DOI: 10.1063/1.1670293. Relaxation of the Molecular Charge Distribution and the Vibrational Force Constant

Relaxation of the Molecular Charge Distribution and the Vibrational Force Constant

10.1063/1.1670293

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The force constants are calculated from Hartree–Fock wavefunctions for the molecules N2, CO, BF (isoelectronic with 14 e−), and BeO, LiF (isoelectronic with 12 e−) by a polynomial fit of the forces exerted on the nuclei as a function of the internuclear separation. The magnitude of the force constant and its variation through the two series of molecules are interpreted in terms of the relaxation of the molecular charge distribution which accompanies a displacement of the nuclei. It is found that the charge distribution of a covalently bound molecule relaxes in such a way as to facilitate the motion of the displaced nuclei. In a molecule with the characteristics of ionic binding, the relaxation of the charge density localized on the cation opposes the nuclear displacement while the charge density on the anion facilitates its nuclear displacement. The relaxations are illustrated in the form of density difference maps between the extended and equilibrium molecular charge distributions. Such relaxation diagrams show a striking correlation with density difference maps which depict the change in the atomic density distributions which result from the formation of a chemical bond. Thus the dominant characteristics of the relaxation, whether it opposes or facilitates the motions of the nuclei, may be inferred from a knowledge of the polarizations present in the static charge distribution when these polarizations are measured relative to valence-state distributions of the undistorted atoms.

Bibliography

Bader, R. F. W., & Bandrauk, A. D. (1968). Relaxation of the Molecular Charge Distribution and the Vibrational Force Constant. The Journal of Chemical Physics, 49(4), 1666â1675.

Authors 2

R. F. W. Bader (first)
A. D. Bandrauk (additional)

References 28 Referenced 69

10.1063/1.1841222 / J. Chem. Phys. (1967)
10.1063/1.1712404 / J. Chem. Phys. (1967)
{'key': '2024020904072366100_r3'}
10.1063/1.1670292 / J. Chem. Phys. (1968)
10.1103/PhysRev.56.340 / Phys. Rev. (1939)
{'key': '2024020904072366100_r6'}
10.1063/1.1725321 / J. Chem. Phys. (1964)
10.1063/1.1726972 / J. Chem. Phys. (1966)
{'key': '2024020904072366100_r9'}
10.1063/1.1726989 / J. Chem. Phys. (1966)
10.1016/S0065-3276(08)60085-4 / Advan. Quantum Chem. (1967)
10.1063/1.1731952 / J. Chem. Phys. (1961)
{'key': '2024020904072366100_r13'}
10.1017/S0305004100033417 / Proc. Cambridge Phil. Soc. (1958)
10.1016/0022-2852(60)90106-5 / J. Mol. Spectry. (1960)
10.1080/00268976000100161 / Mol. Phys. (1960)
10.1063/1.1731469 / J. Chem. Phys. (1960)
10.1063/1.1734135 / J. Chem. Phys. (1963)
10.1063/1.1726434 / J. Chem. Phys. (1966)
10.1063/1.1840571 / J. Chem. Phys. (1967)
10.1063/1.1733827 / J. Chem. Phys. (1963)
10.1063/1.1726725 / J. Chem. Phys. (1966)
{'key': '2024020904072366100_r23', 'first-page': '379', 'volume': '67', 'year': '1955', 'journal-title': 'Svensk Kem. Tidskr.'} / Svensk Kem. Tidskr. (1955)
10.1139/v68-157 / Can. J. Chem. (1968)
{'key': '2024020904072366100_r25'}
10.1103/PhysRev.138.A1303 / Phys. Rev. (1965)
10.1063/1.1696875 / J. Chem. Phys. (1965)
{'key': '2024020904072366100_r27a'}

Dates

Type	When
Created	21 years, 6 months ago (Feb. 6, 2004, 2:22 p.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 11:09 p.m.)
Indexed	4 months, 3 weeks ago (March 30, 2025, 10:29 p.m.)
Issued	57 years ago (Aug. 15, 1968)
Published	57 years ago (Aug. 15, 1968)
Published Print	57 years ago (Aug. 15, 1968)

Funders 0

None

BibTeX

@article{Bader_1968, title={Relaxation of the Molecular Charge Distribution and the Vibrational Force Constant}, volume={49}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1670293}, DOI={10.1063/1.1670293}, number={4}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Bader, R. F. W. and Bandrauk, A. D.}, year={1968}, month=aug, pages={1666–1675} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        3,
        31
      ]
    ],
    "date-time": "2025-03-31T02:29:09Z",
    "timestamp": 1743388149580
  },
  "reference-count": 28,
  "publisher": "AIP Publishing",
  "issue": "4",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1968,
        8,
        15
      ]
    ]
  },
  "abstract": "<jats:p>The force constants are calculated from Hartree\u2013Fock wavefunctions for the molecules N2, CO, BF (isoelectronic with 14 e\u2212), and BeO, LiF (isoelectronic with 12 e\u2212) by a polynomial fit of the forces exerted on the nuclei as a function of the internuclear separation. The magnitude of the force constant and its variation through the two series of molecules are interpreted in terms of the relaxation of the molecular charge distribution which accompanies a displacement of the nuclei. It is found that the charge distribution of a covalently bound molecule relaxes in such a way as to facilitate the motion of the displaced nuclei. In a molecule with the characteristics of ionic binding, the relaxation of the charge density localized on the cation opposes the nuclear displacement while the charge density on the anion facilitates its nuclear displacement. The relaxations are illustrated in the form of density difference maps between the extended and equilibrium molecular charge distributions. Such relaxation diagrams show a striking correlation with density difference maps which depict the change in the atomic density distributions which result from the formation of a chemical bond. Thus the dominant characteristics of the relaxation, whether it opposes or facilitates the motions of the nuclei, may be inferred from a knowledge of the polarizations present in the static charge distribution when these polarizations are measured relative to valence-state distributions of the undistorted atoms.</jats:p>",
  "DOI": "10.1063/1.1670293",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        2,
        6
      ]
    ],
    "date-time": "2004-02-06T19:22:23Z",
    "timestamp": 1076095343000
  },
  "page": "1666-1675",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 69,
  "title": "Relaxation of the Molecular Charge Distribution and the Vibrational Force Constant",
  "prefix": "10.1063",
  "volume": "49",
  "author": [
    {
      "given": "R. F. W.",
      "family": "Bader",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Chemistry, McMaster University, Hamilton, Ontario, Canada"
        }
      ]
    },
    {
      "given": "A. D.",
      "family": "Bandrauk",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Chemistry, McMaster University, Hamilton, Ontario, Canada"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020904072366100_r1",
      "doi-asserted-by": "crossref",
      "first-page": "3341",
      "DOI": "10.1063/1.1841222",
      "volume": "46",
      "year": "1967",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r2",
      "doi-asserted-by": "crossref",
      "first-page": "3381",
      "DOI": "10.1063/1.1712404",
      "volume": "47",
      "year": "1967",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r3"
    },
    {
      "key": "2024020904072366100_r4",
      "doi-asserted-by": "crossref",
      "first-page": "1653",
      "DOI": "10.1063/1.1670292",
      "volume": "49",
      "year": "1968",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r5",
      "doi-asserted-by": "crossref",
      "first-page": "340",
      "DOI": "10.1103/PhysRev.56.340",
      "volume": "56",
      "year": "1939",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020904072366100_r6"
    },
    {
      "key": "2024020904072366100_r7",
      "doi-asserted-by": "crossref",
      "first-page": "1374",
      "DOI": "10.1063/1.1725321",
      "volume": "40",
      "year": "1964",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r8",
      "doi-asserted-by": "crossref",
      "first-page": "1973",
      "DOI": "10.1063/1.1726972",
      "volume": "44",
      "year": "1966",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r9"
    },
    {
      "key": "2024020904072366100_r10",
      "doi-asserted-by": "crossref",
      "first-page": "2115",
      "DOI": "10.1063/1.1726989",
      "volume": "44",
      "year": "1966",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r11",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1016/S0065-3276(08)60085-4",
      "volume": "3",
      "year": "1967",
      "journal-title": "Advan. Quantum Chem."
    },
    {
      "key": "2024020904072366100_r12",
      "doi-asserted-by": "crossref",
      "first-page": "458",
      "DOI": "10.1063/1.1731952",
      "volume": "35",
      "year": "1961",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r13"
    },
    {
      "key": "2024020904072366100_r14",
      "doi-asserted-by": "crossref",
      "first-page": "251",
      "DOI": "10.1017/S0305004100033417",
      "volume": "54",
      "year": "1958",
      "journal-title": "Proc. Cambridge Phil. Soc."
    },
    {
      "key": "2024020904072366100_r15",
      "doi-asserted-by": "crossref",
      "first-page": "446",
      "DOI": "10.1016/0022-2852(60)90106-5",
      "volume": "4",
      "year": "1960",
      "journal-title": "J. Mol. Spectry."
    },
    {
      "key": "2024020904072366100_r16",
      "doi-asserted-by": "crossref",
      "first-page": "137",
      "DOI": "10.1080/00268976000100161",
      "volume": "3",
      "year": "1960",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020904072366100_r17",
      "doi-asserted-by": "crossref",
      "first-page": "1603",
      "DOI": "10.1063/1.1731469",
      "volume": "33",
      "year": "1960",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r18",
      "doi-asserted-by": "crossref",
      "first-page": "3010",
      "DOI": "10.1063/1.1734135",
      "volume": "39",
      "year": "1963",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r19",
      "doi-asserted-by": "crossref",
      "first-page": "119",
      "DOI": "10.1063/1.1726434",
      "volume": "44",
      "year": "1966",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r20",
      "doi-asserted-by": "crossref",
      "first-page": "4474",
      "DOI": "10.1063/1.1840571",
      "volume": "46",
      "year": "1967",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r21",
      "doi-asserted-by": "crossref",
      "first-page": "1227",
      "DOI": "10.1063/1.1733827",
      "volume": "38",
      "year": "1963",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r22",
      "doi-asserted-by": "crossref",
      "first-page": "556",
      "DOI": "10.1063/1.1726725",
      "volume": "44",
      "year": "1966",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r23",
      "first-page": "379",
      "volume": "67",
      "year": "1955",
      "journal-title": "Svensk Kem. Tidskr."
    },
    {
      "key": "2024020904072366100_r24",
      "doi-asserted-by": "crossref",
      "first-page": "953",
      "DOI": "10.1139/v68-157",
      "volume": "46",
      "year": "1968",
      "journal-title": "Can. J. Chem."
    },
    {
      "key": "2024020904072366100_r25"
    },
    {
      "key": "2024020904072366100_r26",
      "doi-asserted-by": "crossref",
      "first-page": "A1303",
      "DOI": "10.1103/PhysRev.138.A1303",
      "volume": "138",
      "year": "1965",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020904072366100_r27",
      "doi-asserted-by": "crossref",
      "first-page": "943",
      "DOI": "10.1063/1.1696875",
      "volume": "43",
      "year": "1965",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020904072366100_r27a"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/49/4/1666/18858256/1666_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/49/4/1666/18858256/1666_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        9
      ]
    ],
    "date-time": "2024-02-09T04:09:43Z",
    "timestamp": 1707451783000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/49/4/1666/779270/Relaxation-of-the-Molecular-Charge-Distribution"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1968,
        8,
        15
      ]
    ]
  },
  "references-count": 28,
  "journal-issue": {
    "issue": "4",
    "published-print": {
      "date-parts": [
        [
          1968,
          8,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1670293",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1968,
        8,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1968,
        8,
        15
      ]
    ]
  }
}