DOI: 10.1063/1.1727214. Relativistic Intermolecular Forces, Moderately Long Range

Relativistic Intermolecular Forces, Moderately Long Range

10.1063/1.1727214

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The generalized Breit—Pauli Hamiltonian is used to give a systematic treatment of magnetic and other relativistic intermolecular energies through O(α2) (where α is the fine-structure constant) for intermolecular separations, R, sufficiently large that the charge distributions of the two molecules do not overlap, but sufficiently small that R&lt;λ/0=(αΔε)−1, where Δε is the excitation energy of the first allowed transition of one of the molecules. The theory is discussed in general and many types of interaction energies are obtained which depend on the spin and orbital angular-momentum states of the molecules. The interaction of two nondegenerate atoms (L=0, S=0) is considered specifically. Of particular interest is an interaction-energy term which varies as α2/R4.

Bibliography

Meath, W. J., & Hirschfelder, J. O. (1966). Relativistic Intermolecular Forces, Moderately Long Range. The Journal of Chemical Physics, 44(9), 3197â3209.

Authors 2

William J. Meath (first)
Joseph O. Hirschfelder (additional)

References 68 Referenced 72

{'key': '2024020900592186400_r1'}
10.1063/1.1743155 / J. Chem. Phys. (1956)
10.1103/PhysRev.73.360 / Phys. Rev. (1948)
{'key': '2024020900592186400_r3a', 'first-page': '977', 'volume': '3', 'year': '1957', 'journal-title': 'Soviet Phys.-JETP'} / Soviet Phys.-JETP (1957)
{'key': '2024020900592186400_r3b', 'first-page': '1152', 'volume': '30', 'year': '1956', 'journal-title': 'Zh. Eksperim. i Teor. Fiz.'} / Zh. Eksperim. i Teor. Fiz. (1956)
10.1007/BF02827754 / Nuovo Cimento (1957)
10.1080/00268976200100721 / Mol. Phys. (1962)
{'key': '2024020900592186400_r3e', 'first-page': '387', 'volume': 'A271', 'year': '1963', 'journal-title': 'Proc. Roy. Soc. (London)'} / Proc. Roy. Soc. (London) (1963)
10.1103/RevModPhys.11.1 / Rev. Mod. Phys. (1939)
{'key': '2024020900592186400_r5', 'first-page': '383', 'volume': 'A237', 'year': '1956', 'journal-title': 'Proc. Roy. Soc. (London)'} / Proc. Roy. Soc. (London) (1956)
{'key': '2024020900592186400_r5a', 'first-page': '413', 'volume': 'A239', 'year': '1957', 'journal-title': 'Proc. R. Soc. London, Ser. A'} / Proc. R. Soc. London, Ser. A (1957)
10.1063/1.1730917 / J. Chem. Phys. (1960)
10.1063/1.1732768 / J. Chem. Phys. (1962)
10.1063/1.1701340 / J. Chem. Phys. (1962)
{'key': '2024020900592186400_r6'}
{'key': '2024020900592186400_r7'}
{'key': '2024020900592186400_r8'}
10.1063/1.1696183 / J. Chem. Phys. (1965)
{'key': '2024020900592186400_r9'}
10.1103/PhysRev.34.553 / Phys. Rev. (1929)
10.1103/PhysRev.36.383 / Phys. Rev. (1930)
10.1103/PhysRev.39.616 / Phys. Rev. (1932)
{'key': '2024020900592186400_r11'}
{'key': '2024020900592186400_r12'}
10.1103/RevModPhys.37.159 / Rev. Mod. Phys. (1965)
{'key': '2024020900592186400_r14'}
{'key': '2024020900592186400_r15'}
{'key': '2024020900592186400_r16'}
{'key': '2024020900592186400_r17'}
{'key': '2024020900592186400_r18'}
10.1080/14786440508636066 / Phil. Mag. (1920)
{'key': '2024020900592186400_r19a'}
{'key': '2024020900592186400_r20'}
10.1016/0016-0032(57)90341-1 / J. Franklin Inst. (1957)
10.1063/1.1733957 / J. Chem. Phys. (1963)
10.1103/PhysRev.133.A1295 / Phys. Rev. (1964)
{'key': '2024020900592186400_r23'}
10.1002/sapm1958371215 / J. Math. Phys. (1958)
{'key': '2024020900592186400_r25'}
{'key': '2024020900592186400_r26'}
{'key': '2024020900592186400_r27'}
{'key': '2024020900592186400_r27a'}
{'key': '2024020900592186400_r28'}
{'key': '2024020900592186400_r29'}
10.1007/BF01397327 / Z. Physik (1927)
10.1103/RevModPhys.2.305 / Rev. Mod. Phys. (1930)
{'key': '2024020900592186400_r31'}
{'key': '2024020900592186400_r31a'}
{'key': '2024020900592186400_r32', 'first-page': '222', 'volume': 'B11', 'year': '1930', 'journal-title': 'Z. Physik. Chem.'} / Z. Physik. Chem. (1930)
{'key': '2024020900592186400_r32a', 'first-page': '8', 'volume': '33', 'year': '1937', 'journal-title': 'Trans. Faraday Soc.'} / Trans. Faraday Soc. (1937)
{'key': '2024020900592186400_r33'}
{'key': '2024020900592186400_r34'}
10.1016/0016-0032(57)90341-1 / J. Franklin Inst. (1957)
{'key': '2024020900592186400_r36', 'first-page': '403', 'volume': '263', 'year': '1957', 'journal-title': 'J. Franklin Inst.'} / J. Franklin Inst. (1957)
10.1007/BF01397633 / Z. Physik (1927)
{'key': '2024020900592186400_r38', 'first-page': '424', 'volume': 'A259', 'year': '1960', 'journal-title': 'Proc. Roy. Soc. (London)'} / Proc. Roy. Soc. (London) (1960)
10.1103/PhysRev.135.A1018 / Phys. Rev. (1964)
{'key': '2024020900592186400_r40'}
{'key': '2024020900592186400_r41', 'first-page': '896', 'volume': '9', 'year': '1938', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1938)
{'key': '2024020900592186400_r41a'}
{'key': '2024020900592186400_r41b', 'first-page': '1812', 'volume': '20', 'year': '1952', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1952)
10.1103/PhysRev.123.1865 / Phys. Rev. (1961)
10.1103/PhysRev.61.186 / Phys. Rev. (1942)
10.1103/PhysRev.62.438 / Phys. Rev. (1942)
10.1103/PhysRev.63.367 / Phys. Rev. (1943)
{'key': '2024020900592186400_r43'}
10.1063/1.1742459 / J. Chem. Phys. (1956)
{'key': '2024020900592186400_r45'}

Dates

Type	When
Created	20 years, 7 months ago (Jan. 9, 2005, 3:17 a.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 7:59 p.m.)
Indexed	1 hour ago (Sept. 3, 2025, 2:19 a.m.)
Issued	59 years, 4 months ago (May 1, 1966)
Published	59 years, 4 months ago (May 1, 1966)
Published Print	59 years, 4 months ago (May 1, 1966)

Funders 0

None

BibTeX

@article{Meath_1966, title={Relativistic Intermolecular Forces, Moderately Long Range}, volume={44}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1727214}, DOI={10.1063/1.1727214}, number={9}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Meath, William J. and Hirschfelder, Joseph O.}, year={1966}, month=may, pages={3197–3209} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        9,
        3
      ]
    ],
    "date-time": "2025-09-03T06:19:28Z",
    "timestamp": 1756880368534
  },
  "reference-count": 68,
  "publisher": "AIP Publishing",
  "issue": "9",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1966,
        5,
        1
      ]
    ]
  },
  "abstract": "<jats:p>The generalized Breit\u2014Pauli Hamiltonian is used to give a systematic treatment of magnetic and other relativistic intermolecular energies through O(\u03b12) (where \u03b1 is the fine-structure constant) for intermolecular separations, R, sufficiently large that the charge distributions of the two molecules do not overlap, but sufficiently small that R&amp;lt;\u03bb/0=(\u03b1\u0394\u03b5)\u22121, where \u0394\u03b5 is the excitation energy of the first allowed transition of one of the molecules.</jats:p>\n               <jats:p>The theory is discussed in general and many types of interaction energies are obtained which depend on the spin and orbital angular-momentum states of the molecules. The interaction of two nondegenerate atoms (L=0, S=0) is considered specifically. Of particular interest is an interaction-energy term which varies as \u03b12/R4.</jats:p>",
  "DOI": "10.1063/1.1727214",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        1,
        9
      ]
    ],
    "date-time": "2005-01-09T08:17:14Z",
    "timestamp": 1105258634000
  },
  "page": "3197-3209",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 72,
  "title": "Relativistic Intermolecular Forces, Moderately Long Range",
  "prefix": "10.1063",
  "volume": "44",
  "author": [
    {
      "given": "William J.",
      "family": "Meath",
      "sequence": "first",
      "affiliation": [
        {
          "name": "University of Wisconsin, Theoretical Chemistry Institute, Madison, Wisconsin"
        }
      ]
    },
    {
      "given": "Joseph O.",
      "family": "Hirschfelder",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "University of Wisconsin, Theoretical Chemistry Institute, Madison, Wisconsin"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020900592186400_r1"
    },
    {
      "key": "2024020900592186400_r2",
      "doi-asserted-by": "crossref",
      "first-page": "986",
      "DOI": "10.1063/1.1743155",
      "volume": "25",
      "year": "1956",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r3",
      "doi-asserted-by": "crossref",
      "first-page": "360",
      "DOI": "10.1103/PhysRev.73.360",
      "volume": "73",
      "year": "1948",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r3a",
      "first-page": "977",
      "volume": "3",
      "year": "1957",
      "journal-title": "Soviet Phys.-JETP"
    },
    {
      "key": "2024020900592186400_r3b",
      "first-page": "1152",
      "volume": "30",
      "year": "1956",
      "journal-title": "Zh. Eksperim. i Teor. Fiz."
    },
    {
      "key": "2024020900592186400_r3c",
      "doi-asserted-by": "crossref",
      "first-page": "7",
      "DOI": "10.1007/BF02827754",
      "volume": "6",
      "year": "1957",
      "journal-title": "Nuovo Cimento"
    },
    {
      "key": "2024020900592186400_r3d",
      "doi-asserted-by": "crossref",
      "first-page": "629",
      "DOI": "10.1080/00268976200100721",
      "volume": "5",
      "year": "1962",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020900592186400_r3e",
      "first-page": "387",
      "volume": "A271",
      "year": "1963",
      "journal-title": "Proc. Roy. Soc. (London)"
    },
    {
      "key": "2024020900592186400_r4",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1103/RevModPhys.11.1",
      "volume": "11",
      "year": "1939",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024020900592186400_r5",
      "first-page": "383",
      "volume": "A237",
      "year": "1956",
      "journal-title": "Proc. Roy. Soc. (London)"
    },
    {
      "key": "2024020900592186400_r5a",
      "first-page": "413",
      "volume": "A239",
      "year": "1957",
      "journal-title": "Proc. R. Soc. London, Ser. A"
    },
    {
      "key": "2024020900592186400_r5b",
      "doi-asserted-by": "crossref",
      "first-page": "1323",
      "DOI": "10.1063/1.1730917",
      "volume": "32",
      "year": "1960",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r5c",
      "doi-asserted-by": "crossref",
      "first-page": "1490",
      "DOI": "10.1063/1.1732768",
      "volume": "36",
      "year": "1962",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r5d",
      "doi-asserted-by": "crossref",
      "first-page": "433",
      "DOI": "10.1063/1.1701340",
      "volume": "37",
      "year": "1962",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r6"
    },
    {
      "key": "2024020900592186400_r7"
    },
    {
      "key": "2024020900592186400_r8"
    },
    {
      "key": "2024020900592186400_r8a",
      "doi-asserted-by": "crossref",
      "first-page": "1717",
      "DOI": "10.1063/1.1696183",
      "volume": "42",
      "year": "1965",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r9"
    },
    {
      "key": "2024020900592186400_r10",
      "doi-asserted-by": "crossref",
      "first-page": "553",
      "DOI": "10.1103/PhysRev.34.553",
      "volume": "34",
      "year": "1929",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r10a",
      "doi-asserted-by": "crossref",
      "first-page": "383",
      "DOI": "10.1103/PhysRev.36.383",
      "volume": "36",
      "year": "1930",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r10b",
      "doi-asserted-by": "crossref",
      "first-page": "616",
      "DOI": "10.1103/PhysRev.39.616",
      "volume": "39",
      "year": "1932",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r11"
    },
    {
      "key": "2024020900592186400_r12"
    },
    {
      "key": "2024020900592186400_r13",
      "doi-asserted-by": "crossref",
      "first-page": "159",
      "DOI": "10.1103/RevModPhys.37.159",
      "volume": "37",
      "year": "1965",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024020900592186400_r14"
    },
    {
      "key": "2024020900592186400_r15"
    },
    {
      "key": "2024020900592186400_r16"
    },
    {
      "key": "2024020900592186400_r17"
    },
    {
      "key": "2024020900592186400_r18"
    },
    {
      "key": "2024020900592186400_r19",
      "doi-asserted-by": "crossref",
      "first-page": "537",
      "DOI": "10.1080/14786440508636066",
      "volume": "39",
      "year": "1920",
      "journal-title": "Phil. Mag."
    },
    {
      "key": "2024020900592186400_r19a"
    },
    {
      "key": "2024020900592186400_r20"
    },
    {
      "key": "2024020900592186400_r21",
      "doi-asserted-by": "crossref",
      "first-page": "331",
      "DOI": "10.1016/0016-0032(57)90341-1",
      "volume": "263",
      "year": "1957",
      "journal-title": "J. Franklin Inst."
    },
    {
      "key": "2024020900592186400_r22",
      "doi-asserted-by": "crossref",
      "first-page": "2248",
      "DOI": "10.1063/1.1733957",
      "volume": "38",
      "year": "1963",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r22a",
      "doi-asserted-by": "crossref",
      "first-page": "A1295",
      "DOI": "10.1103/PhysRev.133.A1295",
      "volume": "133",
      "year": "1964",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r23"
    },
    {
      "key": "2024020900592186400_r24",
      "doi-asserted-by": "crossref",
      "first-page": "215",
      "DOI": "10.1002/sapm1958371215",
      "volume": "37",
      "year": "1958",
      "journal-title": "J. Math. Phys."
    },
    {
      "key": "2024020900592186400_r25"
    },
    {
      "key": "2024020900592186400_r26"
    },
    {
      "key": "2024020900592186400_r27"
    },
    {
      "key": "2024020900592186400_r27a"
    },
    {
      "key": "2024020900592186400_r28"
    },
    {
      "key": "2024020900592186400_r29"
    },
    {
      "key": "2024020900592186400_r30",
      "doi-asserted-by": "crossref",
      "first-page": "624",
      "DOI": "10.1007/BF01397327",
      "volume": "43",
      "year": "1927",
      "journal-title": "Z. Physik"
    },
    {
      "key": "2024020900592186400_r30a",
      "doi-asserted-by": "crossref",
      "first-page": "305",
      "DOI": "10.1103/RevModPhys.2.305",
      "volume": "2",
      "year": "1930",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024020900592186400_r31"
    },
    {
      "key": "2024020900592186400_r31a"
    },
    {
      "key": "2024020900592186400_r32",
      "first-page": "222",
      "volume": "B11",
      "year": "1930",
      "journal-title": "Z. Physik. Chem."
    },
    {
      "key": "2024020900592186400_r32a",
      "first-page": "8",
      "volume": "33",
      "year": "1937",
      "journal-title": "Trans. Faraday Soc."
    },
    {
      "key": "2024020900592186400_r33"
    },
    {
      "key": "2024020900592186400_r34"
    },
    {
      "key": "2024020900592186400_r35",
      "doi-asserted-by": "crossref",
      "first-page": "331",
      "DOI": "10.1016/0016-0032(57)90341-1",
      "volume": "263",
      "year": "1957",
      "journal-title": "J. Franklin Inst."
    },
    {
      "key": "2024020900592186400_r36",
      "first-page": "403",
      "volume": "263",
      "year": "1957",
      "journal-title": "J. Franklin Inst."
    },
    {
      "key": "2024020900592186400_r37",
      "doi-asserted-by": "crossref",
      "first-page": "563",
      "DOI": "10.1007/BF01397633",
      "volume": "43",
      "year": "1927",
      "journal-title": "Z. Physik"
    },
    {
      "key": "2024020900592186400_r38",
      "first-page": "424",
      "volume": "A259",
      "year": "1960",
      "journal-title": "Proc. Roy. Soc. (London)"
    },
    {
      "key": "2024020900592186400_r39",
      "doi-asserted-by": "crossref",
      "first-page": "A1018",
      "DOI": "10.1103/PhysRev.135.A1018",
      "volume": "135",
      "year": "1964",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r40"
    },
    {
      "key": "2024020900592186400_r41",
      "first-page": "896",
      "volume": "9",
      "year": "1938",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r41a"
    },
    {
      "key": "2024020900592186400_r41b",
      "first-page": "1812",
      "volume": "20",
      "year": "1952",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r41c",
      "doi-asserted-by": "crossref",
      "first-page": "1865",
      "DOI": "10.1103/PhysRev.123.1865",
      "volume": "123",
      "year": "1961",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r42",
      "doi-asserted-by": "crossref",
      "first-page": "186",
      "DOI": "10.1103/PhysRev.61.186",
      "volume": "61",
      "year": "1942",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r42a",
      "doi-asserted-by": "crossref",
      "first-page": "438",
      "DOI": "10.1103/PhysRev.62.438",
      "volume": "62",
      "year": "1942",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r42b",
      "doi-asserted-by": "crossref",
      "first-page": "367",
      "DOI": "10.1103/PhysRev.63.367",
      "volume": "63",
      "year": "1943",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020900592186400_r43"
    },
    {
      "key": "2024020900592186400_r44",
      "doi-asserted-by": "crossref",
      "first-page": "225",
      "DOI": "10.1063/1.1742459",
      "volume": "24",
      "year": "1956",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020900592186400_r45"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/44/9/3197/18843862/3197_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/44/9/3197/18843862/3197_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        9
      ]
    ],
    "date-time": "2024-02-09T00:59:37Z",
    "timestamp": 1707440377000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/44/9/3197/82664/Relativistic-Intermolecular-Forces-Moderately-Long"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1966,
        5,
        1
      ]
    ]
  },
  "references-count": 68,
  "journal-issue": {
    "issue": "9",
    "published-print": {
      "date-parts": [
        [
          1966,
          5,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1727214",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1966,
        5,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1966,
        5,
        1
      ]
    ]
  }
}