//44,45//SR FENLMO(T)//46>>
.RW<<SR FENBO(T,OCC,ISCR,NELEC)//44,45//SR SVDNAO(DM)//23,24>>
.RW<<SR FETNBO(T)//44,45//SR FEDNAO(DM)//23,24>>
.RW<<SR SVPNAO(T)//42//SR SVFNBO(F)//34,35>>
.RW<<SR FEPNAO(T)//42//SR FEFNBO(F)//34,35>>
.RW<<SR SVSNAO(S)//11//SR SVNEWD(DM)//25,26>>
.RW<<SR FESNAO(S)//11//SR FENEWD(DM)//25,26>>
.RW<<SR SVTNAB(T)//48//SR FEINFO(ICORE,ISWEAN)//3>>
.RW<<SR FETNAB(T)//48//SR FEBAS(NSHELL,NEXP,ISCR)//5>>
.RW-
.ET
.FJ

\np In turn, the fetch/save routines call the following lower-level,
primitive subprograms,
which open, close, read, write, and test the contents of the DAF
(these are heavily modified versions of the direct
access file subroutines of HONDO):

.RL11
.LM+3
.OS<<3//#_#TSR NBOPEN(NEW,ERROR)#N#/>>

Opens a new or existing unformatted DAF depending in the value of logical
variable NEW.  Record lengths are currently set at 256 (LENGTH) single
precision words (1024 bytes), and
up to 100 (NBDAR) logical records can be written.  Note that logical records
and physical records of the DAF are not equivalent; single logical records
can span several physical records and need not be ordered sequentially.
The array IONBO (in COMMON/NBODAF/) maps each logical record with its
associated physical records.  The first physical record of the DAF is
reserved for COMMON/NBODAF/.  [Note: Some machines may require 
that you alter the parameters LENGTH (the chosen
record length) and ISINGL (a record length scaling factor).#N]

.RL3
.OS<<3//#_#TSR NBWRIT(IX,NX,IDAR)#N#/>>

Writes NX double precision words of array IX to logical record number IDAR
of the NBO DAF.

.RL3
.OS<<3//#_#TSR NBREAD(IX,NX,IDAR)#N#/>>
 
Reads NX double precision words of the logical record number IDAR of the 
NBO DAF.

.RL3
.OS<<3//#_#TSR NBCLOS#N#/>>
 
Rewrites common block /NBODAF/ on the first physical record of the DAF, and
closes the file.

.RL3
.OS<<3//#_#TSR NBINQR(IDAR)#N#/>>

Inquires whether information has been stored in logical record IDAR of
the direct access file, and sets IDAR=0 if the record is empty.
.FJ
.LM10
.RM80
.HF<<C.8 FREE FORMAT INPUT ROUTINES//3//10>>
.RL55
#BC.8 FREE FORMAT INPUT ROUTINES (GROUP IV)#N

\np The routines of Group IV are the small set of system-independent
free-format input routines that are used in reading the various
keylists and datalists of the input 
file.  The routines of this group are the
`primitives' that read and interpret individual keywords or
entries of a keylist.  They are called by higher-level
I/O routines (such as SR JOBOPT of Group I) throughout the NBO program.

The free-format input primitive routines are:

.LM+3
.OS<<3//#_#TSR STRTIN(LFNIN)#N#/>>

Initializes input from the LFNIN input file.

.RL5
.OS<<3//#_#TSR RDCARD#N#/>>

Reads the next `card' (line) of the input file, and stores this line in
the integer array ICD in COMMON/NBCRD1/ with all lower case characters
converted
to upper case.  Logical variable END in COMMON/NBCRD2/ is set to .TRUE. if
the end-of-file is encountered.

.RL6
.OS<<3//#_#TSR IFLD(INT,ERROR)#N#/>>

Searches input file LFNIN for the next string of non-blank characters,
and checks to see if they form an integer.  If so, the numerical value
of the integer is placed in INT.  If not, the logical variable ERROR is
set to .TRUE. and INT is set positive (indicating an ``END'' terminating
mark or end-of-file was encountered) or negative (indicating that the
character string is not an integer).

.RL4
.OS<<3//#_#TSR RFLD(REAL,ERROR)#N#/>>

Similar to SR IFLD, but for a real number REAL.  This routine will accept
real numbers in a variety of different formats.  For example, 1000 can be
represented by 1000, 1000.0, 1.0E3, D3, 1+3, etc.

.RL5
.OS<<3//#_#TSR HFLD(KEYWD,LENG,ENDD)#N#/>>

Similar to SR IFLD and RFLD, but for a Hollerith array KEYWD(LENG).
The logical variable ENDD is set to .TRUE. if the ``END'' terminating
mark or the
end-of-file is encountered.  On return to the calling subroutine, LENG
is set to the length of the string in KEYWD or to zero if the end-of-file
is encountered.

.RL6
.OS<<3//#_#TSR FNDFLD#N#/>>

Searches for the next non-blank field on the input file, reading
additional lines if necessary.  Commas and equal signs are treated as
blanks, and any character string which follows an exclamation point
is treated as an arbitrary comment, and is ignored.
The contents of this field are stored
in the integer array LOOK of length LENGTH in COMMON/NBCRD1/.
 
.OS<<3//#_#TFN EQUAL(IA,IB,L)#N#/>>

This logical function tests the equivalence of the first `L' elements of
the Hollerith strings IA and IB.
.DF\np =\thsp \nthsp
.LM10
.RM80
.HF<<C.9 OTHER SYSTEM-INDEPENDENT I/O ROUTINES//3//10>>
.RL55
#BC.9 OTHER SYSTEM-INDEPENDENT I/O ROUTINES (GROUP V)#N

.FJ
\np This section summarizes the I/O routines of Group V.  These routines
perform a variety of auxiliary I/O tasks, such as the reading
or writing of matrices, or perform functions closely related to I/O.

\np The first set of programs in this group are responsible for
searching for the $GENNBO, $NBO, $CORE, $CHOOSE, and $DEL identifiers
of the job input file LFNIN:

.LM+3
.RL4
.OS<<3//#_#TSR GENINP(NEWDAF)#N#/>>

Searches for the $GENNBO identifier.  In addition, this routine
reads in the keywords of the $GENNBO keylist (see Section B.7),
setting the option flags of COMMON/NBOPT/ and COMMON/NBGEN/ appropriately.

.RL3
.OS<<3//#_#TSR NBOINP(NBOOPT,IDONE)#N#/>>

Searches for the $NBO identifier according to the program version number,
NBOOPT(10).  The integer variable IDONE is
set to 0 if this identifier is located, or 1 otherwise.

.RL3
.OS<<3//#_#TSR CORINP(IESS,ICOR)#N#/>>

Searches for the $CORE identifier according to the program version number,
IESS.  The integer variable ICOR is
set to 1 if this identifier is located, or 0 otherwise.

.RL3
.OS<<3//#_#TSR CHSINP(IESS,ICHS)#N#/>>

Searches for the $CHOOSE identifier according to the program version number,
IESS.  The integer variable ICHS is
set to 1 if this identifier is located, or 0 otherwise.

.RL3
.OS<<3//#_#TSR DELINP(NBOOPT,IDONE)#N#/>>

Searches for the $DEL identifier according to the program version number,
NBOOPT(10).  The integer variable IDONE is
set to 0 if this identifier is located, or 1 otherwise.

.LM10
\np The remaining routines of this group perform miscellaneous I/O functions:

.LM+3
.RL3
.OS<<3//#_#TSR RDCORE(JCORE)#N#/>>

Initializes the atomic core array (IATCR on COMMON/NBATOM/), and reads
the entries of the $CORE keylist.

.RL6
.OS<<3//#_#TSR WRPPNA(T,OCC,IFLG)#N#/>>

Writes the transformation from `pure'
AOs to PNAOs, the NAO labels (NAOCTR, NAOL, and LSTOCC from COMMON/NBBAS/),
and PNAO occupancies (diagonal PNAO density matrix elements) to an external
file (LFN = \minus IFLG).  Pure AOs (PAOs) are obtained
from `raw' cartesian AOs by the transformations of SR DFGORB.

.RL3
.OS<<3//#_#TSR RDPPNA(T,OCC,IFLG)#N#/>>

Reads the transformation from `pure' AOs (PAOs) to PNAOs, NAO labels, and
PNAO occupancies from an external file (LFN = \minus IFLG/1000)  (cf.
SR WRPPNA).

.RL5
.OS<<3//#_#TSR WRTNAO(T,IFLG)#N#/>>

Writes the AO to NAO transformation (fetched from the DAF), NAO labels, and
the PNAO overlap matrix (also fetched from the DAF) to an external file
(LFN = \minus IFLG).  Note that T is the PNAO overlap matrix when control is
returned to the calling routine.

.RL6
.OS<<3//#_#TSR RDTNAO(DM,T,SCR,IFLG)#N#/>>

Reads the AO to NAO transformation, NAO labels, and PNAO overlap matrix from an
external file (LFN = \minus IFLG/1000).  The transformation and overlap
matrices are saved on the
DAF, and the input AO density matrix is transformed to the NAO basis.  Note
that T is the PNAO overlap matrix on return to the calling routine
(cf. SR WRTNAO).

.RL3
.OS<<3//#_#TSR WRTNAB(T,IFLG)#N#/>>
 
Writes the NAO to NBO transformation and NBO info (LABELS and IBXM arrays of
COMMON/NBBAS/) to an external file (LFN = \minus IFLG).

.RL4
.OS<<3//#_#TSR RDTNAB(T,DM,BNDOCC,SCR,IFLG)#N#/>>

Reads the NAO to NBO transformation and NBO info from an external
disk file (LFN = \minus IFLG/1000).  The input NAO density matrix is also
transformed to the NBO basis, and the NBO occupancies are stored in
BNDOCC (cf. WRTNAB).

.RL4
.OS<<3//#_#TSR WRTNBO(T,BNDOCC,ISCR,IFLG)#N#/>>

Writes the AO to NBO transformation, the NBO occupancies, and additional
NBO info (NBOUNI, NBOTYP, LABEL, IBXM, and IATNO arrays) to an external
disk file (LFN = \minus IFLG).

.RL3
.OS<<3//#_#TSR WRNLMO(T,DM,ISCR,IFLG)#N#/>>

Similar to SR WRTNBO but for NLMOs.  Note that the NLMO labels are
identical to the NBO labels.

.RL5
.OS<<3//#_#TSR WRBAS(SCR,ISCR,LFN)#N#/>>

Writes the atomic coordinates and AO basis set information to the `AOINFO'
file LFN.  The information contained in this file is identical to that of the
$COORD, $BASIS, and $CONTRACT datalists of the GENNBO input file (see Section
B.7). For more information on the file format, see the subroutine source code.

.RL2
.OS<<3//#_#TSR WRARC(SCR,ISCR,LFN)#N#/>>

Writes the `ARCHIVE' file LFN (see Section B.7).

.RL6
.OS<<3//#_#TSR AOUT(A,MR,NR,NC,TITLE,INDEX,IFLG)#N#/>>

General utility to write matrix A(MR,1) to an external file (LFN = \minus IFLG)
or print it to the output file (IFLG = number of columns to print, `FULL',
`VAL', or `LEW').  TITLE is a CHARACTER*80 matrix label, and the
rows of A are labelled according to the value of INDEX = 0 (atoms), 1 (AOs),
2 (NAOs), 3 (NHOs), 4 (NBOs), or 5 (NLMOs).  This routine calls SR APRINT or
SR AWRITE.

.RL4
.OS<<3//#_#TSR APRINT(A,MR,NR,NC,TITLE,INDEX,MCOL)#N#/>>

Prints MCOL columns of matrix A to the output file.  The format of the
matrix is chosen according to the magnitude of the largest matrix element
in A (cf. SR AOUT).

.RL2
.OS<<3//#_#TSR AWRITE(A,MR,NR,NC,TITLE,LFN)#N#/>>

Writes matrix A to external disk file LFN (cf. SR AOUT).

.RL5
.OS<<3//#_#TSR AREAD(A,MR,NR,NC,JOB,LFN,ERROR)#N#/>>

Reads NC columns of the matrix A(MR,1) from the external file LFN.
The job title in the external file is returned to the calling subroutine
in the Hollerith array, JOB(20), and the LOGICAL 
variable ERROR is set to .TRUE. if an error occurred while reading.

.RL3
.OS<<3//#_#TSR OUTPUT(A,MR,MC,NR,NC)#N#/>>
 
Prints the matrix A(MR,MC) to the standard output file.  This routine is
called only when the print formats of SR APRINT are unsuitable for matrix A.

.RL9
.OS<<3//#_#TSR INTERP(STRING,LEN,IFLG,LFN,READ,ERROR)#N#/>>

Interprets the Hollerith array STRING(LEN), storing the result in IFLG.  The
contents of STRING can be any of the read/write/print parameters
such as `W38', `PVAL', `R43', etc., described in Section B.2.4,
and the resulting value of IFLG is determined according to the 
discussion of COMMON/NBOPT/ in
Section C.3.  When this routine is called, IFLG should be set to its
default value,
LFN should be the default file for writing or reading, and LOGICAL variable
READ should be set to .TRUE. if reading from an external file is allowed. 
The LOGICAL variable ERROR is set to .TRUE. if STRING is uninterpretable.

.RL3
.OS<<3//#_#TFN IOINQR(IFLG)#N#/>>

Interprets IFLG as to whether the I/O item should be printed (IOINQR = `PRNT'),
read (IOINQR = `READ'), or written out (IOINQR = `WRIT') to an external file.

.RL2
.OS<<3//#_#TSR LBLAO#N#/>>

Forms labels for AOs and stores them in COMMON/NBLBL/.

.RL2
.OS<<3//#_#TSR LBLNAO#N#/>>

Forms labels for NAOs and stores them in COMMON/NBLBL/.

.RL2
.OS<<3//#_#TSR LBLNBO#N#/>>

Forms labels for NBOs and stores them in COMMON/NBLBL/.

.RL2
.OS<<3//#_#TSR LBLNHO(INHO,INBO,ICTR,NCTR)#N#/>>

Forms labels for NHOs and stores them in COMMON/NBLBL/.

.LM10
.RM80
.HF<<C.10 GENERAL UTILITY ROUTINES//3//10>>
.RL55
#BC.10 GENERAL UTILITY ROUTINES (GROUP VI)#N

#NThe utility routines of Group VI perform a variety of mathematical
and other general tasks (such as solving sets of linear
equations), and are called from routines
throughout the NBO program.  They are grouped in alphabetical
order (except for the final group of routines controlled by
the SR LINEQ driver):

.FJ
.LM+3
.RL3
.OS<<3//#_#TSR ANGLES(X,Y,Z,THETA,PHI)#N#/>>

Converts cartesian coordinates (X,Y,Z) to corresponding polar
angle THETA and azi#|muthal angle PHI in spherical polar coordinates.

.RL3
.OS<<3//#_#TFN BDFIND(IAT,JAT)#N#/>>

LOGICAL function BDFIND is set to .TRUE. if there is at least one bond
between atoms IAT, JAT.

.RL4
.OS<<3//#_#TSR CHEM(NAT,NATOMS,LISTA,NL,ISTR)#N#/>>

Builds a `chemical formula' for the list of atoms in LISTA having
been identified as belonging to a particular `molecular unit'.  The
chemical formula is stored in the Hollerith array ISTR(NL). 

.RL3
.OS<<3//#_#TSR CONSOL(AUT,ALT,NDIM,N)#N#/>>

Consolidates an upper-triangular (AUT) and lower-triangular (ALT)
matrix in a single matrix, stored in AUT. 

.NH
.RL3
.OS<<3//#_#TSR CONVIN(IJ,LEN,IK,ERROR)#N#/>> 

Converts the Hollerith array IJ(LEN) into an integer IK.  This is the 
inverse of SR IDIGIT.
.HY

.RL2
.OS<<3//#_#TSR CONVRT(N,NC1,NC2)#N#/>>
 
Converts a 2-digit integer N to two Hollerith characters NC1, NC2.

.RL2
.OS<<3//#_#TSR COPY(A,B,NDIM,NR,NC)#N#/>>
 
Copies matrix A to matrix B.

.RL5
.OS<<3//#_#TSR CORTBL(IAT,ICORE,IECP)#N#/>>
 
Stores the nominal ``core table,'' giving the number of core
#Is#N, #Ip#N, #Id#N, #If#N orbitals for elements 1-105 (H to Lw,
and elements 104, 105).  This table controls the number of
high-occupancy unhybridized NAOs that will be isolated and
removed as core NBOs (taking account also of any effective
core potential).

.RL3
.OS<<3//#_#TSR DEBYTE(I,IBYTE)#N#/>>

Decomposes a Hollerith variable I into its four individual
Hollerith `bytes' IBYTE(4).

.RL3
.OS<<3//#_#TSR HALT(WORD)#N#/>>

Halts the execution of the NBO program if an unrecognizable keyword
is found in the $NBO keylist.

.RL3
.OS<<3//#_#TSR IDIGIT(KINT,IK,ND,MAXD)#N#/>>

Converts the INTEGER variable KINT in the first ND elements of the
Hollerith array IK(MAXD).  This is the inverse of SR CONVIN.

.RL3
.OS<<3//#_#TFN IHTYP(IBO,JBO)#N#/>>
 
This Hollerith function determines whether the IBO\rarr JBO delocalization
is vicinal (`v'), geminal (`g'), or remote (`r'), based on the derived NBO
connectivity.

.RL9
.OS<<3//#_#TSR JACOBI(N,A,EIVU,EIVR,NDIM,NVDIM,ICONTR)#N#/>>

.NH
Diagonalizes a real symmetric matrix by the Jacobi rotations
method.  If ICONTR=0, a standard Jacobi diagonalization (unconstrained
2x2 rotations) is carried out.  If ICONTR=1, the algorithm is
prevented from mixing orbitals that are degenerate within `DIFFER'
if the off-diagonal element connecting them is less 
than `DIFFER'.  [Threshold DIFFER (10#u\minus 5#d) controls
degenerate mixing, DONE (10#u\minus 13#d) is the maximum allowed
off-diagonal element, and EPS (0.5x10#u\minus 13#d) is a number
between DONE and the machine pre#|cision.]
.HY

.RL4
.OS<<3//#_#TSR LIMTRN(T,M,A,B,NDIM,NBAS,NCDIM,NC,IOPT)#N#/>>

This routine carries out a `limited' transformation of a matrix (T),
using only the rows and columns specified by vector M.  The
operations performed are T*A, A#ut#d*T*A, or A#ut#d*T
according to the value of IOPT.

.RL2
.OS<<3//#_#TSR MATMLT(A,B,V,NDIM,N)#N#/>>
 
Multiplies square matrices A*B (using scratch vector V) and
stores result in A.

.RL5
.OS<<3//#_#TSR MATML2(A,B,V,NDIM,N)#N#/>>

Multiplies A#ut#d*B (using scratch vector V) and stores the
result in B.  The algorithm assumes that A*B is a symmetric,
so about half the work is saved.  [SR MATML2 is typically the second step
in a similarity transform of B by A, where B (and thus 
A#ut#d*B*A) is symmetric.]

.RL2
.OS<<3//#_#TFN NAMEAT(IZ)#N#/>>

Returns the (Hollerith) atomic symbol for
atomic number IZ \le  103.

.RL2
.OS<<3//#_#TSR NORMLZ(A,S,M,N)#N#/>>
 
Normalizes the columns of A using the overlap matrix S.

.RL3
.OS<<3//#_#TSR ORDER(RANK,LIST,N,NDIM,ARCRNK)#N#/>>

.NH
Ranks the positive elements of integer LIST(N), lowest values first.  [RANK
and ARCRNK are integer vectors, with I = ARCRNK(N) if LIST(I) is the
element of rank N.]
.HY

.RL3
.OS<<3//#_#TSR PACK(T,NDIM,NBAS,L2)#N#/>>
 
Packs the upper-triangular portion of the symmetric matrix T(NBAS,NBAS)
the first L2 elements of T.

.RL5
.OS<<3//#_#TSR RANK(EIG,N,NDIM,ARCRNK)#N#/>>

Orders the entries of vector EIG, highest values first.  ARCRNK(I)
is the old location of the I#uth#d highest value in EIG.  On return,
EIG(I) is the I#uth#d highest value.  [Entries are not switched
unless they differ by more than a DIFFER (5x10#u\minus 8#d) 
threshold.]

.RL2
.OS<<3//#_#TSR SIMTRN(A,T,V,NDIM,N)#N#/>>

Performs the general similarity transform T#ut#d*A*T of A by T, using
scratch vector V.

.RL3
.OS<<3//#_#TSR SIMTRS(A,S,V,NDIM,N)#N#/>>

Performs the `fast' similarity transform S#ut#d*A*S, assuming the
result is symmetric.

.RL2
.OS<<3//#_#TSR TRANSP(A,NDIM,N)#N#/>>
 
Transposes the matrix A: A\rarr A#ut#d.

.RL3
.OS<<3//#_#TSR UNPACK(T,NDIM,NBAS,L2)#N#/>>
 
Unpacks an upper triangular matrix (vector of length L2) into a
symmetric matrix T(NBAS,NBAS).

.RL3
.OS<<3//#_#TSR VALTBL(IAT,IVAL)#N#/>>

Specifies the nominal ``valence table,'' giving the number of valence
AOs of each symmetry type for elements 1-105.

.RL2
.OS<<3//#_#TFN VECLEN(X,N,NDIM)#N#/>>

Evaluates Euclidean length of vector X.

.RL4
.OS<<3//#_#TSR LINEQ(A,X,B,SCR,N,M,NDIM,MDIM,ZERTOL,EPS,MAXIT,LFNPR,IERR)#/#N>>

This and the three following routines constitute
the linear equations package for solving the system
A*X = B for matrix X by the method of Gaussian elimination.

.RL2
.OS<<3//#_#TSR FACTOR(A,W,D,IPIVOT,N,NDIM,ZERTOL,IFLAG)#N#/>>

Supports SR LINEQ.

.RL2
.OS<<3//#_#TSR FNDSOL(A,X,B,W,R,E,IPIVOT,N,NDIM,EPS,MAXIT,LFNPR,IERR)#N#/>>

Supports SR LINEQ.

.RL2
.OS<<3//#_#TSR SUBST(X,W,B,IPIVOT,N,NDIM)#N#/>>

Supports SR LINEQ.
.LM10
.RM80
.HF<<C.11 SYSTEM-DEPENDENT DRIVER ROUTINES//3//10>>
.RL55
#BC.11 SYSTEM-DEPENDENT DRIVER ROUTINES (GROUP VII)#N

\np The routines of Group VII comprise the set of ESS-dependent
driver routines which initiate the NBO and NBO energetic analyses and
provide the NBO program with a variety of information about the
electronic wavefunction.  This section provides a brief, generic description of
each of the driver routines.  If you intend to write a set of routines
for an ESS program not supported by this distribution, refer to the
driver source code
for additional guidance.  Also, see Section C.13 for helpful
hints for attaching the NBO program to an ESS package.

\np The driver routines are grouped together at the end of the NBO source
code.  Since multiple versions of each driver are provided (one for each
supported ESS package and GENNBO), all of the executable lines in these
routines are `commented out' with an asterisk in the first column.  In
addition, every line of the drivers has an identifier `#IXXX#NDRV' in
columns 73-78, where `#IXXX#N' is a 3-letter identifier for the associated
ESS package.  It is the responsibility of the program ENABLE to `uncomment'
the appropriate lines of the code for the requested program version
(see Section A.2).

\np The system-dependent driver routines are:

.LM+3
.RL4
.OS<<3//#_#TSR RUNNBO#N#/>>

Determines the
logical file numbers for the input and output files (LFNIN and LFNPR)
of the parent program, initializes the NBOOPT job option array 
Section C.5.1),
and initiates the NBO analysis (SR NBO) and energetic analysis
(SR NBOEAN).  This routine is the only routine 
of the NBO program called directly
by the parent ESS package.

.RL6
.OS<<3//#_#TSR FEAOIN(CORE,ICORE,NBOOPT)#N#/>>

Interrogates the scratch files and COMMON blocks of the parent program,
providing the NBO program with required information of the electronic
wavefunction via the NBO COMMON blocks and FILE48 direct access file.
(Note that for GENNBO, this routine directs the input of information
from the GENNBO input file, FILE47.)  The NBO COMMON blocks and FILE48
records which must be initialized by SR FEAOIN are discussed in Sections
C.3, C.4.  Additional information on the COMMON blocks and scratch files
of the parent ESS package is provided in the Appendices.


.RL4
.OS<<3//#_#TSR DELSCF(CORE,ICORE,NBOOPT)#N#/>>

Performs one of two tasks, depending of the value of NBOOPT(1).  If
NBOOPT(1) is set to 2, SR DELSCF provides the parent ESS program with
the modified density matrix generated by the NBO energetic analysis
routines.  The parent program will then compute the ``deletion energy''
for this modified wavefunction.  If NBOOPT(1) is set to 3, SR DELSCF
fetches the deletion energy from the parent program and writes it to
the FILE48 direct access file.  (The NBOOPT array is discussed in
Section C.5.1).

.LM10
.RM80
.HF<<C.12 GENNBO AUXILIARY ROUTINES//3//10>>
.RL55
#BC.12 GENNBO AUXILIARY ROUTINES#N

\np An additional set of routines is provided for the GENNBO stand-alone
program.  These routines are called by the GENNBO driver routine FEAOIN
and are responsible for reading the datalists of the GENNBO input file.
Each of these routines rewinds the input file before searching sequentially
for its associated datalist.  Thus, the order of datalists (as well as
keylists) in the input file is immaterial.  Each routine also checks
that all required information in the datalist is given and stores
this information on the FILE48 direct access file or in the NBO COMMON blocks.

\np Below we list each GENNBO auxiliary routine, indicating its associated
datalist, but without furthur explanation:

.LJ
.LM+10
.TB
.FM<<1L15//0L35>>
.RW-
.RW<<#IDatalist//Auxiliary routine to read datalist#N>>
.RW=
.RW<<$COORD//SR CRDINP(TITLE,ATCOOR,BOHR)>>
.RW<<$BASIS//SR BASINP>>
.RW<<$CONTRACT//SR CONINP(CORE,ICORE)>>
.RW<<$OVERLAP//SR SINP(CORE,UPPER)>>
.RW<<$DENSITY//SR DMINP(CORE,UPPER)>>
.RW<<$FOCK//SR FINP(CORE,UPPER,END)>>
.RW<<$LCAOMO//SR TINP(CORE)>>
.RW<<$DIPOLE//SR DIPINP(CORE,UPPER,BOHR)>>
.RW-
.ET
.FJ

.LM10
.RM80
.HF<<C.13 ATTACHING NBO TO A NEW ESS PROGRAM//3//10>>
.RL55
#BC.13 ATTACHING NBO TO A NEW ESS PROGRAM#N

This section briefly outlines the steps to be considered
when attaching the NBO program to a new ESS package that is not supported
by this distribution.  

In general, you should try to identify the supported
ESS package that is most similar to the ESS package you wish to use,
and try to create driver routines modelled as closely as
possible on those provided for the ESS.  [In fact, examining the source code
for driver routines of #Iall#N supported ESS packages is
good preparation for writing your own drivers.]

.LM+3
.RM-3
.OS<<3//1.>>
Decide where in the parent ESS package you wish to perform the NBO
analysis.  This will necessarily be placed after the calculation of the
wavefunction (and the associated density matrix), usually near 
the wavefunction analysis routines (e.g., the perennial
``Mulliken population
analysis'' section) or wavefunction properties 
section of the code.  If possible,
restrict the modification of your ESS source code to insertion of 
a single ``CALL RUNNBO'' statement at some point where
the information required for NBO analysis is known to be available.

.OS<<3//2.>>
Check carefully for possible conflicts between the parent ESS program and
the NBO program in (1) function or subroutine names, (2) COMMON
block names, and (3) logical file assignments (LFNs) for I/O.  NBO 
common block names all begin with /NB.../, and default
LFN assignments are in the range 31-49.  (Duplicate FN or SR names
are detected by a linker.)

.OS<<3//3.>>
Create new driver (interfacing) subroutines RUNNBO, FEAOIN,
and DELSCF to perform the functions briefly described in Section
C.11, using the drivers provided with this
distribution as templates insofar as possible.  The following 
are a few helpful hints for each driver:

.LM+3
.RM-3
.OS<<3//a.>>
The RUNNBO routine should be relatively straightforward to write, following
an analogous example provided in this distribution.  Note that you
can simply omit the calls to SR NBOEAN and SR DELSCF from RUNNBO if
you do not plan to use the NBO energetic analysis (for example, because
the DELSCF driver is unmanageable).

If your parent program is quite different from any of those supported by this
distribution, choose an alternate version number [NBOOPT(10)], and carefully
consider step 4 below.

.OS<<3//b.>>
Routine FEAOIN should fetch information about the electronic wavefunction
from your ESS package and load it into the NBO COMMON blocks and FILE48
direct access file.  This requires intimate knowledge of where these items
are stored in the ESS program, so the FEAOIN examples of the
distribution may provide little direct guidance.  See Sections 
C.3, C.4 for description of the NBO
COMMON blocks and file records which must be initialized by this routine.

Note that the NBO analysis will perform properly without the information
stored on logical records 2, 5, 9, 30, 31, 40, 41, and 50-52 of the
direct access file.  If information is not provided on these records, the
NBO program will simply shut off (with warnings) any requested keyword
options which are thereby incompatible.  In addition, the overlap matrix
of record 10 need not be provided if the input basis set is orthogonal,
and the energies of record 8 are not required if the NBO energetic analysis
is not implemented for your ESS package.

.OS<<3//c.>>
Creating routine DELSCF will require intimate knowledge of the SCF routines
in the parent ESS program; again, versions of DELSCF
provided with this distribution may only be of minimal 
assistance.  As described in Section C.11, SR DELSCF is
responsible for providing a modified AO density matrix to an SCF energy
evaluator (one pass throught the SCF routines) and returning this
new energy to the NBO deletion routines via the FILE48 direct access 
file.  If you do not intend to employ the NBO
energetic analysis, you need not provide this routine to the 
NBO program.  [Note that the 2nd-order perturbation theory energy analysis
will be carried out (provided the Fock matrix is available)
even if you do not include the NBOEAN and DELSCF
energy analysis routines.]

.LM-3
.RM+3
.OS<<3//4.>>
In addition to the explicitly system-dependent subroutines 
RUNNBO, FEAOIN, and DELSCF, there are
a few routines within the NBO program which can be considered
#Iquasi#N-system dependent, and might, therefore, require modification.
These are SR NBOSET (Section C.5.2) and the `INP' routines NBOINP, CORINP,
CHSINP, and DELINP (Section C.9):

.LM+3
.OS<<3//a.>>
SR NBOSET assigns the logical file
numbers (LFNs) 31-49 to be used by the NBO program.  As mentioned
above, if these are in conflict
with the files employed by the parent ESS program, the conflicting 
LFNs will have to be reassigned in this subroutine.

.OS<<3//b.>>
The `INP' routines may have to be modified according to
the manner in which the input file of the parent program should be processed by
the NBO program.  More specifically, these routines either 
rewind the input file before searching
for their associated keylist identifier, or they simply begin searching
the input file sequentially at the point where the parent program left off,
depending on the version number specified in NBOOPT(10).  Be sure this
parameter is consistent with the way you wish to modify the
ESS input file for NBO input.
.RM+3
.LM-3
.CM---------------------END OF NBOC.MAN---------------------------------------
.CM-----------------------------NBO.APP----------------------------
.TP2
.HF<<D.1 INTRODUCTION//3//10>>
.NF<<D-// >>
.PN1
.DF\*deg =<<000011110000//
001111111100//
011100001110//
011000000110//
110000000011//
110000000011//
110000000011//
110000000011//
011000000110//
011100001110//
001111111100//
000011110000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000//
000000000000>>
.DF\np =\thsp \nthsp
.CM----------------------------------------------------------------





.CJ
#HSection D: APPENDIX#N
.FJ


#BD.1 INTRODUCTION#N

\np This Appendix contains system-dependent information about NBO input
and source code for the ESS (electronic structure system) packages supported
by this distribution.  We assume that the user has basic familiarity with
the ESS program of interest.

\np The Appendix is organized according to the ESS packages supported,
which are described in Sections D.2-D.7, as shown below:

.LM+20
.TB
.FM<<1L15//0C10>>
.RW-
.RW<<ESS package//Section>>
.RW=
.RW<<GAUSSIAN 88//D.2>>
.RW<<GAUSSIAN 86//D.3>>
.RW<<GAUSSIAN 82//D.4>>
.RW<<GAMESS//D.5>>
.RW<<HONDO//D.6>>
.RW<<AMPAC//D.7>>
.RW-
.ET
.LM-20

\np Each ESS section contains information on:

.LM+5
.OS<<3//1.>>
Sample input file for RHF/3-21G methylamine

.OS<<3//2.>>
NBO program installation

.OS<<3//3.>>
Communication between the NBO drivers and the ESS program
.LM-5

\np For most users, only the first section(s) on sample input file will
be required reading.  For the programmer responsible for attaching the NBO
program to an ESS package, the final section on NBO drivers will be
important only if the available ESS version differs significantly from
that assumed in the installation instructions.

\np In the Appendix we use ``SR'' and ``FN'' to denote subroutines
and functions, respectively.

.LM10
.RM80
.FJ
.CM------------------------------------------------------------------
.HF<<D.2 GAUSSIAN 88 VERSION//3//10>>
.RL55
#BD.2 GAUSSIAN 88 VERSION#N

#ID.2.1 GAUSSIAN 88 sample input#N

\np A sample GAUSSIAN 88 input file to
recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry)
output displayed in Section A.3 is shown below:

.DF\@seg =
# RHF/3-21G

Methylamine...RHF/3-21G//Pople-Gordon standard geometry

 0   1
 C
 N   1   CN
 H   1   CH   2   tet
 H   1   CH   2   tet   3   120.  0
 H   1   CH   2   tet   3   240.  0
 H   2   NH   1   tet   3    60.  0
 H   2   NH   1   tet   3   300.  0

 CN        1.47
 CH        1.09
 NH        1.01
 tet     109.4712

$NBO  $END
.ED
.LJ
.RL23
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

.RS#^
\@seg
.RS^#

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NThe keylists of the NBO program should always appear at the bottom of the
GAUSSIAN 88 input file and should be ordered: $NBO, $CORE, $CHOOSE, $DEL.
NBO job options are selected by inserting their
associated keywords (Section B.2) into the $NBO keylist.  All NBO keywords
are applicable to the electronic wavefunctions computed by the GAUSSIAN 88
programs.

\np If the NBO program 
encounters the end-of-file while searching for a keylist, the input file
is rewound and the search for the keylist is continued.  This is particularly
useful for jobs which call the NBO analysis several times.  For example, an
MP2 calculation with the GAUSSIAN 88 option DENSITY=ALL causes Link 601 to
loop over three densities (SCF, Rho2, and MP2), and hence, the NBO analysis
is called three times, once for each density.  A single $NBO keylist
(and $CORE and $CHOOSE keylists) will suffice as input for all three analyses.
Alternatively, separate $NBO keylists, one for each density, could be inserted
at the bottom of the GAUSSIAN 88 input file.

.NP
\np The IOp parameters 40-43 of Link 601 exert additional control over the
NBO program, as listed below:

.LM+5
.RL30
.TB
.FM<<1L10//0C10//0L40>>
.RW-
.RW<<parameter//value//effect>>
.RW=
.RW<<IOp(40)//-2//skip the NBO analysis>>
.RW<< //-1//perform the NPA only>>
.RW<< //0//perform the NBO analysis>>
.RW<< // //(read keywords in $NBO)>>
.RW<< //1//perform the default NBO analysis>>
.RW<< // //(do not read keywords in $NBO)>>
.RW<< //2//initiate NBO energetic analysis>>
.RW<< //3//complete NBO energetic analysis>>
.RW
.RW<<IOp(41)//0//SCF density>>
.RW<< //1//MP first order density>>
.RW<< //2//MP2 density>>
.RW<< //3//MP3 density>>
.RW<< //4//MP4 density>>
.RW<< //5//CI one-particle density>>
.RW<< //6//CI density>>
.RW<< //7//QCI/CC density>>
.RW<< //8//density correct to second order>>
.RW
.RW<<IOp(42)//1//perform the dipole analysis>>
.RW<< // //(force the DIPOLE keyword)>>
.RW
.RW<<IOp(43)//1//allow strongly delocalized structures>>
.RW<< // //(force the RESONANCE keyword)>>
.RW-
.ET
.LM-5

For example, to restrict the NBO output to the Natural Population
analysis (NPA) only, set IOp(40) to \minus 1 in all
Link 601 entries of a GAUSSIAN 88 non-standard route, as shown below:

#T     6/40=-1/1;

#NBy default, the NBO analysis will be performed, reading keywords from
the $NBO keylist [IOp(40)=0], on the density matrix for the current
wavefunction.  The DIPOLE and RESONANCE keywords are generally activated
through the $NBO keylist rather than via the IOp parameters.

.NP
#ID.2.2 NBO energetic analysis#N

\np Due to the overlay structure of the GAUSSIAN 88 programs, a non-standard
route must be employed to perform the NBO energetic analysis.  The following
table lists and describes the tasks of the GAUSSIAN 88 links in the order that
they appear in the non-standard route:

.RL24
.LM+24
.RM-2
.OS<<24//#ILINK#N>>
#IDESCRIPTION#N
.HR<<1//+1//10//32>>
.HR<<1//+1//34//80>>

.OS<<24//6/7=2,8=2,9=2,10=2,19=1/1;>>
Perform the normal NBO analysis, storing information about the NBOs for
the NBO energetic analysis on the FILE48 direct access file.

.OS<<24//6/40=2/1(1);>>
Read the next deletion listed in the $DEL keylist.  If there are no more
deletions, move to the next link.  Otherwise, compute the modified density
matrix, store it on the read-write files, and skip the next link in the
non-standard route.

.OS<<24//99/5=1,9=1/99;>>
Finish GAUSSIAN 88 execution.

.OS<<24//5/7=1,13=1/1,2;>>
Using the modified density matrix, compute the deletion energy by
a single pass through the SCF energy evaluator.  Store the deletion energy
on the read-write files.

.OS<<24//6/40=3/1(-3);>>
Read the deletion energy from the read-write files and complete the energetic
analysis.  Step backwards, in the non-standard route, three links.

.HR<<1//+0//10//80>>
.LM-24
.RM+2

\np The following is a GAUSSIAN 88 input file
that will generate, in addition to the default NBO output, the NLMO
(Section B.6.2), the dipole moment (Section B.6.3), and the NBO energetic
(Section B.6.10) analyses of methylamine:

.DF\@seg =
# NONSTD
1//1;
2//2;
3/5=5,11=1,25=14,30=1/1,2,3,11,14;
4/7=1/1;
5//1;
6/7=2,8=2,9=2,10=2,19=1/1;
6/40=2/1(1);
99/5=1,9=1/99;
5/7=1,13=1/1;
6/40=3/1(-3);

Methylamine...RHF/3-21G//Pople-Gordon standard geometry

 0   1
 C
 N   1   CN
 H   1   CH   2   tet
 H   1   CH   2   tet   3   120.  0
 H   1   CH   2   tet   3   240.  0
 H   2   NH   1   tet   3    60.  0
 H   2   NH   1   tet   3   300.  0

 CN        1.47
 CH        1.09
 NH        1.01
 tet     109.4712

$NBO  NLMO  DIPOLE  $END
$DEL  NOSTAR
      ZERO 2 ATOM BLOCKS   4  BY  3
                           1  3  4  5
                           2  6  7
                           3  BY  4
                           2  6  7
                           1  3  4  5
$END
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

.RS#^
\@seg
.RS^#

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NNote that for the GAUSSIAN 88 version of the NBO program, each deletion
in the $DEL keylist must begin on a new line of the input file (the first
deletion can follow the ``$DEL'' keylist identifier, as shown above).  The
``$END'' keylist terminator must also appear on its own line.

.NP
#ID.2.3 Geometry reoptimization with NBO deletions#N

\np The structural effects of electron delocalization can be examined
by coupling the NBO energetic analysis to the Fletcher-Powell (numerical)
geometry optimization routines of the GAUSSIAN 88 package.  The
following GAUSSIAN 88 input file will reoptimize selected internal
coordinates of RHF/3-21G methylamine in the absence of its strong
#In#N#dN#u\rarr \sigma #u*#d#d#<CH#u hyperconjugative interaction:

.DF\@seg =
#NONSTD
1//1,2;
2//2;
3/5=5,11=1,25=14,30=1/1,2,3,11,14;
4/7=1/1;
5//1;
6/7=2,8=2,9=2,10=2,19=1/1;
6/40=2/1(2);
1//2(3);
99/9=1/99;
5/7=1,13=1/1;
6/40=3/1(-4);
2//2;
3/5=5,11=1,25=14,30=1/1,2,3,11,14;
4/5=5,7=1,16=2/1;
5//1;
6/7=2,8=2,9=2,10=2,19=1/1;
6/40=2/1(3);
1//2(-6);
2//2;
99/9=1/99;
5/7=1,13=1/1;
6/40=3/1(-5);

Methylamine...RHF/3-21G optimization with deletions

 0    1
 C
 N    1    CN
 H    1    CHa    2   alfa
 H    1    CHb    2   beta    3   dlta  0
 H    1    CHb    2   beta    3  -dlta  0
 H    2    NH     1   gama    3   epsn  0
 H    2    NH     1   gama    3  -epsn  0

 CN           1.4713
 CHa          1.0901
 alfa       114.7843

 CHb          1.0825
 NH           1.0035
 beta       108.9484
 gama       113.6544
 dlta       121.4265
 epsn        64.2369

$NBO  PRINT=0  NBO  $END   ! Request reduced NBO output
$DEL
      DELETE 1 ELEMENT  9  24
$END
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

.RS#^
\@seg
.RS^#

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NReoptimization of the internal coordinates specified in this example
leads to lengthening of the C-N bond (1.513\thsp \ang ) and closing of
the H-C-N bond angle (108.3\thsp \*deg ), as expected from
lone pair/antibond overlap arguments.  The C-H bond length contracts
(1.075\thsp \ang ) due to the removal of electron density from its antibond.

\np #NNote that the numerical optimization routines of the GAUSSIAN 88 program
must be employed since analytic gradients are not available for the modified
wavefunction of the NBO energetic analysis.  Hence, these optimizations are
time-consuming, generally requiring 8#In#N-12#In#N single point
calculations (#In#N = number of symmetry unique internal coordinates) before
convergence of the gradients is obtained (the example requires 28 single
point calculations before convergence).  Careful selection of the coordinates
to be optimized is recommended.

.NP
#ID.2.4 NBO program installation#N

\np The NBO interfacing (driver) routines provided
in this distribution were written for the Revision C version of
GAUSSIAN 88, dated 19-AUG-1988.
Section D.2.5 lists the GAUSSIAN 88
dependent elements of the NBO driver routines that may need slight
modification for other versions of the GAUSSIAN 88 programs.

\np Three modifications to SR MulDrv of Link 601 are required to run the
NBO analysis:

.DF\@seg =
*Deck MulDrv
      Subroutine MulDrv(Core)

      .
      .
      .

      IEnd1  = IScr2  + NBasis - 1
      Call GetSCM(-1,Core,NGot,6hMulDrv,0)
C
C     <<< Beginning of first NBO insert >>
C
C     Run the NBO energetic analysis.
C
      If(IOp(40).ge.2) then
        IDens = 0                  ! SCF density for deletion runs
        IOp(41) = IDens
        Call RunNBO(Core,NGot,IOp,IContr)
        go to 999
      endIf
C
C     <<< End of first NBO insert >>
C
C     Put density matrices first.
C
      IPA = IEnd1 + 1

      .
      .
      .

.NP
          Call ElEner(IOut,ISelfE,SCFDen,ISCF,IROHF,NAE,NBE,NBasis,
     $      Core(IPA),Core(IV),MDV)
C
C     <<< Beginning of second NBO insert >>>
C
C     Run the NBO analysis.
C
          If(IOp(40).ne.-2) then
            IOp(41) = IDens
            Call RunNBO(Core,NGot,IOp,IContr)
          endIf
C
C     <<< End of second NBO insert >>>
C
        else if(IDens1.eq.IDSt.and.IDens1.eq.IDEnd) then

      .
      .
      .

      Call PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT,
     $    Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip))
C
C     <<< Beginning of third NBO insert >>>
C
C     The following line has been changed from "Call ChainX(0)" in
C     order to exit the NBO deletion loop after the deletions are done:
C
  999 Call ChainX(IContr)
C
C     <<< End of third NBO insert >>>
C
      Return
      End
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NThe first NBO insert initiates the NBO energetic analysis of
SCF wavefunctions.  The second insert lies within a loop over densities,
and thus, the NBO program is called once for each density matrix analyzed
by this link.  The third insert allows the NBO energetic analysis to exit
from the loop in the non-standard route.

The NBO program installation should continue as discussed in Section A.2.

.NP
#ID.2.5 NBO communication with GAUSSIAN 88#N

\np The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following
GAUSSIAN 88 routines, read-write files, and COMMON blocks:

#_GAUSSIAN 88 routines:#/#T

    SR CharPn(IString)
    SR DENGET(IOut,IODens,IMeth,LenDen,GotIt,P)
    FN ILSW(IOPER,WHERE,WHAT)
    FN InToWP(Nints)
    FN ITqry(Ifile)
    SR TRead(IARN,X,M,N,MM,NN,K)
    SR TWrite(IARN,X,M,N,MM,NN,K)

#N#_GAUSSIAN 88 read-write files:#/

.LM+5
.TB
.FM<<1C8//2L45>>
.RW-
.RW<<file//contents>>
.RW=
.RW<<501//Total energy>>
.RW<<502//Job title>>
.RW<<506//Basis set information>>
.RW<<512//Effective core potential information>>
.RW<<514//AO overlap matrix>>
.RW<<518//AO dipole integrals>>
.RW<<524//MO coefficients (alpha)>>
.RW<<526//MO coefficients (beta)>>
.RW<<528//SCF density matrix (alpha)>>
.RW<<530//SCF density matrix (beta)>>
.RW<<536//AO Fock matrix (alpha)>>
.RW<<538//AO Fock matrix (beta)>>
.RW<<603//AO density matrix>>
.RW-
.ET
.LM-5

#_GAUSSIAN 88 COMMON blocks:#/#T

    COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401),
   +           ATMCHG(400),C(1200)
    COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5),
   +  KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400)
    COMMON/B/EXX(6000),C1(6000),C2(6000),C3(6000),X(2000),Y(2000),
   +     Z(2000),JAN(2000),SHELLA(2000),SHELLN(2000),SHELLT(2000),
   +     SHELLC(2000),AOS(2000),AON(2000),NSHELL,MAXTYP
    INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
    DIMENSION C4(2000),SHLADF(2000)
    EQUIVALENCE(C4(1),C3(2001)),(SHLADF(1),C3(4001))
 #N
.LM10
.RM80
.BM70
.FJ
.CM------------------------------------------------------------------
.HF<<D.3 GAUSSIAN 86 VERSION//3//10>>
.RL55
#BD.3 GAUSSIAN 86 VERSION#N

#ID.3.1 GAUSSIAN 86 sample input#N

\np See Section D.2.1.  Note that the NBO IOp parameters of Link 601
are set to 40-43 (changed from 20-23 in previous distributions of the NBO
program).

#ID.3.2 NBO energetic analysis#N

\np See Section D.2.2.

#ID.3.3 Geometry reoptimization with NBO deletions#N

\np See Section D.2.3.

.NP
#ID.3.4 NBO program installation#N

\np The NBO interfacing (driver) routines provided
in this distribution were written for the Revision C version of
GAUSSIAN 86, dated 30-APR-1986.
Section D.3.5 lists the GAUSSIAN 86
dependent elements of the NBO driver routines that may need slight
modification for other versions of the GAUSSIAN 86 programs.

\np Two modifications to SR MulDrv of Link 601 are required to run the
NBO analysis:

.DF\@seg =
*Deck MulDrv
      Subroutine MulDrv(Core)
      .
      .
      .

      If(NGot.lt.IEnd1) Write(IOut,2002) IEnd1, NGot
      Len2 = (NGot-I2A+1)/NTT
C
C     <<< Beginning of first NBO insert >>>
C
      IF(IOp(40).GE.2.OR.IOp(41).NE.0) GO TO 999
C
C     <<< End of first NBO insert >>>
C
C     Do population analysis.
C
      CALL MULPOP(MaxAtm,IOP,IROHF,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,

      .
      .
      .

      Call PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT,
     $    Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip))
C
C     <<< Beginning of second NBO insert >>>
C
  999 Call GetSCM(-1,Core(1),NGot,3HNBO,0)
      Call RunNBO(Core,NGot,IOp,IContr)
C
C     The following line has been changed from "999 Call ChainX(0)" in
C     order to exit the NBO deletion loop after deletions are complete.
C
      Call ChainX(IContr)
C
C     <<< End of second NBO insert >>>
C
      Return
      End
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.NP
.BM60
.FJ
.LM10
.RM80

\np #NThe first NBO insert allows Link 601 to by-pass the Mulliken
Population and electric moment analysis routines if the NBO energetic
analysis is to be performed or if a correlated wavefunction is being
analyzed.  The second insert requests all available memory be allocated
for the NBO program and initiates the NBO analysis.  Note that the call
to SR ChainX has been altered from the original code.

The NBO program installation should continue as discussed in Section A.2.

.NP
#ID.3.5 NBO communication with GAUSSIAN 86#N

\np The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following
GAUSSIAN 86 routines, read-write files, and COMMON blocks:

#_GAUSSIAN 86 routines:#/#T

    SR CharPn(IString)
    FN ILSW(IOPER,WHERE,WHAT)
    FN InToWP(Nints)
    FN ITqry(Ifile)
    SR TRead(IARN,X,M,N,MM,NN,K)
    SR TWrite(IARN,X,M,N,MM,NN,K)

#N#_GAUSSIAN 86 read-write files:#/

.LM+5
.TB
.FM<<1C8//2L45>>
.RW-
.RW<<file//contents>>
.RW=
.RW<<203//CI density matrix (alpha)>>
.RW<<204//CI density matrix (beta)>>
.RW<<501//Total energy>>
.RW<<502//Job title>>
.RW<<506//Basis set information>>
.RW<<512//Effective core potential information>>
.RW<<514//AO overlap matrix>>
.RW<<518//AO dipole integrals>>
.RW<<524//MO coefficients (alpha)>>
.RW<<526//MO coefficients (beta)>>
.RW<<528//SCF density matrix (alpha)>>
.RW<<530//SCF density matrix (beta)>>
.RW<<536//AO Fock matrix (alpha)>>
.RW<<538//AO Fock matrix (beta)>>
.RW-
.ET
.LM-5

#_GAUSSIAN 86 COMMON blocks:#/#T

    COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401),
   +           ATMCHG(400),C(1200)
    COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5),
   +  KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400)
    COMMON/B/EXX(1200),C1(1200),C2(1200),C3(1200),X(400),Y(400),
   +     Z(400),JAN(400),SHELLA(400),SHELLN(400),SHELLT(400),
   +     SHELLC(400),AOS(400),AON(400),NSHELL,MAXTYP
    INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
    DIMENSION C4(400),SHLADF(400)
    EQUIVALENCE(C4(1),C3(401)),(SHLADF(1),C3(801))
 #N
.LM10
.RM80
.FJ
.CM------------------------------------------------------------------
.HF<<D.4 GAUSSIAN 82 VERSION//3//10>>
.RL55
#BD.4 GAUSSIAN 82 VERSION#N

#ID.4.1 GAUSSIAN 82 sample input#N

\np See Section D.2.1.  Note that the NBO IOp parameters of Link 601
are set to 40-43 (changed from 20-23 in previous distributions of the NBO
program).

#ID.4.2 NBO energetic analysis#N

\np See Section D.2.2.

#ID.4.3 Geometry reoptimization with NBO deletions#N

\np See Section D.2.3.

.NP
#ID.4.4 NBO program installation#N

\np The NBO interfacing (driver) routines provided
in this distribution were written for the Revision H version of
GAUSSIAN 82, dated 28-NOV-1983.
Section D.4.5 lists the GAUSSIAN 82
dependent elements of the NBO driver routines that may need slight
modification for other versions of the GAUSSIAN 82 programs.

\np Two modifications to SR MulDrv of Link 601 are required to run the
NBO analysis:

.DF\@seg =
*Deck MulDrv
      Subroutine MulDrv(Core)

      .
      .
      .

      IF(IPRINT.NE.0)
     $WRITE(IOUT,2001)I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,IEND
C
C     <<< Beginning of first NBO insert >>>
C
C     The following line has been changed from "CALL GETSCM(IEND,...)",
C     in order to ask for all available memory.
C
      CALL GETSCM(-1,CORE(1),JJJMEM,6HMULDRV,0)
C
      IF(IOP(40).GE.2.OR.IOP(41).NE.0) GO TO 100
C
C     <<< End of first NBO insert >>>
C
C     DO THE POPULATION ANALYSIS.
      CALL MULPOP(IOP,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,IAN,AtmChg,
     $  C,Core(I1),CORE(I2),CORE(I3),CORE(I4),CORE(I5),
     $  CORE(I6),CORE(I7),CORE(I8),CORE(I9),CORE(I10))
C
C     <<< Beginning of second NBO insert >>>
C
  100 CALL RUNNBO(CORE,JJJMEM,IOP,ICONTR)
C
C     The following line has been changed from "CALL CHAINX(0)" in
C     order to exit the NBO deletion loop after deletions are complete.
C
      CALL CHAINX(ICONTR)
C
C     <<< End of second NBO insert >>>
C
      RETURN
      END
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.NP
.FJ
.LM10
.RM80
\np #NThe first NBO insert allows Link 601 to by-pass the Mulliken
Population analysis routines if the NBO energetic
analysis is to be performed or if a correlated wavefunction is being
analyzed.  The second insert initiates the NBO analysis.  Note that the calls
to routines GETSCM and CHAINX have been altered from the original code.

The NBO program installation should continue as discussed in Section A.2.

.NP
#ID.4.5 NBO communication with GAUSSIAN 82#N

\np The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following
GAUSSIAN 82 routines, read-write files, and COMMON blocks:

#_GAUSSIAN 82 routines:#/#T

    SR CharPn(IString)
    FN ILSW(IOPER,WHERE,WHAT)
    FN InToWP(Nints)
    FN ITqry(Ifile)
    SR TRead(IARN,X,M,N,MM,NN,K)
    SR TWrite(IARN,X,M,N,MM,NN,K)

#N#_GAUSSIAN 82 read-write files:#/

.LM+5
.TB
.FM<<1C8//2L45>>
.RW-
.RW<<file//contents>>
.RW=
.RW<<203//CI density matrix (alpha)>>
.RW<<204//CI density matrix (beta)>>
.RW<<501//Total energy>>
.RW<<502//Job title>>
.RW<<506//Basis set information>>
.RW<<512//Effective core potential information>>
.RW<<514//AO overlap matrix>>
.RW<<518//#Ix#N dipole integrals>>
.RW<<519//#Iy#N dipole integrals>>
.RW<<520//#Iz#N dipole integrals>>
.RW<<524//MO coefficients (alpha)>>
.RW<<526//MO coefficients (beta)>>
.RW<<528//SCF density matrix (alpha)>>
.RW<<530//SCF density matrix (beta)>>
.RW<<536//AO Fock matrix (alpha)>>
.RW<<538//AO Fock matrix (beta)>>
.RW-
.ET
.LM-5

#_GAUSSIAN 82 COMMON blocks:#/#T

    COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(101),
   +           ATMCHG(100),C(300)
    COMMON/LP2/NLP(400),CLP(400),ZLP(400),KFIRST(100,5),
   +  KLAST(100,5),LMAX(100),LPSKIP(100),NFroz(100)
    COMMON/B/EXX(240),C1(240),C2(240),C3(240),X(80),Y(80),
   +     Z(80),JAN(80),SHELLA(80),SHELLN(80),SHELLT(80),
   +     SHELLC(80),AOS(80),AON(80),NSHELL,MAXTYP
    INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
    DIMENSION C4(80),SHLADF(80)
    EQUIVALENCE(C4(1),C3(81)),(SHLADF(1),C3(161))
 #N
.LM10
.RM80
.FJ
.CM------------------------------------------------------------------
.HF<<D.5 GAMESS VERSION//3//10>>
.RL55
#BD.5 GAMESS VERSION#N

#ID.5.1 GAMESS sample input#N

\np A sample GAMESS input file to
recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry)
output displayed in Section A.3 is shown below:

.DF\@seg =
 $CONTRL  SCFTYP=RHF  RUNTYP=ENERGY  $END
 $DATA
Methylamine...RHF/3-21G//Pople-Gordon standard geometry
CS       0

Carbon       6.       -0.713673           -0.014253            0.000000
    1   SV    3  N21

Nitrogen     7.        0.749817            0.123940            0.000000
    1   SV    3  N21

Hydrogen     1.       -0.978788           -1.071520            0.000000
    1   SV    3  N21

Hydrogen     1.       -1.123702            0.463146           -0.889982
    1   SV    3  N21

Hydrogen     1.        1.129752           -0.318420            0.824662
    1   SV    3  N21

 $END
 $GUESS  GUESS=EXTGUESS  $END
 $NBO  $END
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NNBO job options are selected by inserting their associated keywords
(Section B.2) into the $NBO keylist.  All NBO keywords are applicable to the
electronic wavefunctions computed by GAMESS.

\np The following is a modified GAMESS input file that will generate, in
addition to the default NBO output, the NLMO (Section B.6.2), the dipole
moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of
methylamine:

.DF\@seg =
 $CONTRL  SCFTYP=RHF  RUNTYP=ENERGY  $END
 $DATA
Methylamine...RHF/3-21G//Pople-Gordon standard geometry
CS       0

Carbon       6.       -0.713673           -0.014253            0.000000
    1   SV    3  N21

Nitrogen     7.        0.749817            0.123940            0.000000
    1   SV    3  N21

Hydrogen     1.       -0.978788           -1.071520            0.000000
    1   SV    3  N21

Hydrogen     1.       -1.123702            0.463146           -0.889982
    1   SV    3  N21

Hydrogen     1.        1.129752           -0.318420            0.824662
    1   SV    3  N21

 $END
 $GUESS  GUESS=EXTGUESS  $END
 $NBO  NLMO  DIPOLE  $END
 $DEL  NOSTAR
       ZERO 2 ATOM BLOCKS     4  BY  3
                              1  3  4  5
                              2  6  7
                              3  BY  4
                              2  6  7
                              1  3  4  5
 $END
.ED
.NP
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NIn general, the $NBO, $CORE, $CHOOSE, and $DEL keylists can be inserted
in any order within the GAMESS input file; the NBO program rewinds the
input file each time it searches for a keylist.

.LM10
.RM80
.NP
#ID.5.2 NBO program installation#N

\np The NBO interfacing (driver) routines provided in this
distribution were written for the GAMESS program dated 6-DEC-1989.
Section D.5.3 lists the GAMESS
dependent elements of the NBO driver routines that may need slight
modification for other versions of the GAMESS program.

\np Only one command line is added to the GAMESS source code to run the
NBO analysis.  A call (``IF(RHO) CALL RUNNBO'') should be inserted at the
end of the GAMESS properties package (SR HFPROP in module PRPLIB),
as shown below:

.DF\@seg =
C*MODULE PRPLIB  *DECK HFPROP
      SUBROUTINE HFPROP(SCFTYP)

                 .
                 .
                 .

C
C     ----- SELECT DESIRED ELECTROSTATIC PROPERTIES -----
C
      CALL PRSELC(SCFTYP)
C
      WRITE(IW,FMT='('' ...... END OF PROPERTY EVALUATION ......'')')
      CALL TIMIT(1)
C
C     <<< BEGINNING OF NBO INSERT >>>
C
      IF(RHO) CALL RUNNBO
C
C     <<< END OF NBO INSERT >>>
C
      RETURN
      END
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.LM10
.RM80
.FJ

\np #NIf the density matrix is available (RHO = .TRUE.), the NBO analysis
is performed each time the properties package is called within GAMESS.
For example, the NBO analysis of the computed wavefunction will be performed
for every single point calculation and for both the
initial and final points of a geometry optimization.  The NBO output will
appear immediately after the Mulliken Population Analysis and the electric
properties in the GAMESS output file.

\np The NBO program installation should continue as discussed in Section A.2.
.LM10
.RM80
.BM70
.NP
#ID.5.3 NBO communication with GAMESS#N

\np The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following
GAMESS routines, records of the dictionary file, and COMMON blocks:

#_GAMESS routines:#T#/

    SR DAREAD(IDAF,IODA,V,LEN,NREC,NAV)
    FN ENUC(N,Z,C)
    ENTRY GOTFM(IPAR)
    SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK)
    SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK)
    SR SYMH(F,H,IA)
    FN TRACEP(A,B,N)
    SR VADD(A,I,B,J,C,K,N)
    ENTRY VALFM(IPAR)
 
#_#NGAMESS dictionary file:#/

.LM+5
.TB
.FM<<1C8//2L40>>
.RW-
.RW<<record//contents>>
.RW=
.RW<<2//total energy>>
.RW<<12//AO overlap matrix>>
.RW<<14//AO Fock matrix (alpha)>>
.RW<<15//AO to MO transformation matrix (alpha)>>
.RW<<16//AO density matrix (alpha bond-order matrix)>>
.RW<<18//AO Fock matrix (beta)>>
.RW<<19//AO to MO transformation matrix (beta)>>
.RW<<20//AO density matrix (beta bond-order matrix)>>
.RW<<23//#Ix#N dipole integrals>>
.RW<<24//#Iy#N dipole integrals>>
.RW<<25//#Iz#N dipole integrals>>
.RW-
.ET
.LM-5

#_#NGAMESS COMMON blocks:#T#/

    PARAMETER (MXGTOT=5000, MXSH=1000, MXATM=50)                      
    COMMON /ECP2  / CLP(400),ZLP(400),NLP(400),KFIRST(MXATM,6),       
   +                KLAST(MXATM,6),LMAX(MXATM),LPSKIP(MXATM),         
   +                IZCORE(MXATM)                                     
    COMMON /FMCOM / CORE(1)
    COMMON /INFOA / NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(MXATM),C(3,MXATM) 
    COMMON /INTFIL/ NINTMX,NHEX,NTUPL,PACK2E,INTG76
    COMMON /IOFILE/ IR,IW,IP,IS,IPK,IDAF,NAV,IODA(99)
    COMMON /NSHEL / EX(MXGTOT),CS(MXGTOT),CP(MXGTOT),CD(MXGTOT),      
   +                KSTART(MXSH),KATOM(MXSH),KTYPE(MXSH),KNG(MXSH),   
   +                KLOC(MXSH),KMIN(MXSH),KMAX(MXSH),NSHELL           
    COMMON /OUTPUT/ NPRINT,ITOL,ICUT,NORMF,NORMP,NOPK
    COMMON /RUNLAB/ TITLE(10),A(MXATM),B(MXATM),BFLAB(2047)
    COMMON /SCFOPT/ SCFTYP,BLKTYP,MAXIT,MCONV,NCONV,NPUNCH
    COMMON /XYZPRP/ X(3)
.NP
.LM10
.RM80
.BM60
.FJ
.CM------------------------------------------------------------------
.HF<<D.6 HONDO VERSION//3//10>>
#BD.6 HONDO VERSION#N

#ID.6.1 HONDO sample input#N

\np A sample HONDO input file to
recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry)
output displayed in Section A.3 is shown below:

.DF\@seg =
 $CNTRL  RUNFLG=0  $END
 $BASIS
Methylamine...RHF/3-21G//Pople-Gordon standard geometry
    0    0   15    1  N21
CS       0

Carbon       6.       -0.713673           -0.014253            0.000000
Nitrogen     7.        0.749817            0.123940            0.000000
Hydrogen     1.       -0.978788           -1.071520            0.000000
Hydrogen     1.       -1.123702            0.463146           -0.889982
Hydrogen     1.        1.129752           -0.318420            0.824662
 $END
 $GUESS  NGUESS=4  $END
 $INTGRL  $END
 $WFN  WFNFLG=0  $END
 $SCF  NCO=9  $END
 $NBO  $END
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NNBO job options are selected by inserting their associated keywords
(Section B.2) into the $NBO keylist.  All NBO keywords are applicable to the
electronic wavefunctions computed by HONDO.

\np The following is a modified HONDO input file that will generate, in
addition to the default NBO output, the NLMO (Section B.6.2), the dipole
moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of
methylamine:

.DF\@seg =
 $CNTRL  RUNFLG=0  $END
 $BASIS
Methylamine...RHF/3-21G//Pople-Gordon standard geometry
    0    0   15    1  N21
CS       0

Carbon       6.       -0.713673           -0.014253            0.000000
Nitrogen     7.        0.749817            0.123940            0.000000
Hydrogen     1.       -0.978788           -1.071520            0.000000
Hydrogen     1.       -1.123702            0.463146           -0.889982
Hydrogen     1.        1.129752           -0.318420            0.824662
 $END
 $GUESS  NGUESS=4  $END
 $INTGRL  $END
 $WFN  WFNFLG=0  $END
 $SCF  NCO=9  $END
 $NBO  NLMO  DIPOLE  $END
 $DEL  NOSTAR
       ZERO 2 ATOM BLOCKS     4  BY  3
                              1  3  4  5
                              2  6  7
                              3  BY  4
                              2  6  7
                              1  3  4  5
 $END
.ED
.NP
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NIn general, the $NBO, $CORE, $CHOOSE, and $DEL keylists can be inserted
in any order within the HONDO input file; the NBO program rewinds the
input file each time it searches for a keylist.

.LM10
.RM80
.NP
#ID.6.2 NBO program installation#N

\np The NBO interfacing (driver) routines provided in this
distribution were written for HONDO 7.0, dated 18-JAN-1988.
Section D.6.3 lists the HONDO
dependent elements of the NBO driver routines that may need slight
modification for other versions of the HONDO program.

\np Only one command line is added to the HONDO source code to run the
NBO analysis.  A call (``CALL RUNNBO'') should be inserted at the
end of the HONDO properties package (SR PROPTY in module PRP),
as shown below:

.DF\@seg =
      SUBROUTINE PROPTY

      .
      .
      .

C
C     ----- ELECTRON AND SPIN DENSITIES -----
C
      IF(NODEN.EQ.0) CALL ELDENS
C
C     <<< BEGINNING OF NBO INSERT >>>
C
      CALL RUNNBO
C
C     <<< END OF NBO INSERT >>>
C
      NCALL=0
      IF(SOME) NCALL=1
      CALL TIMIT(NCALL)
      RETURN

      .
      .
      .

      END
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.LM10
.RM80
.FJ

\np #NThe NBO analysis
is performed each time the properties package is called within HONDO.
For example, the NBO analysis of the computed wavefunction will be performed
(unless NOPROP=1 in the $CONTRL namelist) for every single point calculation,
for each point on a scan of a potential energy surface, and for both the
initial and final points of a geometry optimization.  The NBO output will
appear immediately after the Mulliken Population Analysis and the electric
properties in the HONDO output file.

\np The NBO program installation should continue as discussed in Section A.2.
.LM10
.RM80
.NP
#ID.6.3 NBO communication with HONDO#N

\np The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following
HONDO routines, records of the dictionary file, and COMMON blocks:

#_HONDO routines:#T#/

    SR DAREAD(IDAF,IODA,IX,NX,IDAR)
    SR DIPAMS(BMASS,NCALL,NCODE,SOME)
    FN DOTTRI(A,B,N)
    FN ENUC(N,Z,C)
    SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK)
    SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK)
    SR SYMFCK(F,H,IA)
 
#_#NHONDO dictionary file:#/

.LM+5
.TB
.FM<<1C8//2L40>>
.RW-
.RW<<record//contents>>
.RW=
.RW<<2//total energy>>
.RW<<12//AO overlap matrix>>
.RW<<14//AO Fock matrix (alpha)>>
.RW<<15//AO to MO transformation matrix (alpha)>>
.RW<<16//AO density matrix (alpha bond-order matrix)>>
.RW<<18//AO Fock matrix (beta)>>
.RW<<19//AO to MO transformation matrix (beta)>>
.RW<<20//AO density matrix (beta bond-order matrix)>>
.RW<<33//#Ix#N dipole integrals>>
.RW<<34//#Iy#N dipole integrals>>
.RW<<35//#Iz#N dipole integrals>>
.RW-
.ET
.LM-5

#_#NHONDO COMMON blocks:#T#/

    COMMON/IJPAIR/IA(1)
    COMMON/INFOA/NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(50),C(3,50)
    COMMON/INTFIL/NOPK,NOK,NOSQUR,NINTMX,NHEX,NTUPL,PACK2E
    COMMON/IOFILE/IR,IW,IP,IJK,IPK,IDAF,NAV,IODA(99)
    COMMON/MEMORY/MAXCOR,MAXLCM
    COMMON/MOLNUC/NUC(50)
    COMMON/NSHEL/EX(440),CS(440),CP(440),CD(440),CF(440),CG(440),
   +             KSTART(120),KATOM(120),KTYPE(120),KNG(120),
   +             KLOC(120),KMIN(120),KMAX(120),NSHELL
    COMMON/RUNLAB/TITLE(10),ANAM(50),BNAM(50),BFLAB(512)
    COMMON/SCFOPT/SCFTYP
    COMMON/SCM/CORE(1)
    COMMON/WFNOPT/WFNTYP
 #N
.LM10
.RM80
.FJ
.CM------------------------------------------------------------------
.HF<<D.7 AMPAC VERSION//3//10>>
.RL55
#BD.7 AMPAC VERSION#N

#ID.7.1 AMPAC sample input#N

\np A sample AMPAC input file that will create default methylamine
(AM1 at Pople-Gordon idealized geometry) output similar to the
#Iab initio#N output displayed in Section A.3 is shown below:

.DF\@seg =
AM1

CH3NH2...AM1//Pople-Gordon standard geometry
   C      0.000000  0    0.000000  0    0.000000  0   0  0  0
   N      1.470000  0    0.000000  0    0.000000  0   1  0  0
   H      1.090000  0  109.471230  0    0.000000  0   1  2  0
   H      1.090000  0  109.471230  0  120.000000  0   1  2  3
   H      1.090000  0  109.471230  0  240.000000  0   1  2  3
   H      1.010000  0  109.471230  0   60.000000  0   2  1  3
   H      1.010000  0  109.471230  0  300.000000  0   2  1  3

$NBO  $END

.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NThe keylists of the NBO program should always appear at the bottom of the
AMPAC input file and should be ordered: $NBO, $CORE, $CHOOSE, $DEL.
NBO job options are selected by inserting their associated keywords
(Section B.2) into the $NBO keylist.

\np Due to the implicit orthogonality of the basis functions, the
following NBO keywords are not applicable to the wavefunctions
computed by AMPAC (or other semi-empirical packages):
.LJ
 #T
       AOPNAO        AOPNLMO       NAONHO        SPNAO
       AONAO         DINAO         NAONLMO       SPNHO
       AOPNHO        DMNAO         NAOMO         SPNBO
       AOPNBO        FNAO          SAO           SPNLMO

.FJ
#NIn addition, the NBO keywords that require access to the AO dipole
integrals (DIPOLE, DIAO, DINAO, DINHO, DINBO, DINLMO) are not applicable
with AMPAC, since these integrals are unavailable to the NBO program.

.NP
\np The following is a modified AMPAC input file that will generate, in
addition to the default NBO output, the NLMO and the
NBO energetic analyses of methylamine:

.DF\@seg =
AM1

CH3NH2...AM1//Pople-Gordon standard geometry
   C      0.000000  0    0.000000  0    0.000000  0   0  0  0
   N      1.470000  0    0.000000  0    0.000000  0   1  0  0
   H      1.090000  0  109.471230  0    0.000000  0   1  2  0
   H      1.090000  0  109.471230  0  120.000000  0   1  2  3
   H      1.090000  0  109.471230  0  240.000000  0   1  2  3
   H      1.010000  0  109.471230  0   60.000000  0   2  1  3
   H      1.010000  0  109.471230  0  300.000000  0   2  1  3

$NBO  NLMO  $END
$DEL  NOSTAR
      ZERO 2 ATOM BLOCKS  3 BY 4
                          1 3 4 5
                          2 6 7
                          4 BY 3
                          2 6 7
                          1 3 4 5
$END
.ED
.LJ
.HR<<3//+1//5//85>>
.LM5
.RM85
 #T

\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80
.NP
#ID.7.2 Sample NBO output for AMPAC wavefunctions#N

\np Since the AMPAC output differs in significant respects from the
#Iab initio#N examples presented in Sections A,B, we present
some excerpts from the NBO output and a
brief discussion of the NBO analysis of the AM1 wavefunction for
methylamine (Pople-Gordon idealized geometry).  The numerical values
in these exerpts (summary tables) should be adequate for checking
purposes.

\np The summary of the Natural Population Analysis (NPA)
for methylamine is shown below:
.DF\@seg =
Summary of Natural Population Analysis:                  
                                                         
                                      Natural Population 
              Natural   -----------------------------------------------
   Atom #     Charge        Core      Valence    Rydberg      Total
-----------------------------------------------------------------------
     C  1   -0.13281      2.00000     4.13281    0.00000     6.13281
     N  2   -0.34739      2.00000     5.34739    0.00000     7.34739
     H  3    0.03346      0.00000     0.96654    0.00000     0.96654
     H  4    0.08488      0.00000     0.91512    0.00000     0.91512
     H  5    0.08488      0.00000     0.91512    0.00000     0.91512
     H  6    0.13849      0.00000     0.86151    0.00000     0.86151
     H  7    0.13849      0.00000     0.86151    0.00000     0.86151
=======================================================================
  * Total *  0.00000      4.00000    14.00000    0.00000    18.00000
.ED
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.RS#^
\@seg
.RS^#

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NNote that the core electrons of all heavy atoms (neglected in the
semi-empirical AMPAC procedure) are incorporated into the NPA, along the
lines of the treatment of effective core potentials (Section B.6.12).
Note also that the numerical values of AM1 natural charges (and other
quantities) differ significantly from those presented in Section A.3.2,
reflecting a tendency toward somewhat reduced bond polarities in AM1
wavefunctions.

.NP
The NBO summary table is shown below:
.DF\@seg =
Natural Bond Orbitals (Summary):

                                                    Principal Delocalizations
          NBO              Occupancy    Energy      (geminal,vicinal,remote)
===============================================================================
Molecular unit  1  (CH5N)
  1. BD ( 1) C 1- N 2       1.99095   -20.60408    9(g),10(g),11(g),12(g),13(g)
  2. BD ( 1) C 1- H 3       1.99184   -17.81012    8(g),10(g),11(g),9(g)
  3. BD ( 1) C 1- H 4       1.98864   -17.75195    12(v),9(g),11(g),8(g)
  4. BD ( 1) C 1- H 5       1.98864   -17.75195    13(v),9(g),10(g),8(g)
  5. BD ( 1) N 2- H 6       1.98916   -19.74256    13(g),8(g),10(v)
  6. BD ( 1) N 2- H 7       1.98916   -19.74256    12(g),8(g),11(v)
  7. LP ( 1) N 2            1.98489   -15.52775    9(v)
  8. BD*( 1) C 1- N 2       0.01048     4.75597
  9. BD*( 1) C 1- H 3       0.02306     4.29359
 10. BD*( 1) C 1- H 4       0.01070     4.57248
 11. BD*( 1) C 1- H 5       0.01070     4.57248
 12. BD*( 1) N 2- H 6       0.01090     5.27834
 13. BD*( 1) N 2- H 7       0.01090     5.27834
      -------------------------------
             Total Lewis   17.92328  ( 99.5738%)
       Valence non-Lewis    0.07672  (  0.4262%)
       Rydberg non-Lewis    0.00000  (  0.0000%)
      -------------------------------
           Total unit  1   18.00000  (100.0000%)
          Charge unit  1    0.00000
.ED
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\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
.RM80

\np #NNote that in this case the orbital energies and other matrix elements
of the Fock operator are printed in electron volts, the energy units of the
AMPAC package.  Note also that the physical pattern of delocalization effects
differs significantly from that shown in Section A.3.6, the AM1 results
portraying numerous strong #Igeminal#N interactions that are not present
in the #Iab initio#N output.  Other differences between the AM1 and
#Iab initio#N wavefunctions will be evident throughout the NBO output.

.NP
\np Finally, we include the output segment showing the NBO energetic analysis
of methylamine:
.DF\@seg =
NOSTAR: Delete all Rydberg/antibond NBOs
Deletion of the following orbitals from the NBO Fock matrix:
   8   9  10  11  12  13

Occupations of bond orbitals:

      Orbital                   No deletions   This deletion   Change
------------------------------------------------------------------------------
  1. BD ( 1) C 1- N 2               1.99095        2.00000    0.00905
  2. BD ( 1) C 1- H 3               1.99184        2.00000    0.00816
  3. BD ( 1) C 1- H 4               1.98864        2.00000    0.01136
  4. BD ( 1) C 1- H 5               1.98864        2.00000    0.01136
  5. BD ( 1) N 2- H 6               1.98916        2.00000    0.01084
  6. BD ( 1) N 2- H 7               1.98916        2.00000    0.01084
  7. LP ( 1) N 2                    1.98489        2.00000    0.01511
  8. BD*( 1) C 1- N 2               0.01048        0.00000   -0.01048
  9. BD*( 1) C 1- H 3               0.02306        0.00000   -0.02306
 10. BD*( 1) C 1- H 4               0.01070        0.00000   -0.01070
 11. BD*( 1) C 1- H 5               0.01070        0.00000   -0.01070
 12. BD*( 1) N 2- H 6               0.01090        0.00000   -0.01090
 13. BD*( 1) N 2- H 7               0.01090        0.00000   -0.01090

NEXT STEP:  Evaluate the energy of the new density matrix
            that has been constructed from the deleted NBO
            Fock matrix by doing one SCF cycle.

------------------------------------------------------------------------------
  Energy of deletion :        22.024
    Total SCF energy :        -5.051
                         -------------------
       Energy change :        27.075 kcal/mol,          27.075 kcal/mol
------------------------------------------------------------------------------
.ED
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\@seg

.HR<<3//+0//5//85>>
.FJ
.LM10
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\np #NNote that the ``energy of deletion'' (22.0 kcal/mol), ``total SCF
energy'' (-5.1 kcal/mol) and ``energy change'' (27.1 kcal/mol) are all
given in terms of heats of formation, the standard AM1 form of expressing
molecular energies.

.FJ
.LM10
.RM80
.NP
#ID.7.3 NBO program installation#N

\np The NBO interfacing (driver) routines provided in this
distribution were written for AMPAC, version 1.00.
Section D.7.4 lists the AMPAC
dependent elements of the NBO driver routines that may need slight
modification for other versions of the AMPAC program.

\np Only one command line is added to the AMPAC source code to run the
NBO analysis.  A command ``CALL RUNNBO'' should be inserted in the
AMPAC properties package (SR WRITE in module WRITE), as shown below:

.DF\@seg =
      SUBROUTINE WRITE(TIME0,FUNCT)

      .
      .
      .

         X=MECI(EIGS,C,CBETA,EIGB, NORBS,NMOS,NCIS, .TRUE.)
      ENDIF
C
C     <<< BEGINNING OF NBO INSERT >>>
C
      CALL RUNNBO
C
C     <<< END OF NBO INSERT >>>
C
      IF (INDEX(KEYWRD,'MULLIK') +INDEX(KEYWRD,'GRAPH') .NE. 0) THEN
         IF (INDEX(KEYWRD,'MULLIK') .NE. 0) THEN

      .
      .
      .
.ED
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\@seg

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\np #NThe NBO analysis is performed each time SR WRITE is called.
For example, the NBO analysis of the computed wavefunction will be performed
for every single point calculation and at the end of geometry optimizations.
The NBO output will appear immediately after the Mulliken Population Analysis
in the AMPAC output file.

\np The NBO program installation should continue as discussed in Section A.2.
.LM10
.RM80
.NP
#ID.7.4 NBO communication with AMPAC#N

\np The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following
AMPAC routines and COMMON blocks:

#_AMPAC routines:#T#/

    SR GMETRY(GEO,COORD)
    SR HCORE(COORD,H,W,WJ,WK,ENUCLR)
    SR FOCK2(F,PTOT,P,W,WJ,WK,NUMAT,NFIRST,NMIDLE,NLAST)
    SR FOCK1(F,PTOT,PA,PB)
    FN HELECT(N,P,H,F)
 
#_#NAMPAC COMMON blocks:#T#/

    INCLUDE 'SIZES'
    COMMON /ATHEAT/ ATHEAT
    COMMON /DENSTY/ P(MPACK),PA(MPACK),PB(MPACK)
    COMMON /ENUCLR/ ENUCLR
    COMMON /FOKMAT/ F(MPACK),FB(MPACK)
    COMMON /GEOKST/ NATOM,LABELS(NUMATM),NA(NUMATM),NB(NUMATM),
   +                NC(NUMATM)
    COMMON /GEOM  / GEO(3,NUMATM)
    COMMON /HMATRX/ H(MPACK)
    COMMON /KEYWRD/ KEYWRD
    COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
   +                NLAST(NUMATM),NORBS,NELECS,NALPHA,NBETA,NCLOSE,
   +                NOPEN,NDUMY,FRACT
    COMMON /NATORB/ NATORB(107)
    COMMON /TITLES/ COMENT(10),TITLE(10)
    COMMON /VECTOR/ C(MORB2),EIGS(MAXORB),CBETA(MORB2),EIGB(MAXORB)
    COMMON /WMATRX/ WJ(N2ELEC),WK(N2ELEC)
 #N
.TP2
.LJ
#N
.HF<<INDEX//3//10>>
.NF<<I-// >>
.PN1



.CJ
#HINDEX#N
.LJ


.LN12
.PF<<10//44//46//80>>
 Acceptor orbital,A21
 ACS Software,A11
 AMPAC version,A2,A7,A8,B66,C17
 Angular symmetry labels,A5,#IB68#N,C7
 Antiperiplanar interaction,A19,A23,B50
 Archive file (FILE47),A5,
        #IB62-71#N,C8,C14,C31,C36
 Arrays
      IBXM,C9,C22,C23
      JPRINT,C6
      NBOOPT,C16,#IC17#N,C18,
            C26,C30,C36,C39
 Atom-centered basis functions,A1
 Atomic charge,A14
 Atomic orbitals,A1,A5,A6,B67-68
      Contracted gaussian,A6,B69-70
      Pure (PAO),#IB11#N,B67-68,C19,C30
      Slater-type,A6
      #Isee#N Atomic shell
      #Isee#N Core orbitals
      #Isee#N Pre-orthogonal orbitals
 Atomic shell
      Core,A7,A8,A13,A14,A16,C24
      Rydberg,A2,A8,A13,A14,A16,C25
      Valence,A8,A13,A14,A16
 Atomic units,A13,B65,C4,C13
 Attaching NBO to ESS program,
        A10-11,C36,C38-39
 AUHF method
      #Isee#N Wavefunction type
 Azimuthal angle (\phi ),A20,C33
 
 Basis set
      #Isee#N Atomic orbitals
 Benzene (C#d6#uH#d6#u),B3,B32-36
 Bond bending,A8,A20
      #Isee#N Hybrid direction
 BONDO program,A7
 Bond order,B29-31
      Matrix,B11,B65,C19
 Boys LMOs,B3
 Brunck, T. K.,A7
 
 Canonical MOs,B6,B27-28,B71,C20
 Carpenter, J. E.,A7
 Chemical fragment,#IB16#N,B19
.RL2
 $CHOOSE list
      #Isee#N Keylists
 Comments (!),B1,B63,C29
 Comment statements,C1
 COMMON blocks
      /NBAO/,C7
      /NBATOM/,C7
      /NBBAS/,C9,C22,C31,C30
      /NBCRD1/,C11,C29
      /NBCRD2/,C12,C29
      /NBDAF/,C12,C27,C28
      /NBDXYZ/,C11
      /NBFLAG/,C5
      /NBGEN/,C13,C30
      /NBINFO/,C4
      /NBIO/,C8,C18
      /NBLBL/,C10,C32
      /NBMOL/,C10
      /NBNAO/,C10
      /NBONAV/,C12
      /NBOPT/,C6-7,C18,C30
      /NBTHR/,C9,C18
      /NBTOPO/,C11,C22
 Contour plotting program,A8,B9,B69
 Contracted gaussian orbitals
      #Isee#N Atomic orbitals
 Copper dimer (Cu#d2#u),B56-61
 $CORE list
      #Isee#N Keylists
 Core orbitals,A6,A7,A8,A16,
        B12-13,B56-61,B66,C24,C30,C33
 Core polarization,A8,B12
 Core table,B12,C33

 DAF
      #Isee#N Direct access file
 Datalists,B63-64
      $BASIS,#IB67-68#N,B71,C31,C37
      $CONTRACT,#IB69-70#N,C31,C37
      $COORD,B63,B65,#IB66#N,C31,C37
      $DENSITY,B71
      $DIPOLE,B65,B71,C37
      $FOCK,B65,B71,C37
      $LCAOMO,B71,C37
      Matrix,B71
      $OVERLAP,B65,B71,C37
 #Id#N-orbitals,B53,B56,B61
 Default output,A12,B10
 Deletion types,B17-19
.RL2
 $DEL (deletions) list
      #Isee#N Keylists
 Delocalization,A1,A2,A21,B3,B32,B51
 Delocalization tail,A22,B23
.RL3
 Density matrix,A1,A5,A6,B6-7,C13
      #Isee#N Bond-order matrix
      #Isee#N Spin density matrices
 Depletion of density matrix,C24
 Diborane (B#d2#uH#d6#u),B40-43
 Dictionary file,A4
 Different Lewis structures for
   different spin
      #Isee#N Open-shell calculation
 Dimension specification,C4
 Dipole moment,A5,A6,A8,B5,B6-7,
        #IB24-25#N,B65,B71,C11,C15,C24
.RL3
 Direct access file (FILE48),A3,A4,A5,
        B9,B65,C12,#IC14-15#N,C16,C27,
        C28,C36-39
 Directed NBO search
      #Isee#N Keylists, $CHOOSE
 Directional analysis
      #Isee#N Hybrid direction
 Distribution tape,A10
 Donor orbital,A21,A22
 Double-bond, no-bond resonance,B44-47
 Driver routines,A3
      #Isee#N Subroutines RUNNBO, etc.
 
 Edmiston-Ruedenberg LMOs,B3
 Effective core potential (ECP),
        A8,#IB56-61#N,B66
 Electronic structure system (ESS),A3
      Common blocks,A4
      Connection to NBO program,A3,A4,A7,
         A10-11,B56,B62,C36,C38-39
      Input file,A5,A11,A12
      Output file,A5,A12
      Scratch files,A4
      #Isee#N AMPAC, GAUSSIAN-8X, #Ietc.#N
 ENABLE program,A10,C36
 Energetic analysis,A3,A5,#IB16-19#N,
        C2,C26,C38,C39
      #Isee#N Perturbation theory...
 Excited state,A6,A8,A15,B56,C23
 
.RL3
 #If#N-orbitals
      #Isee#N Angular symmetry labels
      #Isee#N Keyword CUBICF
.RL2
 Fenske-Hall method
      #Isee#N MEDVL 
 Fetch/Save routines,C15,C27
.RL2
 FILE48
      #Isee#N Direct access file
.RL2
 FILE47 
      #Isee#N Archive file
 Flow chart,A4,C3,C16
 Fock matrix,A2,A5,A6,A8,A14,A21,
        B6,B16-20,B26,B48-51,B65,B71,
        C2,C23,C26,C39
 Fortran 77,A6,A10
 Foster, J.P.,C22
 Free format,B1,C29
 Freezing a transformation,B8
 Functions
      EQUAL,C29
      IHTYP,C34
      IOINQR,C32
      IWPRJ,C24
      NAMEAT,C34
      VECLEN,C35
 
 GAMESS version,A1,A2,A7,A10,A12,C17
 Gaussian elimination,C35
 GAUSSIAN-8X version,A2,A7,
        A10,B56,C17
 Geminal interaction,A22,B18,C33
 Generalized eigenvalue problem,C20
.RL2
 GENNBO input file 
      #Isee#N Archive file
.RL2
 GENNBO stand-alone program
        A10,B9,B62-71,C13,C36,C37,C38
 Geometry,B66
 Glendening, E. D.,A7
 Groups of routines
      I   (NAO/NBO/NLMO),C2,C16-25
      II  (energy analysis),C2,C26
      III (direct access file),C2,C27-28
      IV  (free format input),C2,C29
      V   (other I/O),C2,C30-32
      VI  (general utility),C2,C33-35
      VII (system-dependent),C2,C36
 GUGA formalism,A1
 GVB method
      #Isee#N Wavefunction type
 
 Hay-Wadt ECP,B56
 HONDO version,A2,A10,C17,C27
 Hybrid composition,A19,B23
 Hybrid direction,A8,#IA20#N,B4,C23
 Hydrogen fluoride (HF),B37-39
 
 I/O routines
      #Isee#N Groups of routines
 INP routines,C30,C39
 Input file,A5,B62,C14
 Installation procedure,A10-11
 Ionic hybrids,B37-39
 
 Job control keywords,B2,B3
 Job initialization routines,C16,C18
 Job threshold keywords,B2,B4-5
 
 Kekul\acute e structure,B36
 Keylist,A5,A11,A12,#IB1#N
.RL3
 Keylists
      $CHOOSE,B1,B2,B12,#IB14-15#N,#IB44-47#N,
           B62,B63,B65,C6,C22,C30
      $CORE,B1,B2,#IB12-B13#N,
           B62,B63,B65,C3,C6-7,C30
      $DEL,B1,B2,B12,#IB16-20#N,
           #IB48-51#N,B62,C17,C26,C30
      $GENNBO,#IB65#N,B66,C30
      $NBO,B1,#IB2-11#N,B21-43,B62,B63,
           B65,B69,C6,C17,C18,C22,C30
 Keyword names (matrix output),B6-7
 Keyword parameters (matrix output),B7-8
 Keywords
      AOINFO,B2,#IB9#N,B69,B71,C6,C31
      AOMO,B2,B6,B71,C6
      AONAO,B2,B6,C6,C30-31
      AONBO,B2,B6,C6,C31
      AONHO,B2,B6,C6
      AONLMO,B2,B3,B6,C6,C31
      AOPNAO,B2,B6,B71,C6
      AOPNBO,B2,B6,B71,C6
      AOPNHO,B2,B6,B71,C6
      AOPNLMO,B2,B6,B71,C6
      ARCHIVE,B2,#IB9#N,#IB62-71#N,C6,C31
      BEND,A8,#IA20#N,B2,#IB4#N,B5,B10,C6,C23
      BNDIDX,B2,#IB9#N,B10,B21,
         #IB29-B31#N,C6
      BOAO,B11,C6
      BODM,#IB65#N,C6,C13
      BOHR,#IB65#N,B66,,C13
      CUBICF,#IB65#N,B68,C6
      DESTAR,B18
      DETAIL,B2,#IB9#N,C6
      DIAO,B2,B7,B71,C6
      DINAO,B2,B7,B71,C6
      DINBO,B2,B7,B71,C6
      DINHO,B2,B7,B71,C6
      DINLMO,B2,B6,B7,B71,C6
      DIPOLE,A8,B2,B3,#IB5#N,B10,B21,
         #IB24-25#N,B71,C6,C17,C24
      DMAO,B2,B7,C6
      DMNAO,B2,B7,C6
      DMNBO,B2,B7,C6
      DMNHO,B2,B7,C6
      DMNLMO,B2,B7,C6
      E2PERT,#IA21#N,B2,#IB4#N,B5,B10,B71,C6
      EV,B65
      FAO,B2,B7,B71,C6
      FNAO,B2,B7,B71,C6
      FNBO,B2,B6-8,B7,B71,C6
      FNHO,B2,B7,#IB26#N,B71,C6
      FNLMO,B2,B7,B71,C6
      LFNPR,B2,#IB9#N,C8
      Matrix output,B6-8,B26-28
      MULAT,B11,C6
      MULORB,B11
      NAOMO,B2,B6-8,B71,C6
      NAONBO,B6-8,C6
      NAONHO,B6-8,C6
      NAONLMO,B6-8,C6
      NATOMS,B65
      NBAS,B65
      NBODAF,B2,B9
      NBO,#IA16-19#N,B2,#IB3#N,B10,C6
      NBOMO,B2,B6-8,#IB27-28#N,B71,C6
      NBONLMO,B2,B6-8,C6
      NBOSUM,#IA22-23#N,B2,#IB3#N,B10,C6,C23
      NHOMO,B2,B6-8,B71,C6
      NHONBO,B2,B6-8,C6
      NHONLMO,B2,B6-8,C6
      NLMO,B2,#IB3#N,B5,B10,#IB22-23#N,C6
      NLMOMO,B2,B6-8,B71,C6
      NOBOND,B2,#IB3#N,B21,#IB37-39#N,C6
      NOGEM,B18
      NOSTAR,B18,#IB48-49#N
      NOVIC,B18
      NPA,#IA13-15#N,B2,#IB3#N,B10,C6,C20
      OPEN,B65
      ORTHO,B65
      PAOPNAO,B11,C6
      PLOT,A8,B2,#IB9#N,B69,B71,C6
      PRINT,B2,B5,#IB10#N,B71,C18,C6
      PRJTHR,B11
      RESONANCE,A16,B2,#IB3#N,B21,
         #IB32-36#N,C6,C17,C25
      REUSE,#IB65#N,B66,B67,C13
      RPNAO,B11,C6
      SAO,B2,B7,B71,C6
      SKIPBO,B2,#IB3#N,B10,C6
      SPNAO,B2,B6-8,B7,B71,C6
      SPNBO,B2,B7,B71,C6
      SPNHO,B2,B7,B71,C6
      SPNLMO,B2,B3,B7,B71,C6
      3CBOND,B2,#IB3#N,B14,B21,#IB40-43#N,C6
      THRESH,B11
      UPPER,B65,B71,C13
      ZERO,B19,#IB49-51#N
.RL2
 Kinks
      #Isee#N Hybrid direction, Bond bending
 
.RL2
 Labelled COMMON blocks,A3,A6,C4-13
      #Isee#N COMMON blocks
.RL2
 Lewis orbitals
      #Isee#N Natural bond orbitals
 Linear equations package,C35
 Linear independence,A1,C22,C24
 Logical file number (LFN),C8,C38,C39
 L\umlaut owdin, P.-O.,A1
 L\umlaut owdin orthogonalization,C21
 
 Matrix multiplication,C34
.RL2
 Matrix output keywords,
        B2,#IB6-8#N,B9,#IB26-28#N,C7
 Mayer-Mulliken bond-order,C19
 MCSCF method
      #Isee#N Wavefunction type
 MEDVL version,A10
 Memory allocation,
        A6,A12,C16,C18,C19,C22
 Methylamine (CH#d3#uNH#d2#u),
        A12-23,B21-31,B44-51,B63-71
 Methyl radical (CH#d3#u),B52-55
 Molecular units,#IB16#N,B18,B19,C10,C23
 M\not oller-Plesset method
      #Isee#N Wavefunction type
 MOPAC version,A10
.RL2
 Mulliken population analysis,
         A10,B11,C19,C38
 Multiple bonds,A19,B14,B44-47,B56-61
 
 Naaman, R.,A7
 NAO formation routines,C16,C19-21
.RL3
 Natural atomic orbital (NAO)
      Formation,A1,A7,C16,C19-21
      Labels,A13-14,C10
      Listing,A13,C10
      Summary table,A7
      #Isee#N Natural population analysis
.RL3
 Natural bond orbital (NBO)
      Analysis,A1-2,A16-19
      Formalism,A1-A2,A7
      Labels,A8,A19,B27-28,B43,C9,C10,C32
      Lewis,A2,A16,A19,A21,A23,B48-51,B17
      Listing,#IA17-19#N,B2
      Non-Lewis,A2,A16,A19,
         A21,A23,B17,B18,B48-51
      Summary table,#IA22-23#N,C23
      3-center,A16,#IB40-43#N
      #Isee#N Perturbation theory...
      #Isee#N NBO/NLMO formation routines
.RL2
 Natural electron configuration (NEC),
        A7,#IA15#N,C20
.RL3
 Natural hybrid orbital (NHO)
      Directional analysis,A20
      Formation,A1-2
      Labels,B26,C10
      Listing,A-19
      #Isee#N Natural bond orbitals
      #Isee#N Hybrid direction
.RL3
 Natural Lewis structure,A1-2,A16,
        A19,B3,B18,B48,B49
      Energy,B18,B48
.RL3
 Natural localized molecular orbital (NLMO)
      Formation,A7,B3,C25
      Listing,B3,#IB22-23#N
 Natural minimal basis (NMB) set,A2,A14
 Natural population analysis (NPA),
         A3,A6,A7,#IA13-14#N,B3,
         B10,B21,B56-57,C20
 Natural Rydberg basis (NRB) set,A2,A18
 NBO direct access file
      #Isee#N Direct access file
 $NBO keylist
      #Isee#N Keylists
 NBO energetic analysis
      #Isee#N Energetic analysis
      #Isee#N Perturbation theory...
 NBO.MAN file,A10,A11
 NBO/NLMO formation routines,
        C16,C22-25
 NBO program,Section C
      I/O,A5,A12,C27-32
      Installation,A10-11
      Organization,A3-4,C2-4
      Restrictions,A6
      #Isee#N Electronic structure system
 NBO.SRC file,A10,C1,C2
 NBO summary table,#IA22-23#N,C23
 NLMO/NPA bond order,B30-31
 Non-Lewis orbitals
      #Isee#N Natural Bond Orbital
 
 Open-shell calculation,
        A1,A5,B14,B25,#IB52-55#N,B65,C5
      #Isee#N Wavefunction type
 Orbital contour plotting program,
        A8,B9,B69
 Orthogonalization,C20
      L\umlaut owdin (symmetric),C24
      Occupancy-weighted (OWSO),C20,C21
      Schmidt,C20
 Output control keywords,B2,#IB9-10#N
 Output file,A8,A12,C1
.RL2
 Overlap matrix,A5,A6,A8,B6,B71,C38
      singularities,C25
 Overlap-weighted NAO bond order,B30
 
.RL2
 Perturbation theory energy analysis,
        A8,#IA21#N,B3,B4,C23,C39
 Phi,A20,C33
.RL2
 PNAO, PNBO, PNHO, PNLMO
      #Isee#N Pre-orthogonal orbitals
 Polar angle (\theta ),A20,C33
 Polarization coefficients,A2,A19,C25
 Pople-Gordon geometry,A12,A20,B21,B32
.RL3
 Population analysis
      #Isee#N Mulliken population analysis
      #Isee#N Natural population analysis
 Population inversion,A14,B57
.RL2
 Pre-orthogonal orbitals,
         A1-2,A6,A8,B6,B65,B71
.RL2
 Print parameters,B2,#IB7-8#N,
         B11,B27-28,C7,C10
.RL2
 Program groups,C2
      #Isee#N Groups of routines
.RL3
 Program limits
      Atoms,A6,C4
      Basis functions,A6,C4
 Program precedence,C2,C3
 Pseudopotential
      #Isee#N Effective core potential
 Pure AOs,B11
      #Isee#N Atomic orbital
 
 QCPE,A7,A8
 
 Read (R) parameter
      #Isee#N Print parameters
 Read-write file,A4
 Reed, A. E.,A7,B11,B31,C19
 References,A7
 Remote interaction,A22,C33
 Resonance structures,A9,B14-15,B32-33,
        B38,B39,B44-47,C11,C25
 Rewind input file,C39
 RHF method
      #Isee#N Wavefunction type
 Rives, A. B.,A7
 ROHF method
      #Isee#N Wavefunction type
 
 Schleyer, P. v.R.,B31
 2nd-order perturbation theory analysis
      #Isee#N Perturbation theory energy...
 Semi-documented keywords,B2,#IB11#N
 Similarity transformation,C19,C26,C34
.RL2
 Slater-type orbitals
      #Isee#N AO basis functions
.RL2
 Spin
      #Isee#N Open-shell calculations
.RL2
 Spin-annihilated UHF (AUHF) method
      #Isee#N Wavefunction type
 Spin density matrices,A1,B52-55,C5
.RL2
 Storage
      #Isee#N Memory allocation
.RL2
 Subroutines,C2,C3
      ANGLES,C33
      ANLYZE,C23
      AOUT,C31
      APRINT,C31,C32
      AREAD,C31
      ATDIAG,C20
      AUGMNT,C25
      AWRITE,C31
      BDFIND,C33
      BLDSTR,C23
      CHEM,C33
      CHOOSE,C22,C23,C24
      CHSDRV,C22
      CHSINP,C30
      CONSOL,C33
      CONVIN,C33
      CONVRT,C33
      COPY,C33
      CORE,C24
      CORINP,C30
      CORTBL,C33
      CYCLES,C22,C25
      DEBYTE,C33
      DELETE,C26
      DELINP,C30
      DELSCF,A3,A4,A5,C2,#IC36#N,C38,C39
      DEPLET,C24
      DFGORB,C19,C30
      DIPANL,A6,C22,C24
      DIPELE,C24
      DIPNUC,C24
      DMNAO,C19
      DMSIM,C19
      FACTOR,C35
      FEAOIN,A3,A4,A5,C2,C6,
         C14,#IC36#N,C38,C39
      FEAOMO,C27
      FEAOM,C27
      FEBAS,C27
      FECOOR,C27
      FEDNAO,C27
      FEDRAW,C27
      FEDXYZ,C27
      FEE0,C27
      FEFAO,C27
      FEFNBO,C27
      FEINFO,C27
      FENBO,C27
 Subroutines (#Icontinued#N)
      FENEWD,C27
      FENLMO,C27
      FEPNAO,C27
      FEPPAO,C27
      FESNAO,C27
      FESRAW,C27
      FETITL,C27
      FETLMO,C27
      FETNAB,C27
      FETNAO,C27
      FETNBO,C27
      FETNHO,C27
      FNBOAN,C23
      FNDFLD,C29
      FNDMOL,C23
      FNDSOL,C35
      FORMT,C25
      FRMHYB,C23
      FRMPRJ,C25
      FRMTMO,C20
      GENINP,C30
      GETDEL,C23
      HALT,C33
      HFLD,C29
      HTYPE,C23
      HYBCMP,C23
      HYBDIR,C23
      IDIGIT,C33
      IFLD,C29
      INTERP,C32
      JACOBI,C25,C34
      JOBOPT,C18,C29
      LBLAO,C32
      LBLNAO,C32
      LBLNBO,C32
      LBLNHO,C32
      LIMTRN,C34
      LINEQ,C33,C35
      LMOANL,C24
      LOADAV,C20
      LOAD,C24
      MATML2,C34
      MATMLT,C34
      MULANA,C19
      NAOANL,C21
      NAODRV,C2,C19
      NAOSIM,C19
      NAO,C19
      NATHYB,C22,C23,C24
      NBCLOS,C16,C28
      NBINQR,C28
      NBOCLA,C23
      NBODEL,C26
      NBODIM,C18
      NBODRV,C2,C19,C22
      NBOEAN,A3,A4,A6,C3,C26,C36,C39
      NBOINP,C30
      NBOPEN,C16,C27
      NBOSET,C18,C39
      NBO,A3,A4,C2,C16,C36
      NBOSUM,C23
      NBREAD,C28
      NBWRIT,C28
      NEWDM,C26
      NEWRYD,C20
      NEWWTS,C20
      NLMO,C22,C24
      NORMLZ,C34
      ORDER,C34
      ORTHYB,C24
      OUTPUT,C32
      PACK,C34
      PRJEXP,C24
      RANK,C34
      RDCARD,C29
      RDCORE,C30
      RDPPNA,C30
      RDTNAB,C31
      RDTNAO,C31
      REDBLK,C21
      REDIAG,C21
      REPOL,C25
      RFLD,C29
      RNKEIG,C26
      RUNNBO,A3,A4,#IC36#N,C38,C39
      RYDIAG,C20
      RYDSEL,C21
      SETBAS,C20
      SHMDT,C20
      SIMLTR,C26
      SIMTRM,C19
      SIMTRN,C34
      SIMTRS,C34
      SRTNBO,C22
      STASH,C24
      STRTIN,C29
      SUBST,C35
      SVDNAO,C27
      SVE0,C27
      SVFNBO,C27
      SVNBO,C27
      SVNEWD,C27
      SVNLMO,C27
      SVPNAO,C27
      SVPPAO,C27
      SVSNAO,C27
      SVTLMO,C27
 Subroutines (#Icontinued#N)
      SVTNAB,C27
      SVTNAO,C27
      SVTNHO,C27
      SYMORT,C25
      SYMUNI,C25
      TRANSP,C34
      UNPACK,C35
      VALTBL,C35
      WRARC,C31
      WRBAS,C31
      WRMLMO,C31
      WRPPNA,C30
      WRTNAB,C31
      WRTNAO,C30,C31
      WRTNBO,C312
      XCITED,C23
 Symmetric orthogonalization,C24,C25
 Symmetry,B16
 System-dependent driver routines,C36
 
 TechSet,A11,A20
 Theta,A20,C33
 3-center bonds
      #Isee#N Natural bond orbitals
 Thresholds,C9
      ALLOW2,C20
      ALLOW,C20
      ANG,B4
      ATHR,C23
      DANGER,C20,C25
      DIAGTH,C20,C25
      DIFFER,C24,C34,C34
      DONE,C34
      DVAL,B5,B25
      EPS,C24,C34
      ETHR1,C23
      ETHR2,C23
      ETHR,C23
      EVAL,B4
      OCC,B4
      PCT,B4
      PRJINC,C22
      PRJTHR,B11,C22
      PTHR,C23
      TEST2,C20
      TEST,C20
      THRESH,C22
      THR1,C23
      THR2,C23
      THRESH,B11,C25
      TOOSML,C24
      WORTH,C20
      WTTHR,C20,C21
 2e-stabilization,A21
 
.RL2
 UHF method
      #Isee#N Wavefunction type
.RL2
 Upper triangular matrix,
        B65,B71,C13,C33,C34
 
 Vager, Z.,A7
.RL2
 Valency index
      #Isee#N Bond order
 Versions, previous,#IA7#N,A9,B13
.RL2
 Vicinal interaction,A22-23,B18,
        B23,B25,B51,C33
 
 Warnings,B16,B17,B36,B55
.RL3
 Wavefunction type
      AUHF,C5,C17
      CI,A6,C5,C17
      Complex,A6,C5
      Correlated,B25
      GVB,A6
      MCSCF,A1,A6,C5
      M\not oller-Plesset,A6,C17
      RHF,A6,A12,B16,B56,C2
      ROHF,A6,C5
      SCF,A6,B16,B25,C17
      Semi-empirical,A7,A8,B66
      UHF,A6,B16,B20,B52-55,C2,C5
 Weinhold, F.,A7,B11,C19,C22
 Weinstock, R. B.,A7,B11,C19
 Wiberg bond index,A16,B9,B29,C20,C22
 Write (W) parameter
      #Isee#N Print parameters