Complete active space self-consistent field (CASSCF)

Description

CASSCF simultaneously optimizes the orbital coefficients and the CI coefficients of all the possible determinants generated from the active space. The state-averaging scheme can be used for calculating excited states. When reference wavefunctions are given as a input to a CASSCF calculation, a Hartree–Fock calculation is performed by default prior to CASSCF. For the Hartree–Fock options, see the SCF section.

A two-step second-order algorithm is implemented in BAGEL. At each macroiteration, the CI coefficient is optimized by FCI calculations and the orbitals are updated. Microiterations are used for iteratively solving augmented Hessian problems for orbital updates.

The CASSCF algorithm in BAGEL is very robust. If it fails to converge, it is highly likely that your active space is wrong, or your guess orbitals are wrong.

Title: casscf

Keywords

nstate

Description: Number of states included in the state averaging.
Datatype: int
Default: 1.

nact

Description: Number of active orbitals.
Datatype: int
Default: 0.

nclosed

Description: Number of closed orbitals.
Datatype: int
Default: Number of electrons / 2.

active

Description: Specify active orbitals. Note that the orbital index starts from 1.
Datatype: vector<int>
Default: Nact / 2 orbitals lower and higher from the valence orbital.
Example:
[36, 37, 39] : include 36th, 37th, and 39th orbitals.

algorithm

Description: Orbital optimization algorithm.
Datatype: string
Values:
second: second-order algorithm.
noopt: no orbital optimization.
Default: second

fci_algorithm

Description: FCI algorithm employed in each macroiteration.
Datatype: string
Values:
knowles, handy, kh: Knowles–Handy Algorithm.
harrison, zarrabian, hz: Harrison–Zarrabian Algorithm.
parallel, dist: Parallel FCI algorithm.
Default: parallel (when the number of active orbital is larger than 9 and number of process is larger than 8), knowles (otherwise)

thresh

Description: Convergence threshold in macroiteration.
Datatype: double precision
Default: 1.0e-8.

thresh_micro

Description: Convergence threshold in microiteration.
Datatype: double precision
Default: 5.0e-6.

conv_ignore

Description: If set to “true,” BAGEL will continue running even if the maximum iterations is reached without convergence. Normally an error is thrown and the program terminates.
Datatype: bool
Default: false.

restart_cas

Description: If set to “true”, after each macroiteration the orbitals will be written to a binary archive with filename “casscf_<iter>.archive”. They can be read back in using the “load_ref” module.
Datatype: bool
Default: false.

natocc

Description: If set to “true,” occupation numbers of natural orbitals within the active space will be printed to casscf.log after each macroiteration.
Datatype: bool
Default: false.

charge

Description: Molecular charge.
Datatype: int
Default: 0

nspin

Description: The spin multiplicity of the wavefunction (2S+1).
Datatype: int
Default: 0

maxiter

Description: Maximum number of macroiteration.
Datatype: int
Default: 50.
Recommendation: Increase if convergence is not obtained.

maxiter_micro

Description: Maximum number of microiteration.
Datatype: int
Default: 100.

maxiter_fci

Description: Maximum number of iterations in CI coefficient optimization
Datatype: int
Default: copied from maxiter

Example

Two-state CASSCF calculation of benzene. The active space of (6e,6o), which comprises three \(\pi\) and three \(\pi^*\) orbitals, is used.

Sample input

{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "svp",
  "df_basis" : "svp-jkfit",
  "geometry" : [
  { "atom" : "C", "xyz" : [     -0.079002,      2.543870,      0.000000 ] },
  { "atom" : "C", "xyz" : [      2.557470,      2.543870,      0.000000 ] },
  { "atom" : "C", "xyz" : [      3.875630,      4.826190,      0.000000 ] },
  { "atom" : "C", "xyz" : [      2.557250,      7.109950,     -0.002266 ] },
  { "atom" : "C", "xyz" : [     -0.078588,      7.109800,     -0.003171 ] },
  { "atom" : "C", "xyz" : [     -1.396870,      4.826620,     -0.001289 ] },
  { "atom" : "H", "xyz" : [     -1.117900,      0.744245,      0.000850 ] },
  { "atom" : "H", "xyz" : [      3.595900,      0.743875,      0.002485 ] },
  { "atom" : "H", "xyz" : [      5.953730,      4.826340,      0.001198 ] },
  { "atom" : "H", "xyz" : [      3.596980,      8.909240,     -0.002377 ] },
  { "atom" : "H", "xyz" : [     -1.118170,      8.909350,     -0.004972 ] },
  { "atom" : "H", "xyz" : [     -3.474820,      4.826960,     -0.001629 ] }
  ]
},
{
  "title" : "hf"
},
{
  "title" : "casscf",
  "nstate" : 2,
  "nact" : 6,
  "nclosed" : 18,
  "active" : [17, 20, 21, 22, 23, 30]
}
]}

the out of which is shown below. Note that the specified active orbitals are printed in the output.

---------------------------
    CASSCF calculation
---------------------------


  ==== Active orbitals : =====
       Orbital 17
       Orbital 20
       Orbital 21
       Orbital 22
       Orbital 23
       Orbital 30
  ============================

  * nstate   :      2
  * nclosed  :     18
  * nact     :      6
  * nvirt    :     90
=== CASSCF iteration (svp) ===

  * Using the second-order algorithm

    0  0      -230.58939332     3.18e-03      0.06
    0  1      -230.39960500     0.00e+00      0.06

       res : 9.89e-02   lamb: 1.00e+00   eps : -3.06e-02   step: 3.40e-01    0.02
       res : 2.13e-02   lamb: 1.00e+00   eps : -3.21e-02   step: 3.56e-01    0.02
       res : 2.72e-03   lamb: 1.00e+00   eps : -3.23e-02   step: 3.48e-01    0.02
       res : 2.64e-04   lamb: 1.00e+00   eps : -3.23e-02   step: 3.49e-01    0.03
       res : 3.09e-05   lamb: 1.00e+00   eps : -3.23e-02   step: 3.49e-01    0.04

    1  0      -230.60443140     3.79e-04      0.37
    1  1      -230.42264578     0.00e+00      0.37

       res : 1.06e-02   lamb: 1.00e+00   eps : -3.62e-04   step: 3.57e-02    0.02
       res : 2.13e-03   lamb: 1.00e+00   eps : -3.81e-04   step: 3.76e-02    0.02
       res : 3.31e-04   lamb: 1.00e+00   eps : -3.82e-04   step: 3.69e-02    0.02
       res : 4.53e-05   lamb: 1.00e+00   eps : -3.82e-04   step: 3.69e-02    0.03
       res : 4.21e-06   lamb: 1.00e+00   eps : -3.82e-04   step: 3.69e-02    0.04
       res : 5.33e-07   lamb: 1.00e+00   eps : -3.82e-04   step: 3.69e-02    0.02

    2  0      -230.60501843     1.17e-05      0.36
    2  1      -230.42244692     0.00e+00      0.36

       res : 2.38e-04   lamb: 1.00e+00   eps : -1.11e-07   step: 2.86e-04    0.02
       res : 3.75e-05   lamb: 1.00e+00   eps : -1.21e-07   step: 3.32e-04    0.02
       res : 8.19e-06   lamb: 1.00e+00   eps : -1.21e-07   step: 3.41e-04    0.02
       res : 1.11e-06   lamb: 1.00e+00   eps : -1.21e-07   step: 3.41e-04    0.03
       res : 8.72e-08   lamb: 1.00e+00   eps : -1.21e-07   step: 3.41e-04    0.02
       res : 2.97e-08   lamb: 1.00e+00   eps : -1.21e-07   step: 3.41e-04    0.03

    3  0      -230.60502169     3.97e-07      0.36
    3  1      -230.42244379     0.00e+00      0.36

       res : 6.62e-06   lamb: 1.00e+00   eps : -1.91e-10   step: 1.92e-05    0.02
       res : 1.37e-06   lamb: 1.00e+00   eps : -1.98e-10   step: 1.91e-05    0.02
       res : 2.63e-07   lamb: 1.00e+00   eps : -1.99e-10   step: 1.82e-05    0.02
       res : 4.76e-08   lamb: 1.00e+00   eps : -1.99e-10   step: 1.82e-05    0.03
       res : 5.65e-09   lamb: 1.00e+00   eps : -1.99e-10   step: 1.82e-05    0.02
       res : 1.68e-09   lamb: 1.00e+00   eps : -1.99e-10   step: 1.82e-05    0.03

    4  0      -230.60502176     2.01e-08      0.36
    4  1      -230.42244372     0.00e+00      0.36

       res : 3.09e-07   lamb: 1.00e+00   eps : -6.58e-13   step: 1.33e-06    0.03
       res : 7.14e-08   lamb: 1.00e+00   eps : -6.74e-13   step: 1.33e-06    0.03
       res : 1.28e-08   lamb: 1.00e+00   eps : -6.76e-13   step: 1.28e-06    0.04
       res : 2.75e-09   lamb: 1.00e+00   eps : -6.76e-13   step: 1.28e-06    0.02

    5  0      -230.60502177     1.21e-09      0.33
    5  1      -230.42244372     0.00e+00      0.33

  * Second-order optimization converged. *

References

The second-order orbital optimization is implemented with an assistance of Takeshi Yanai (Institute for Molecular Science, Japan).