DOI: 10.1063/1.1733420. Orbital Theories of Electronic Structure

Orbital Theories of Electronic Structure

10.1063/1.1733420

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We show that in the Hartree—Fock approximation there exists a uniquely defined Hermitian potential which describes the interaction of a model subgroup of electrons with the rest of the system. This potential can be divided into two parts. The first part is the difference between the Hartree—Fock Hamiltonian for the system and the model Hamiltonian. The second part is a nonlocal potential which cancels (screens) some of the first part. The essential point in the derivation is our choice of definition for model orbitals in the system. The only condition that must be satisfied by the occupied orbitals of the system is that they be linearly independent. It is also shown that there exist equations describing the best orbitals to use in a calculation by a linear combination of atomic orbitals method. They are the best orbitals to use because they give the exact answer. As a concrete example of our ideas we have treated numerically the LiH molecule. In order to link our method with others that have been described we indicate how the pseudopotential form of the orthogonalized plane wave method may be derived.

Bibliography

Adams, W. H. (1962). Orbital Theories of Electronic Structure. The Journal of Chemical Physics, 37(9), 2009â2018.

Authors 1

William H. Adams (first)

References 48 Referenced 170

10.1063/1.1731622 / J. Chem. Phys. (1961)
{'key': '2024020821094061100_r2'}
10.1063/1.1700666 / J. Chem. Phys. (1952)
{'key': '2024020821094061100_r4'}
10.1063/1.1747632 / J. Chem. Phys. (1950)
10.1103/PhysRev.97.1490 / Phys. Rev. (1955)
10.1080/00018735600101155 / Advances in Phys. (1956)
{'key': '2024020821094061100_r8'}
{'key': '2024020821094061100_r9'}
{'key': '2024020821094061100_r10'}
{'key': '2024020821094061100_r11'}
10.1103/PhysRev.86.552 / Phys. Rev. (1952)
10.1080/00018735600101155 / Advances in Phys. (1956)
10.1063/1.1777106 / J. Applied Phys. (1962)
10.1103/RevModPhys.23.69 / Revs. Modern Phys. (1951)
10.1063/1.1740588 / J. Chem. Phys. (1955)
{'key': '2024020821094061100_r16', 'first-page': '419', 'volume': 'A169', 'year': '1939', 'journal-title': 'Proc. Roy. Soc. (London)'} / Proc. Roy. Soc. (London) (1939)
{'key': '2024020821094061100_r16a', 'first-page': '197', 'volume': 'A201', 'year': '1950', 'journal-title': 'Proc. Roy. Soc. (London)'} / Proc. Roy. Soc. (London) (1950)
10.1088/0034-4885/22/1/301 / Rept. Progr. Phys. (1959)
10.1103/RevModPhys.32.300 / Revs. Modern Phys. (1960)
{'key': '2024020821094061100_r17b'}
10.1063/1.1730164 / J. Chem. Phys. (1959)
10.1063/1.1730163 / J. Chem. Phys. (1959)
{'key': '2024020821094061100_r20', 'first-page': '547', 'volume': '8', 'year': '1935', 'journal-title': 'Physik. Z. Sowjetunion'} / Physik. Z. Sowjetunion (1935)
{'key': '2024020821094061100_r21'}
10.1103/PhysRev.122.1821 / Phys. Rev. (1961)
10.1103/PhysRev.112.685 / Phys. Rev. (1958)
10.1103/PhysRev.116.287 / Phys. Rev. (1959)
10.1103/PhysRev.57.1169 / Phys. Rev. (1940)
{'key': '2024020821094061100_r25'}
10.1103/PhysRev.89.67 / Phys. Rev. (1953)
10.1103/PhysRev.89.237 / Phys. Rev. (1953)
{'key': '2024020821094061100_r28', 'first-page': '191', 'volume': '51', 'year': '1937', 'journal-title': 'Phys. Rev.'} / Phys. Rev. (1937)
{'key': '2024020821094061100_r29', 'first-page': '1', 'volume': 'A198', 'year': '1949', 'journal-title': 'Proc. Roy. Soc. (London)'} / Proc. Roy. Soc. (London) (1949)
{'key': '2024020821094061100_r30', 'first-page': '361', 'volume': '8', 'year': '1959', 'journal-title': 'Soviet. Phys.-JETP'} / Soviet. Phys.-JETP (1959)
10.1143/PTP.25.653 / Progr. Theoret. Phys. (1961)
10.1016/0029-5582(60)90048-1 / Nuclear Phys. (1960)
{'key': '2024020821094061100_r31a'}
{'key': '2024020821094061100_r32'}
{'key': '2024020821094061100_r32a'}
10.1088/0034-4885/23/1/307 / Repts. Progr. in Phys. (1960)
10.1103/PhysRev.125.109 / Phys. Rev. (1962)
{'key': '2024020821094061100_r34', 'first-page': '312', 'volume': 'A230', 'year': '1955', 'journal-title': 'Proc. Roy. Soc. (London)'} / Proc. Roy. Soc. (London) (1955)
10.1103/RevModPhys.33.28 / Revs. Modern Phys. (1961)
10.1103/PhysRev.82.538 / Phys. Rev. (1951)
{'key': '2024020821094061100_r36'}
10.1103/PhysRev.97.1509 / Phys. Rev. (1955)
10.1063/1.1777106 / J. Appl. Phys. (1962)

Dates

Type	When
Created	20 years, 7 months ago (Jan. 5, 2005, 10:29 p.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 4:10 p.m.)
Indexed	3 weeks ago (Aug. 2, 2025, 1:16 a.m.)
Issued	62 years, 9 months ago (Nov. 1, 1962)
Published	62 years, 9 months ago (Nov. 1, 1962)
Published Print	62 years, 9 months ago (Nov. 1, 1962)

Funders 0

None

BibTeX

@article{Adams_1962, title={Orbital Theories of Electronic Structure}, volume={37}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1733420}, DOI={10.1063/1.1733420}, number={9}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Adams, William H.}, year={1962}, month=nov, pages={2009–2018} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        2
      ]
    ],
    "date-time": "2025-08-02T05:16:51Z",
    "timestamp": 1754111811216
  },
  "reference-count": 48,
  "publisher": "AIP Publishing",
  "issue": "9",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1962,
        11,
        1
      ]
    ]
  },
  "abstract": "<jats:p>We show that in the Hartree\u2014Fock approximation there exists a uniquely defined Hermitian potential which describes the interaction of a model subgroup of electrons with the rest of the system. This potential can be divided into two parts. The first part is the difference between the Hartree\u2014Fock Hamiltonian for the system and the model Hamiltonian. The second part is a nonlocal potential which cancels (screens) some of the first part. The essential point in the derivation is our choice of definition for model orbitals in the system. The only condition that must be satisfied by the occupied orbitals of the system is that they be linearly independent. It is also shown that there exist equations describing the best orbitals to use in a calculation by a linear combination of atomic orbitals method. They are the best orbitals to use because they give the exact answer. As a concrete example of our ideas we have treated numerically the LiH molecule. In order to link our method with others that have been described we indicate how the pseudopotential form of the orthogonalized plane wave method may be derived.</jats:p>",
  "DOI": "10.1063/1.1733420",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        1,
        6
      ]
    ],
    "date-time": "2005-01-06T03:29:54Z",
    "timestamp": 1104982194000
  },
  "page": "2009-2018",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 170,
  "title": "Orbital Theories of Electronic Structure",
  "prefix": "10.1063",
  "volume": "37",
  "author": [
    {
      "given": "William H.",
      "family": "Adams",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Quantum Chemistry Group, University of Uppsala, Uppsala, Sweden"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020821094061100_r1",
      "doi-asserted-by": "crossref",
      "first-page": "89",
      "DOI": "10.1063/1.1731622",
      "volume": "34",
      "year": "1961",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020821094061100_r2"
    },
    {
      "key": "2024020821094061100_r3",
      "doi-asserted-by": "crossref",
      "first-page": "1057",
      "DOI": "10.1063/1.1700666",
      "volume": "20",
      "year": "1952",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020821094061100_r4"
    },
    {
      "key": "2024020821094061100_r5",
      "doi-asserted-by": "crossref",
      "first-page": "365",
      "DOI": "10.1063/1.1747632",
      "volume": "18",
      "year": "1950",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020821094061100_r6",
      "doi-asserted-by": "crossref",
      "first-page": "1490",
      "DOI": "10.1103/PhysRev.97.1490",
      "volume": "97",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r7",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1080/00018735600101155",
      "volume": "5",
      "year": "1956",
      "journal-title": "Advances in Phys."
    },
    {
      "key": "2024020821094061100_r8"
    },
    {
      "key": "2024020821094061100_r9"
    },
    {
      "key": "2024020821094061100_r10"
    },
    {
      "key": "2024020821094061100_r11"
    },
    {
      "key": "2024020821094061100_r12",
      "doi-asserted-by": "crossref",
      "first-page": "552",
      "DOI": "10.1103/PhysRev.86.552",
      "volume": "86",
      "year": "1952",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r12a",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1080/00018735600101155",
      "volume": "5",
      "year": "1956",
      "journal-title": "Advances in Phys."
    },
    {
      "key": "2024020821094061100_r13",
      "doi-asserted-by": "crossref",
      "first-page": "251",
      "DOI": "10.1063/1.1777106",
      "volume": "33",
      "year": "1962",
      "journal-title": "J. Applied Phys."
    },
    {
      "key": "2024020821094061100_r14",
      "doi-asserted-by": "crossref",
      "first-page": "69",
      "DOI": "10.1103/RevModPhys.23.69",
      "volume": "23",
      "year": "1951",
      "journal-title": "Revs. Modern Phys."
    },
    {
      "key": "2024020821094061100_r15",
      "doi-asserted-by": "crossref",
      "first-page": "1833",
      "DOI": "10.1063/1.1740588",
      "volume": "23",
      "year": "1955",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020821094061100_r16",
      "first-page": "419",
      "volume": "A169",
      "year": "1939",
      "journal-title": "Proc. Roy. Soc. (London)"
    },
    {
      "key": "2024020821094061100_r16a",
      "first-page": "197",
      "volume": "A201",
      "year": "1950",
      "journal-title": "Proc. Roy. Soc. (London)"
    },
    {
      "key": "2024020821094061100_r17",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1088/0034-4885/22/1/301",
      "volume": "22",
      "year": "1959",
      "journal-title": "Rept. Progr. Phys."
    },
    {
      "key": "2024020821094061100_r17a",
      "doi-asserted-by": "crossref",
      "first-page": "300",
      "DOI": "10.1103/RevModPhys.32.300",
      "volume": "32",
      "year": "1960",
      "journal-title": "Revs. Modern Phys."
    },
    {
      "key": "2024020821094061100_r17b"
    },
    {
      "key": "2024020821094061100_r18",
      "doi-asserted-by": "crossref",
      "first-page": "1241",
      "DOI": "10.1063/1.1730164",
      "volume": "30",
      "year": "1959",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020821094061100_r19",
      "doi-asserted-by": "crossref",
      "first-page": "1232",
      "DOI": "10.1063/1.1730163",
      "volume": "30",
      "year": "1959",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020821094061100_r20",
      "first-page": "547",
      "volume": "8",
      "year": "1935",
      "journal-title": "Physik. Z. Sowjetunion"
    },
    {
      "key": "2024020821094061100_r21"
    },
    {
      "key": "2024020821094061100_r22",
      "doi-asserted-by": "crossref",
      "first-page": "1821",
      "DOI": "10.1103/PhysRev.122.1821",
      "volume": "122",
      "year": "1961",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r23",
      "doi-asserted-by": "crossref",
      "first-page": "685",
      "DOI": "10.1103/PhysRev.112.685",
      "volume": "112",
      "year": "1958",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r23a",
      "doi-asserted-by": "crossref",
      "first-page": "287",
      "DOI": "10.1103/PhysRev.116.287",
      "volume": "116",
      "year": "1959",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r24",
      "doi-asserted-by": "crossref",
      "first-page": "1169",
      "DOI": "10.1103/PhysRev.57.1169",
      "volume": "57",
      "year": "1940",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r25"
    },
    {
      "key": "2024020821094061100_r26",
      "doi-asserted-by": "crossref",
      "first-page": "67",
      "DOI": "10.1103/PhysRev.89.67",
      "volume": "89",
      "year": "1953",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r27",
      "doi-asserted-by": "crossref",
      "first-page": "237",
      "DOI": "10.1103/PhysRev.89.237",
      "volume": "89",
      "year": "1953",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r28",
      "first-page": "191",
      "volume": "51",
      "year": "1937",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r29",
      "first-page": "1",
      "volume": "A198",
      "year": "1949",
      "journal-title": "Proc. Roy. Soc. (London)"
    },
    {
      "key": "2024020821094061100_r30",
      "first-page": "361",
      "volume": "8",
      "year": "1959",
      "journal-title": "Soviet. Phys.-JETP"
    },
    {
      "key": "2024020821094061100_r30a",
      "doi-asserted-by": "crossref",
      "first-page": "653",
      "DOI": "10.1143/PTP.25.653",
      "volume": "25",
      "year": "1961",
      "journal-title": "Progr. Theoret. Phys."
    },
    {
      "key": "2024020821094061100_r31",
      "doi-asserted-by": "crossref",
      "first-page": "225",
      "DOI": "10.1016/0029-5582(60)90048-1",
      "volume": "21",
      "year": "1960",
      "journal-title": "Nuclear Phys."
    },
    {
      "key": "2024020821094061100_r31a"
    },
    {
      "key": "2024020821094061100_r32"
    },
    {
      "key": "2024020821094061100_r32a"
    },
    {
      "key": "2024020821094061100_r33",
      "doi-asserted-by": "crossref",
      "first-page": "355",
      "DOI": "10.1088/0034-4885/23/1/307",
      "volume": "23",
      "year": "1960",
      "journal-title": "Repts. Progr. in Phys."
    },
    {
      "key": "2024020821094061100_r33a",
      "doi-asserted-by": "crossref",
      "first-page": "109",
      "DOI": "10.1103/PhysRev.125.109",
      "volume": "125",
      "year": "1962",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r34",
      "first-page": "312",
      "volume": "A230",
      "year": "1955",
      "journal-title": "Proc. Roy. Soc. (London)"
    },
    {
      "key": "2024020821094061100_r34a",
      "doi-asserted-by": "crossref",
      "first-page": "28",
      "DOI": "10.1103/RevModPhys.33.28",
      "volume": "33",
      "year": "1961",
      "journal-title": "Revs. Modern Phys."
    },
    {
      "key": "2024020821094061100_r35",
      "doi-asserted-by": "crossref",
      "first-page": "538",
      "DOI": "10.1103/PhysRev.82.538",
      "volume": "82",
      "year": "1951",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r36"
    },
    {
      "key": "2024020821094061100_r36a",
      "doi-asserted-by": "crossref",
      "first-page": "1509",
      "DOI": "10.1103/PhysRev.97.1509",
      "volume": "97",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020821094061100_r37",
      "doi-asserted-by": "crossref",
      "first-page": "251",
      "DOI": "10.1063/1.1777106",
      "volume": "33",
      "year": "1962",
      "journal-title": "J. Appl. Phys."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/37/9/2009/18827645/2009_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/37/9/2009/18827645/2009_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        8
      ]
    ],
    "date-time": "2024-02-08T21:10:04Z",
    "timestamp": 1707426604000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/37/9/2009/205818/Orbital-Theories-of-Electronic-Structure"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1962,
        11,
        1
      ]
    ]
  },
  "references-count": 48,
  "journal-issue": {
    "issue": "9",
    "published-print": {
      "date-parts": [
        [
          1962,
          11,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1733420",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1962,
        11,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1962,
        11,
        1
      ]
    ]
  }
}