DOI: 10.1063/1.442958. Numerical Hartree–Fock–Slater calculations on diatomic molecules

Numerical Hartree–Fock–Slater calculations on diatomic molecules

10.1063/1.442958

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A completely numerical method is presented for the calculation of Hartree–Fock–Slater wave functions in diatomic systems. The method is numerical in the sense that no LCAO basis sets are employed. Muffin tin or other cellular approximations are also avoided. All molecular functions are defined on a two-dimensional discrete mesh in prolate spheroidal coordinate space. The method is mathematically very simple, and numerical accuracy is easily controlled by changing the number of mesh points. Calculations on the molecules B2, C2, N2, CO, O2, and F2 are reported, and we compare dissociation energies, bond lengths, vibrational frequencies, and charge moments with recent LCAO results and with experiment. These calculations indicate that the method works very nicely for the molecules considered, and also that the Hartree–Fock–Slater theory describes molecular systems remarkably well.

Bibliography

Becke, A. D. (1982). Numerical HartreeâFockâSlater calculations on diatomic molecules. The Journal of Chemical Physics, 76(12), 6037â6045.

Authors 1

A. D. Becke (first)

References 55 Referenced 130

10.1103/PhysRev.81.385 / Phys. Rev. (1951)
10.1007/BF03156228 / Acta Phys. Acad. Sci. Hung. (1954)
10.1103/PhysRev.140.A1133 / Phys. Rev. (1965)
10.1103/PhysRevB.5.2466 / Phys. Rev. B (1972)
10.1063/1.1728065 / J. Chem. Phys. (1966)
10.1016/S0065-3276(08)60561-4 / Adv. Quantum Chem. (1973)
10.1016/0031-8914(47)90013-X / Physica (Ultrecht) (1947)
10.1103/PhysRev.94.1111 / Phys. Rev. (1954)
10.1063/1.1701494 / J. Chem. Phys. (1965)
10.1103/PhysRev.51.846 / Phys. Rev. (1937)
10.1063/1.1682462 / J. Chem. Phys. (1974)
10.1063/1.1682463 / J. Chem. Phys. (1974)
10.1016/0009-2614(77)85231-7 / Chem. Phys. Lett. (1977)
10.1016/0009-2614(73)80238-6 / Chem. Phys. Lett. (1973)
10.1063/1.1682531 / J. Chem. Phys. (1974)
{'key': '2024020922191253300_r16', 'first-page': '89', 'volume': '8', 'year': '1974', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1974)
10.1002/qua.560090403 / Int. J. Quantum Chem. (1975)
10.1063/1.438305 / J. Chem. Phys. (1979)
{'key': '2024020922191253300_r19', 'first-page': '141', 'volume': '13', 'year': '1979', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1979)
10.1080/00268977300102171 / Mol. Phys. (1973)
10.1063/1.435414 / J. Chem. Phys. (1977)
10.1103/PhysRevB.2.2887 / Phys. Rev. B (1970)
10.1016/0301-0104(73)80059-X / Chem. Phys. (1973)
10.1016/0301-0104(73)80060-6 / Chem. Phys. (1973)
10.1016/0301-0104(75)80152-2 / Chem. Phys. (1975)
10.1016/0301-0104(76)80083-3 / Chem. Phys. (1976)
{'key': '2024020922191253300_r27', 'first-page': '169', 'volume': '12', 'year': '1978', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1978)
10.1063/1.430555 / J. Chem. Phys. (1975)
10.1063/1.438728 / J. Chem. Phys. (1979)
10.1063/1.438313 / J. Chem. Phys. (1979)
10.1016/0009-2614(74)80212-5 / Chem. Phys. Lett. (1974)
10.1063/1.430322 / J. Chem. Phys. (1975)
10.1063/1.435144 / J. Chem. Phys. (1977)
10.1002/qua.560100210 / Int. J. Quantum Chem. (1976)
{'key': '2024020922191253300_r35'}
{'key': '2024020922191253300_r36', 'first-page': '1', 'volume': '6', 'year': '1972', 'journal-title': 'Adv. Quantum Chem.'} / Adv. Quantum Chem. (1972)
{'key': '2024020922191253300_r37'}
{'key': '2024020922191253300_r38'}
{'key': '2024020922191253300_r39'}
{'key': '2024020922191253300_r40'}
{'key': '2024020922191253300_r41'}
10.6028/jres.045.026 / J. Res. Natl. Bur. Stand. (1950)
{'key': '2024020922191253300_r43'}
{'key': '2024020922191253300_r44', 'first-page': '123', 'volume': '9', 'year': '1977', 'journal-title': 'Adv. Nucl. Phys.'} / Adv. Nucl. Phys. (1977)
10.1016/0375-9474(77)90079-3 / Nucl. Phys. A (1977)
{'key': '2024020922191253300_r46'}
10.1007/BF00551551 / Theor. Chim. Acta (1977)
10.1063/1.432830 / J. Chem. Phys. (1976)
10.1021/ja01014a023 / J. Am. Chem. Soc. (1968)
10.1016/0092-640X(74)90006-0 / At. Data Nucl. Data (1974)
10.1016/0092-640X(75)90001-7 / At. Data Nucl. Data (1975)
10.1016/S0092-640X(74)80016-1 / At. Data Nucl. Data (1974)
{'key': '2024020922191253300_r51'}
10.1063/1.1680880 / J. Chem. Phys. (1974)
{'key': '2024020922191253300_r53'}

Dates

Type	When
Created	22 years, 5 months ago (Feb. 28, 2003, 11:17 a.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 6:58 p.m.)
Indexed	1 month, 2 weeks ago (July 2, 2025, 1:29 p.m.)
Issued	43 years, 2 months ago (June 15, 1982)
Published	43 years, 2 months ago (June 15, 1982)
Published Print	43 years, 2 months ago (June 15, 1982)

Funders 0

None

BibTeX

@article{Becke_1982, title={Numerical Hartree–Fock–Slater calculations on diatomic molecules}, volume={76}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.442958}, DOI={10.1063/1.442958}, number={12}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Becke, A. D.}, year={1982}, month=jun, pages={6037–6045} }

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      "URL": "https://pubs.aip.org/jcp/article/76/12/6037/971759/Numerical-Hartree-Fock-Slater-calculations-on"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1982,
        6,
        15
      ]
    ]
  },
  "references-count": 55,
  "journal-issue": {
    "issue": "12",
    "published-print": {
      "date-parts": [
        [
          1982,
          6,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.442958",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1982,
        6,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1982,
        6,
        15
      ]
    ]
  }
}