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¶

{ "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, J. Chem. Theory Comput. 14, 1228 (2018)

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).