Multireference configuration interaction (MRCI) — BAGEL Manual

# Multireference configuration interaction (MRCI)

## Description

Fully internally contracted multireference configuration interactions up to the two-electron excitation (MRCISD). This is implemented with the automatical code generator SMITH3. By default, the Davidson corrected (+Q) energy is also printed.

Title: `smith`, method: `mrci`

## Prerequisites

A reference wavefunction generated by a HF or CASSCF calculation.

## Keywords

### CASSCF keywords

See Complete active space self-consistent field (CASSCF).

### SMITH keywords

The default values are recommended unless mentioned otherwise.

`thresh`

Description: Convergence threshold.
Datatype: double precision
Default: 1.0e-8 (gradient) 1.0e-6 (otherwise)

`thresh_overlap`

Description: Overlap threshold.
Datatype: double precision
Default: 1.0e-9

`frozen`

Description: Freeze core orbitals.
Datatype: bool
Default: true

`ncore`

Description: Number of frozen core orbitals.
Datatype: int
Default: If `frozen` is true, subvalence orbitals are frozen. If false, zero.

`nfrozenvirt`

Description: Number of frozen virtual orbitals.
Datatype: int
Default: 0

`maxiter`

Description: Maximum number of iterations in MRCI calculations.
Datatype: int
Default: 50

`maxtile`

Description: Maximum number of orbitals in a single data tile used in SMITH3.
Datatype: int
Default: 10

`davidson_subspace`

Description: Number of vectors retained in the limited-memory Davidson algorithm.
Datatype: int
Default: 10
Recommendation: Reduce if an insufficient amount of memory is available (do not reduce to a value lower than 3).

## Example

    { "bagel" : [

    {
      "title" : "molecule",
      "basis" : "svp",
      "df_basis" : "svp-jkfit",
      "angstrom" : true,
      "geometry" : [
         { "atom" : "O",  "xyz" : [   -0.000000,     -0.000000,      1.210000]},
         { "atom" : "O",  "xyz" : [   -0.000000,     -0.000000,      0.000000]}
      ]
    },

    {
      "title" : "casscf",
      "nclosed" : 7,
      "nact" : 2
    },

    {
      "title" : "smith",
      "method" : "mrci"
    }

    ]}

from which one obtains

    * freezing 2 orbitals
    * XMS rotation is only appropriate for CASPT2, and will not be used with mrci
       - MO integral evaluation                    0.01
    - linear dependency detected:    3 /    4    min eigenvalue:     0.0000e+00    max eigenvalue:     0.0000e+00
    - linear dependency detected:    3 /    4    min eigenvalue:    -3.9968e-15    max eigenvalue:    -1.1102e-15
    - linear dependency detected:    4 /    8    min eigenvalue:    -1.0380e-15    max eigenvalue:     2.9134e-15
    - linear dependency detected:    6 /    8    min eigenvalue:     0.0000e+00    max eigenvalue:     0.0000e+00
    - linear dependency detected:    6 /    8    min eigenvalue:    -1.2102e-15    max eigenvalue:     9.1101e-16
       - RDM + denominator evaluation              0.00

    * Zeroth order energy : state  0       -0.4388085255

      ---- iteration ----

        0   0  -149.74880423     0.00455295      0.06
        1   0  -149.76848791     0.00088584      0.06
        2   0  -149.76925804     0.00021094      0.06
        3   0  -149.76932381     0.00006783      0.07
        4   0  -149.76932906     0.00001772      0.07
        5   0  -149.76932932     0.00000337      0.06
        6   0  -149.76932933     0.00000065      0.07

      -------------------

       - MRCI energy evaluation                    0.46

        0   0  -149.80276480     0.00000000      0.00

       - MRCI+Q energy evaluation                  0.00

    * METHOD: SMITH                                0.48

## References

Fully internally contracted MRCI itself is not particularly new.

### BAGEL References

Description of Reference | Reference
--- | ---
SMITH3 | M. K. MacLeod and T. Shiozaki, J. Chem. Phys. 142, 010507 (2015)
Relativistic extension | T. Shiozaki and W. Mizukami, J. Chem. Theory Comput. 11, 4733 (2015)

### General References

Description of Reference | Reference
--- | ---
Fully internally contracted MRCI | H.-J. Werner and E.-A. Reinsch, J. Chem. Phys. 76, 3144 (1982)
Modern implementation | M. Saitow, Y. Kurashige, and T. Yanai, J. Chem. Phys. 139, 044118 (2013)