DOI: 10.1098/rspa.1951.0240. The molecular orbital theory of chemical valency IX. The interaction of paired electrons in chemical bonds

The molecular orbital theory of chemical valency IX. The interaction of paired electrons in chemical bonds

10.1098/rspa.1951.0240

Crossref journal-article

The Royal Society

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (175)

Abstract

In previous parts of this series the molecular orbital theory has been developed in a way which, while dealing satisfactorily with the interaction of electrons in different orbitals, is not adequate to describe the wave theory of two paired electrons in the same orbital. This paper is an attempt to improve this part of the theory. Most of the work is restricted to the problem of two electrons in the bond of a homonuclear diatomic molecule. The method is based on expansions of the wave function and the interelectronic repulsion term of the Hamiltonian over the irreducible representations of the symmetry group. A series of coupled equations are obtained for the terms of the wave-function expansion. These exact equations form a useful background against which to examine some approximate wave functions, including the simple molecular orbital function and the electron-pair function. Some approximate calculations on the hydrogen molecule indicate that inclusion of higher terms in the wave-function expansion substantially reduces the calculated electron repulsion energy.

Bibliography

The molecular orbital theory of chemical valency IX. The interaction of paired electrons in chemical bonds. (1951). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 210(1101), 190â206.

Authors 0

None

References 18 Referenced 57

{'key': 'p_1', 'first-page': '542', 'article-title': 'Proc. Roy', 'volume': '200', 'author': 'Boys S. F.', 'year': '1950', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Boys S. F. (1950)
10.1080/14786444908521726
Craig D. P . 1950a 6 c Proc. Roy. Soc. A 200 272 390 401. (10.1098/rspa.1950.0024)
Fock V. 1930 Z .Phys. 61 126. (10.1007/BF01340294)
{'key': 'p_5', 'first-page': '541', 'article-title': 'Proc. Roy', 'volume': '205', 'year': '1951', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy (1951)
{'key': 'p_6', 'first-page': '156', 'article-title': 'Proc. Roy', 'volume': '202', 'author': 'Lennard-Jones J .', 'year': '1950', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Lennard-Jones J . (1950)
{'key': 'p_7', 'first-page': '455', 'article-title': 'Z', 'volume': '44', 'author': 'London F.', 'year': '1927', 'journal-title': 'Phys.'} / Phys. / Z by London F. (1927)
{'key': 'p_8', 'first-page': '130', 'article-title': 'J', 'volume': '18', 'year': '1950', 'journal-title': 'Phys.'} / Phys. / J (1950)
{'key': 'p_9', 'first-page': '825', 'article-title': 'J', 'volume': '1', 'author': 'Jam H .', 'year': '1933', 'journal-title': 'Chem. Phys.'} / Chem. Phys. / J by Jam H . (1933)
{'key': 'p_10', 'first-page': '469', 'article-title': 'Proc', 'volume': '27', 'author': 'Jones J .', 'year': '1931', 'journal-title': 'Camb. Phil. Soc.'} / Camb. Phil. Soc. / Proc by Jones J . (1931)
{'key': 'p_11', 'first-page': '1', 'article-title': 'Proc. Roy', 'volume': '198', 'author': 'Jones J .', 'year': '1949', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Jones J . (1949)
{'key': 'p_12', 'first-page': '14', 'article-title': '6 Proc. Roy', 'volume': '198', 'author': 'Jones J .', 'year': '1949', 'journal-title': 'Soc. A'} / Soc. A / 6 Proc. Roy by Jones J . (1949)
L ennard-Jones J . E . & Pople J . A.
{'key': 'p_14', 'first-page': '166', 'article-title': 'Proc. Roy', 'volume': '202', 'author': 'Jones J .', 'year': '1950', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Jones J . (1950)
10.1021/ja01355a027
Pople J . A. 1950 Proc. Roy. Soc. A
Pople J . A. 1951 Proc. Roy. Soc. A
10.1103/PhysRev.37.481

Dates

Type	When
Created	18 years, 8 months ago (Dec. 15, 2006, 3:03 p.m.)
Deposited	2 years, 3 months ago (May 9, 2023, 8:19 p.m.)
Indexed	1 month, 3 weeks ago (July 2, 2025, 2:13 p.m.)
Issued	73 years, 8 months ago (Dec. 20, 1951)
Published	73 years, 8 months ago (Dec. 20, 1951)
Published Online	28 years, 7 months ago (Jan. 1, 1997)
Published Print	73 years, 8 months ago (Dec. 20, 1951)

Funders 0

None

BibTeX

@article{1951, volume={210}, ISSN={2053-9169}, url={http://dx.doi.org/10.1098/rspa.1951.0240}, DOI={10.1098/rspa.1951.0240}, number={1101}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1951}, month=dec, pages={190–206} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        2
      ]
    ],
    "date-time": "2025-07-02T18:13:01Z",
    "timestamp": 1751479981155
  },
  "reference-count": 18,
  "publisher": "The Royal Society",
  "issue": "1101",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1951,
            12,
            20
          ]
        ],
        "date-time": "1951-12-20T00:00:00Z",
        "timestamp": -569116800000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://royalsociety.org/journals/ethics-policies/data-sharing-mining/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1951,
        12,
        20
      ]
    ]
  },
  "abstract": "<jats:p>In previous parts of this series the molecular orbital theory has been developed in a way which, while dealing satisfactorily with the interaction of electrons in different orbitals, is not adequate to describe the wave theory of two paired electrons in the same orbital. This paper is an attempt to improve this part of the theory. Most of the work is restricted to the problem of two electrons in the bond of a homonuclear diatomic molecule. The method is based on expansions of the wave function and the interelectronic repulsion term of the Hamiltonian over the irreducible representations of the symmetry group. A series of coupled equations are obtained for the terms of the wave-function expansion. These exact equations form a useful background against which to examine some approximate wave functions, including the simple molecular orbital function and the electron-pair function. Some approximate calculations on the hydrogen molecule indicate that inclusion of higher terms in the wave-function expansion substantially reduces the calculated electron repulsion energy.</jats:p>",
  "DOI": "10.1098/rspa.1951.0240",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        12,
        15
      ]
    ],
    "date-time": "2006-12-15T20:03:58Z",
    "timestamp": 1166213038000
  },
  "page": "190-206",
  "source": "Crossref",
  "is-referenced-by-count": 57,
  "title": "The molecular orbital theory of chemical valency IX. The interaction of paired electrons in chemical bonds",
  "prefix": "10.1098",
  "volume": "210",
  "member": "175",
  "published-online": {
    "date-parts": [
      [
        1997,
        1
      ]
    ]
  },
  "reference": [
    {
      "key": "p_1",
      "first-page": "542",
      "article-title": "Proc. Roy",
      "volume": "200",
      "author": "Boys S. F.",
      "year": "1950",
      "journal-title": "Soc. A"
    },
    {
      "key": "p_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1080/14786444908521726"
    },
    {
      "key": "p_3",
      "doi-asserted-by": "crossref",
      "unstructured": "Craig D. P . 1950a 6 c Proc. Roy. Soc. A 200 272 390 401.",
      "DOI": "10.1098/rspa.1950.0024"
    },
    {
      "key": "p_4",
      "doi-asserted-by": "crossref",
      "unstructured": "Fock V. 1930 Z .Phys. 61 126.",
      "DOI": "10.1007/BF01340294"
    },
    {
      "key": "p_5",
      "first-page": "541",
      "article-title": "Proc. Roy",
      "volume": "205",
      "year": "1951",
      "journal-title": "Soc. A"
    },
    {
      "key": "p_6",
      "first-page": "156",
      "article-title": "Proc. Roy",
      "volume": "202",
      "author": "Lennard-Jones J .",
      "year": "1950",
      "journal-title": "Soc. A"
    },
    {
      "key": "p_7",
      "first-page": "455",
      "article-title": "Z",
      "volume": "44",
      "author": "London F.",
      "year": "1927",
      "journal-title": "Phys."
    },
    {
      "key": "p_8",
      "first-page": "130",
      "article-title": "J",
      "volume": "18",
      "year": "1950",
      "journal-title": "Phys."
    },
    {
      "key": "p_9",
      "first-page": "825",
      "article-title": "J",
      "volume": "1",
      "author": "Jam H .",
      "year": "1933",
      "journal-title": "Chem. Phys."
    },
    {
      "key": "p_10",
      "first-page": "469",
      "article-title": "Proc",
      "volume": "27",
      "author": "Jones J .",
      "year": "1931",
      "journal-title": "Camb. Phil. Soc."
    },
    {
      "key": "p_11",
      "first-page": "1",
      "article-title": "Proc. Roy",
      "volume": "198",
      "author": "Jones J .",
      "year": "1949",
      "journal-title": "Soc. A"
    },
    {
      "key": "p_12",
      "first-page": "14",
      "article-title": "6 Proc. Roy",
      "volume": "198",
      "author": "Jones J .",
      "year": "1949",
      "journal-title": "Soc. A"
    },
    {
      "key": "p_13",
      "unstructured": "L ennard-Jones J . E . & Pople J . A."
    },
    {
      "key": "p_14",
      "first-page": "166",
      "article-title": "Proc. Roy",
      "volume": "202",
      "author": "Jones J .",
      "year": "1950",
      "journal-title": "Soc. A"
    },
    {
      "key": "p_15",
      "doi-asserted-by": "publisher",
      "DOI": "10.1021/ja01355a027"
    },
    {
      "key": "p_16",
      "unstructured": "Pople J . A. 1950 Proc. Roy. Soc. A"
    },
    {
      "key": "p_17",
      "unstructured": "Pople J . A. 1951 Proc. Roy. Soc. A"
    },
    {
      "key": "p_18",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRev.37.481"
    }
  ],
  "container-title": "Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1951.0240",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1951.0240",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        5,
        10
      ]
    ],
    "date-time": "2023-05-10T00:19:08Z",
    "timestamp": 1683677948000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://royalsocietypublishing.org/doi/10.1098/rspa.1951.0240"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1951,
        12,
        20
      ]
    ]
  },
  "references-count": 18,
  "journal-issue": {
    "issue": "1101",
    "published-print": {
      "date-parts": [
        [
          1951,
          12,
          20
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1098/rspa.1951.0240"
  ],
  "URL": "http://dx.doi.org/10.1098/rspa.1951.0240",
  "relation": {},
  "ISSN": [
    "0080-4630",
    "2053-9169"
  ],
  "subject": [],
  "container-title-short": "Proc. R. Soc. Lond. A",
  "published": {
    "date-parts": [
      [
        1951,
        12,
        20
      ]
    ]
  }
}