Full configuration interaction (FCI) — BAGEL Manual

# Full configuration interaction (FCI)

## Description

FCI exactly diagonalizes the molecular Hamiltonian within the space spanned by all of the Slater determinants. This FCI section is closely related to that for the Complete active space self-consistent field (CASSCF) method.

## Prerequisites

A reference wavefunction generated by a HF or CASSCF calculation.

## Keywords

`maxiter (or maxiter_fci)`

Description: Maximum number of iterations in the FCI algorithm.
Datatype: int
Default: 100

`thresh (or thresh_fci)`

Description: Threshold for the convergence of the selected CI algorithm.
Datatype: double
Default: 1.0e-10

`algorithm`

Description: FCI algorithm to be used.
Datatype: string
Values:
`KH, Knowles, Handy`: Use the Knowles–Handy algorithm.
`HZ, Harrison, Zarrabian`: Use the Harrison–Zarrabian algorithm.
`Dist, parallel`: Use a parallel algorithm based on HZ.
Default: KH or Dist depending on the size of the calculation and the number of MPI processes.

`frozen`

Description: Use of the freeze core approximation.
Datatype: bool
Default: false

`ncore`

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

`norb`

Description: Number of correlated orbitals. Any high-energy orbitals in excess of this number will be excluded.
Datatype: int
Default: All molecular orbitals except those excluded using ncore.

`active`

Description: Orbital indices for the orbitals to be included. Note that orbital numbers start from 1.
Datatype: vector<int>
Default: Frontier orbitals are used.

`charge`

Description: The total charge of the system.
Datatype: int
Default: 0

`nspin`

Description: The number associated with the spin states: 0 for singlet, 1 for doublet, 2 for triplet, etc.
Datatype: int
Default: 0

`nstate`

Description: Number of states to be calculated.
Datatype: int
Default: 1

`davidson_subspace`

Description: Number of vectors retained in the limited-memory Davidson algorithm.
Datatype: int
Default: 20
Recommendation: Reduce if an insufficient amount of memory is available (do not reduce to a value lower than 3).

`nguess`

Description: Number of guess configurations
Datatype: int
Default: `nstate`

`only_ints`

Description: If true, calculates integrals and dumps to a file. This is used to interface BAGEL to an external program.
Datatype: bool
Default: false

`dipoles`

Description: Calculate dipoles
Datatype: bool
Default: false

`restart`

Description: Generate binary archive files that can be used to restart a calculation.
Datatype: bool
Default: false

`print_thresh`

Description: Threshold below which CI coefficients are not printed
Datatype: double
Default: 0.05

## Example

A Hartree–Fock and FCI calculation on an oxygen molecule with an elongated bond. The HF calculation is a references for the FCI calculation. Please refer to MOLDEN for more information on the print input block.

### Sample input

    { "bagel" : [

    {
      "title" : "molecule",
      "basis" : "sto-3g",
      "df_basis" : "cc-pvdz-jkfit",
      "angstrom" : true,
      "geometry" : [
        { "atom" : "H",  "xyz" : [ 0.0, 0.0, 1.5 ]},
        { "atom" : "F",  "xyz" : [ 0.0, 0.0, 0.0 ]}
      ]
    },

    {
      "title" : "hf"
    },

    {
      "title" : "fci",
      "thresh" : 1.0e-6,
      "nstate" : 2
    }

    ]}

from which one obtains

    ---------------------------
          FCI calculation
    ---------------------------

    Performs exactly the same way as Knowles & Handy 1984 CPL

    o alpha-beta strings
        length:            12
    o size of the space
        determinant space:  36
        spin-adapted space: 21

    o single displacement lists (alpha)
        length:            60
    o single displacement lists (beta)
        length:            60
      * Integral transformation done. Elapsed time: 0.00

       guess   0:   closed 11111.               open ......
       guess   1:   closed 111.1.               open ...1.1

    === FCI iteration ===

        0  0       -98.41480561     4.76e-02      0.00
        0  1       -98.26379090     4.50e-02      0.00

        1  0       -98.51664721     1.09e-02      0.00
        1  1       -98.41322803     1.00e-02      0.00

        2  0       -98.51931832     1.71e-03      0.00
        2  1       -98.41524119     1.91e-04      0.00

        3  0       -98.51940404     3.13e-04      0.00
        3  1 *     -98.41524124     2.55e-14      0.00

        4  0       -98.51940654     4.91e-05      0.00
        4  1 *     -98.41524124     2.80e-14      0.00

        5  0       -98.51940660     2.62e-06      0.00
        5  1 *     -98.41524124     1.86e-14      0.00

        6  0 *     -98.51940660     1.96e-07      0.00
        6  1 *     -98.41524124     2.02e-14      0.00

       * ci vector, state   0, <S^2> = 0.0000
         22222.    -0.9320921105
         2222.2     0.3574718122

       * ci vector, state   1, <S^2> = -0.0000
         222a2b     0.6167681811
         222b2a     0.6167681811
         222ab2    -0.3441653374
         222ba2    -0.3441653374

      * METHOD: FCI                                  0.00

## References

Description of Reference | Reference
--- | ---
Efficient calculation of sigma vectors (KH) | P. J. Knowles and N. C. Handy, Chem. Phys. Lett. 111, 315 (1984).
Efficient calculation of sigma vectors (HZ) | R. J. Harrison and S. Zarrabian, Chem. Phys. Lett. 158, 393 (1989).