Hartree–Fock

Description

SCF can be run by specifying the following values to the keyword title:

  • Restricted HF for closed-shell systems: rhf or hf
  • Restricted open-shell HF: rohf
  • Unrestricted HF: uhf
  • Two-component HF using ECP basis sets spin-orbit SCF: soscf

RHF can be run with the fast multipole method (FMM). For RHF-FMM, "cfmm" : "true" has to be specified in Molecule specification.

Keywords

The default values are recommended unless mentioned otherwise.

thresh

Description: SCF convergence threshold for the root-mean-square of the error vector.
Datatype: double
Default: \(1.0\times 10^{-8}\)

maxiter/maxiter_scf

Description: number of iterations and number of SCF interations, after which the program will terminate if convergence is not reached.
Datatype: int
Default: \(100\)

diis_start

Description: after the specified iteration, we will begin using the DIIS algorithm to accelerate the convergence.
Datatype: int
Default: \(1\)

thresh_overlap

Description: Overlap threshold used to identify linear dependancies in the atomic basis set.
Datatype: double
Default: \(1.0\times 10^{-8}\)

multipole

Description: rank of Cartesian multipole moments to be printed out.
Datatype: int
Values : \(1, 2\)
Default : \(1\) (dipoles)

dma

Description: options to print out multipole moments from distributed multipole analysis.
Datatype: int
Values : \(0, 1, 2, 3\)
Default : \(0\) (not print out)

charge

Description: molecular charge
Datatype: int
Default : \(0\)

nopen

Description: number of unpaired electrons in high-spin unrestricted Hartree–Fock
Datatype : int
Default : (number of electrons - charge) % 2

restart

Description: save an archive in each iteration to allow for restarting the calculation
Datatype: bool
Default: false

Keywords for RHF-FMM

ns

Description: level of descritization which controls the number of lowest-level boxes in one dimension for FMM
Datatype: int
Default: \(4\)

ws

Description: well-separatedness index, which is the number of boxes that must separate two collections of charges before they are considered distant and can interact through multipole expansions
Datatype: int
Default: \(0\)

lmax

Description: order of the multipole expansions in FMM-J
Datatype: int
Default: \(10\)

exchange

Description: whether to include far-field exchange using occ-RI-FMM
Datatype: bool
Default: true

lmax_exchange

Description: order of the multipole expansions in FMM-K
Datatype: int
Default: \(2\)

Examples

Below are some examples for SCF calculations using RHF, ROHF, UHF, SOSCF, and RHF-FMM.

RHF

{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "svp",
  "df_basis" : "svp-jkfit",
  "angstrom" : "false",
  "geometry" : [
    { "atom" : "F",  "xyz" : [ -0.000000,     -0.000000,      2.720616]},
    { "atom" : "H",  "xyz" : [ -0.000000,     -0.000000,      0.305956]}
  ]
},

{
  "title" : "hf",
  "thresh" : 1.0e-8
}

]}

The converged SCF energy is \(-99.84772354\) after \(11\) iterations.

ROHF

{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "svp",
  "df_basis" : "svp-jkfit",
  "angstrom" : "false",
  "geometry" : [
    { "atom" : "C",  "xyz" : [   -0.000000,     -0.000000,      3.000000] },
    { "atom" : "H",  "xyz" : [    0.000000,      0.000000,      0.000000] }
  ]
},

{
  "title" : "rohf",
  "nopen" : 1
}

]}

The converged SCF energy is \(-38.16810629\) after \(10\) iterations.

UHF

{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "svp",
  "df_basis" : "svp-jkfit",
  "angstrom" : false,
  "geometry" : [
    { "atom" : "O",  "xyz" : [  -0.000000,     -0.000000,      1.500000]},
    { "atom" : "H",  "xyz" : [  -0.000000,     -0.000000,      0.000000]}
  ]
},

{
  "title" : "uhf",
  "nopen" : 1
}

]}

The converged SCF energy is \(-75.28410147\) after \(12\) iterations. The expectation value of \(S^2\) is \(0.7536\).

SOSCF

{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "ecp28mdf",
  "df_basis" : "tzvpp-jkfit",
  "angstrom" : "true",
  "geometry" : [
    { "atom" : "Br",  "xyz" : [  0.000000,      0.000000,      0.000000]},
    { "atom" :  "H",  "xyz" : [  0.000000,      1.420000,      0.000000],
                     "basis" : "sto-3g"}
  ]
},

{
  "title" : "soscf"
}

]}

RHF-FMM

alternate text
{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "3-21g",
  "angstrom" : "true",
  "cfmm" : "true",
  "schwarz_thresh" : "1.0e-8",
  "geometry" : [
    { "atom" : "C", "xyz" : [     -0.710000000,    1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [      0.710000000,    1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [      1.420000000,    0.000000000,    0.000000000] },
    { "atom" : "C", "xyz" : [      0.710000000,   -1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [     -0.710000000,   -1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [     -1.420000000,    0.000000000,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.810000000,    1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.100000000,    0.000000000,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.810000000,   -1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.810000000,    3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.100000000,    2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.810000000,   -3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.100000000,   -2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.100000000,    4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.100000000,   -4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [     -3.550000000,    1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [     -2.840000000,    0.000000000,    0.000000000] },
    { "atom" : "C", "xyz" : [      3.550000000,   -1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [     -4.970000000,    1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [     -5.680000000,    0.000000000,    0.000000000] },
    { "atom" : "C", "xyz" : [      4.970000000,   -1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [     -3.550000000,    3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [     -2.840000000,    2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [      3.550000000,   -3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [      2.840000000,   -2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [     -4.970000000,    3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [     -5.680000000,    2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [      4.970000000,   -3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [      5.680000000,   -2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [     -3.550000000,    6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [     -2.840000000,    4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [      3.550000000,   -6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [      2.840000000,   -4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [     -4.970000000,    6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [     -5.680000000,    4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [      4.970000000,   -6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [      5.680000000,   -4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [     -2.840000000,    7.378536440,    0.000000000] },
    { "atom" : "C", "xyz" : [     -2.840000000,   -7.378536440,    0.000000000] },
    { "atom" : "C", "xyz" : [      0.710000000,    3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [      1.420000000,    2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [     -0.710000000,   -3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [     -1.420000000,   -2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [     -0.710000000,    3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [     -1.420000000,    2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [      0.710000000,   -3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [      1.420000000,   -2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [      0.710000000,    6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [      1.420000000,    4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [     -0.710000000,   -6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [     -1.420000000,   -4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [     -0.710000000,    6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [     -1.420000000,    4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [      0.710000000,   -6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [      1.420000000,   -4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [      0.710000000,    8.608292514,    0.000000000] },
    { "atom" : "C", "xyz" : [      1.420000000,    7.378536440,    0.000000000] },
    { "atom" : "C", "xyz" : [     -0.710000000,   -8.608292514,    0.000000000] },
    { "atom" : "C", "xyz" : [     -1.420000000,   -7.378536440,    0.000000000] },
    { "atom" : "C", "xyz" : [     -0.710000000,    8.608292514,    0.000000000] },
    { "atom" : "C", "xyz" : [     -1.420000000,    7.378536440,    0.000000000] },
    { "atom" : "C", "xyz" : [      0.710000000,   -8.608292514,    0.000000000] },
    { "atom" : "C", "xyz" : [      1.420000000,   -7.378536440,    0.000000000] },
    { "atom" : "C", "xyz" : [      4.970000000,    1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [      5.680000000,    0.000000000,    0.000000000] },
    { "atom" : "C", "xyz" : [     -4.970000000,   -1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [      3.550000000,    1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [      2.840000000,    0.000000000,    0.000000000] },
    { "atom" : "C", "xyz" : [     -3.550000000,   -1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [      4.970000000,    3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [      5.680000000,    2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [     -4.970000000,   -3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [     -5.680000000,   -2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [      3.550000000,    3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [      2.840000000,    2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [     -3.550000000,   -3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [     -2.840000000,   -2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [      4.970000000,    6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [      5.680000000,    4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [     -4.970000000,   -6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [     -5.680000000,   -4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [      3.550000000,    6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [      2.840000000,    4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [     -3.550000000,   -6.148780367,    0.000000000] },
    { "atom" : "C", "xyz" : [     -2.840000000,   -4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [      2.840000000,    7.378536440,    0.000000000] },
    { "atom" : "C", "xyz" : [      2.840000000,   -7.378536440,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.810000000,    1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.100000000,    0.000000000,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.810000000,   -1.229756073,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.810000000,    3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.100000000,    2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.810000000,   -3.689268220,    0.000000000] },
    { "atom" : "C", "xyz" : [     -7.100000000,   -2.459512147,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.100000000,    4.919024293,    0.000000000] },
    { "atom" : "C", "xyz" : [      7.100000000,   -4.919024293,    0.000000000] },
    { "atom" : "H", "xyz" : [      1.250000000,    9.543599950,    0.000000000] },
    { "atom" : "H", "xyz" : [     -1.250000000,   -9.543599950,    0.000000000] },
    { "atom" : "H", "xyz" : [      5.510000000,    7.084087803,    0.000000000] },
    { "atom" : "H", "xyz" : [     -5.510000000,   -7.084087803,    0.000000000] },
    { "atom" : "H", "xyz" : [      3.380000000,    8.313843876,    0.000000000] },
    { "atom" : "H", "xyz" : [      3.380000000,   -8.313843876,    0.000000000] },
    { "atom" : "H", "xyz" : [      7.640000000,    5.854331730,    0.000000000] },
    { "atom" : "H", "xyz" : [      7.640000000,   -5.854331730,    0.000000000] },
    { "atom" : "H", "xyz" : [     -7.640000000,    5.854331730,    0.000000000] },
    { "atom" : "H", "xyz" : [     -7.640000000,   -5.854331730,    0.000000000] },
    { "atom" : "H", "xyz" : [     -5.510000000,    7.084087803,    0.000000000] },
    { "atom" : "H", "xyz" : [      5.510000000,   -7.084087803,    0.000000000] },
    { "atom" : "H", "xyz" : [     -3.380000000,    8.313843876,    0.000000000] },
    { "atom" : "H", "xyz" : [     -3.380000000,   -8.313843876,    0.000000000] },
    { "atom" : "H", "xyz" : [     -1.250000000,    9.543599950,    0.000000000] },
    { "atom" : "H", "xyz" : [      1.250000000,   -9.543599950,    0.000000000] },
    { "atom" : "H", "xyz" : [      8.890000000,    1.229756073,    0.000000000] },
    { "atom" : "H", "xyz" : [     -8.890000000,   -1.229756073,    0.000000000] },
    { "atom" : "H", "xyz" : [      8.890000000,    3.689268220,    0.000000000] },
    { "atom" : "H", "xyz" : [     -8.890000000,   -3.689268220,    0.000000000] },
    { "atom" : "H", "xyz" : [     -8.890000000,    1.229756073,    0.000000000] },
    { "atom" : "H", "xyz" : [      8.890000000,   -1.229756073,    0.000000000] },
    { "atom" : "H", "xyz" : [     -8.890000000,    3.689268220,    0.000000000] },
    { "atom" : "H", "xyz" : [      8.890000000,   -3.689268220,    0.000000000] }
  ]
},

{
  "df" : false,
  "ns" : "5",
  "lmax" : "10",
  "ws" : "0.0",
  "exchange" : true,
  "lmax_exchange" : "2",
  "title" : "hf",
  "thresh" : 1.0e-6
}

]}

The converged SCF energy is \(-3629.48403990\) after \(11\) iterations, and the far-field exchange contribution is \(7.736\) milli-hartree.

References

BAGEL References

Description of Reference Reference
Exact exchange evaluation using occ-RI-FMM H.-A. Le and T. Shiozaki, submitted, arXiv:1708.05353 (2017)

General References

Description of Reference Reference
General text on electronic structure theory A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (McGraw-Hill, New York, 1989).
References for fast multipole method in quantum chemistry C. A. White, B. G. Johnson, P. M. W. Gill, and M. Head-Gordon, Chem. Phys. Lett. 230, 8 (1994).
  M. C. Strain, G. E. Scuseria, and M. J. Frisch, Science 271, 51 (1996).