Relativistic Multireference configuration interaction (RelMRCI) — BAGEL Manual

# Relativistic Multireference configuration interaction (RelMRCI)

## Description

Relativistic version of the fully internally contracted multireference configuration interaction. This is implemented with the automatical code generator SMITH3. By default, the Davidson corrected (+Q) energy is also printed.

Title: `relsmith`, method: `mrci`

## Keywords

### CASSCF keywords

See Relativistic complete active space self-consistent field (RelCASSCF).

### 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" : [ 0.000, 0.000, 1.210 ]},
        { "atom" : "O",  "xyz" : [ 0.000, 0.000, 0.000 ]}
      ]
    },

    {
      "title" : "hf",
      "charge" : "+2"
    },

    {
      "title" : "dhf",
      "charge" : "+2"
    },

    {
      "title"  : "zcasscf",
      "algorithm" : "second",
      "charge" : "0",
      "state" : [0, 0, 1],
      "thresh" : 1.0e-7,
      "nclosed"  : 7,
      "nact"   : 2
    },

    {
      "title" : "relsmith",
      "method" : "mrci",
      "ncore" : 2
    }

    ]}

from which one obtains

    * Zeroth order energy : state  0       -0.4311850170
    * Zeroth order energy : state  1       -0.4310720094
    * Zeroth order energy : state  2       -0.4310720094

      ---- iteration ----

        0   0  -149.90092252     0.00065697     67.36
        0   1  -149.90091061     0.00065698      0.41
        0   2  -149.90091061     0.00065698      0.41

        1   0  -149.92100585     0.00012080     69.68
        1   1  -149.92099523     0.00012080      0.37
        1   2  -149.92099523     0.00012080      0.39

        2   0  -149.92179156     0.00003649     68.67
        2   1  -149.92178091     0.00003649      0.36
        2   2  -149.92178091     0.00003649      0.37

        3   0  -149.92186506     0.00000959     70.71
        3   1  -149.92185440     0.00000959      0.36
        3   2  -149.92185440     0.00000959      0.37

        4   0  -149.92187033     0.00000231     70.11
        4   1  -149.92185967     0.00000230      0.39
        4   2  -149.92185967     0.00000230      0.39

        5   0  -149.92187064     0.00000056     68.53
        5   1  -149.92185998     0.00000055      0.00
        5   2  -149.92185998     0.00000055      0.00

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

       - MRCI energy evaluation                  420.87

        0   0  -149.95278455     0.00000000      0.00
        0   1  -149.95277356     0.00000000      0.00
        0   2  -149.95277356     0.00000000      0.00

       - MRCI+Q energy evaluation                  0.44

    * METHOD: RELSMITH                           422.34

## 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)