DOI: 10.1002/qua.560050506. Bounds to second‐order perturbation energies (particularly dispersion) for excited states

Bounds to second‐order perturbation energies (particularly dispersion) for excited states

10.1002/qua.560050506

Crossref journal-article

Wiley

International Journal of Quantum Chemistry (311)

Abstract

AbstractUpper and lower bound expressions are derived to the second‐order energy relating to an unperturbed degenerate excited state in those cases where both the first‐order energy and the off diagonal matrix elements in the secular equation vanish, making use of the partitioning technique, operator inequalities and inner projection approach. These expressions, which involve an arbitrary basis, are then developed to yield reasonably good bounds to van der Waals dispersion energies for systems of the type H (first excited state) — other atom b (ground state). The particular choice of basis used in the development yields the latter bounds easy to evaluate by expressing them in terms of the ground state sum rule values, S(k) of atom b. This same choice is also utilized in Lindner and Löwdin's expressions [1] to obtain bounds to systems of the type H (ground state) — other atom b (ground state) that are comparable to those found by other more elaborate semi‐empirical methods.

Bibliography

Abdulnur, S. F. (1971). Bounds to secondâorder perturbation energies (particularly dispersion) for excited states. International Journal of Quantum Chemistry, 5(5), 525â537. Portico.

Authors 1

Suheil F. Abdulnur (first)

References 29 Referenced 8

10.1002/qua.560020717 / Int. J. Quantum Chem. by Lindner P. (1968)
10.1007/BF01397633
10.1007/BF01397032
10.1016/S0065-3276(08)60381-0
10.1063/1.1734192
10.1002/qua.560040208
10.1002/qua.560020604
10.1063/1.1669717
10.1016/S0076-5392(08)62673-9
10.1063/1.1673771
10.1016/0009-2614(70)85204-6
{'key': 'e_1_2_1_13_2', 'first-page': '255', 'volume-title': 'Perturbation Theory and its Applications in Quantum Mechanics', 'author': 'Löwdin P. O.', 'year': '1966'} / Perturbation Theory and its Applications in Quantum Mechanics by Löwdin P. O. (1966)
10.1002/qua.560020612
10.1103/PhysRev.139.A357
J. H.Choi University of Florida Quantum Theory Project Preprint No. 89 (1966).
10.1002/qua.560030517
10.1063/1.1664814
10.1063/1.1724312
10.1063/1.1701554
10.1002/9780470143582.ch1
10.1063/1.1742296
10.1002/9780470143582.ch3
10.1364/JOSA.59.000863
10.1103/PhysRevLett.13.127
10.1098/rspa.1960.0237
10.1088/0370-1328/86/1/303
{'key': 'e_1_2_1_28_2', 'first-page': '299', 'volume': '4', 'author': 'Dutta N. C.', 'year': '1970', 'journal-title': 'Int. J. Quantum Chem.'} / Int. J. Quantum Chem. by Dutta N. C. (1970)
10.1103/PhysRev.40.387
10.1080/00268975900100231

Dates

Type	When
Created	20 years, 8 months ago (Dec. 27, 2004, 9:58 p.m.)
Deposited	1 year, 10 months ago (Oct. 15, 2023, 9:20 a.m.)
Indexed	1 year, 6 months ago (Feb. 9, 2024, 9:57 a.m.)
Issued	54 years ago (Sept. 1, 1971)
Published	54 years ago (Sept. 1, 1971)
Published Online	20 years, 10 months ago (Oct. 12, 2004)
Published Print	54 years ago (Sept. 1, 1971)

Funders 0

None

BibTeX

@article{Abdulnur_1971, title={Bounds to second‐order perturbation energies (particularly dispersion) for excited states}, volume={5}, ISSN={1097-461X}, url={http://dx.doi.org/10.1002/qua.560050506}, DOI={10.1002/qua.560050506}, number={5}, journal={International Journal of Quantum Chemistry}, publisher={Wiley}, author={Abdulnur, Suheil F.}, year={1971}, month=sep, pages={525–537} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        2,
        9
      ]
    ],
    "date-time": "2024-02-09T14:57:32Z",
    "timestamp": 1707490652739
  },
  "reference-count": 29,
  "publisher": "Wiley",
  "issue": "5",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2004,
            10,
            12
          ]
        ],
        "date-time": "2004-10-12T00:00:00Z",
        "timestamp": 1097539200000
      },
      "content-version": "vor",
      "delay-in-days": 12095,
      "URL": "http://onlinelibrary.wiley.com/termsAndConditions#vor"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1971,
        9
      ]
    ]
  },
  "abstract": "<jats:title>Abstract</jats:title><jats:p>Upper and lower bound expressions are derived to the second\u2010order energy relating to an unperturbed degenerate excited state in those cases where both the first\u2010order energy and the off diagonal matrix elements in the secular equation vanish, making use of the partitioning technique, operator inequalities and inner projection approach. These expressions, which involve an arbitrary basis, are then developed to yield reasonably good bounds to van der Waals dispersion energies for systems of the type H (first excited state) \u2014 other atom <jats:italic>b</jats:italic> (ground state). The particular choice of basis used in the development yields the latter bounds easy to evaluate by expressing them in terms of the ground state sum rule values, <jats:italic>S</jats:italic>(<jats:italic>k</jats:italic>) of atom <jats:italic>b</jats:italic>. This same choice is also utilized in Lindner and L\u00f6wdin's expressions [1] to obtain bounds to systems of the type H (ground state) \u2014 other atom <jats:italic>b</jats:italic> (ground state) that are comparable to those found by other more elaborate semi\u2010empirical methods.</jats:p>",
  "DOI": "10.1002/qua.560050506",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        12,
        28
      ]
    ],
    "date-time": "2004-12-28T02:58:23Z",
    "timestamp": 1104202703000
  },
  "page": "525-537",
  "source": "Crossref",
  "is-referenced-by-count": 8,
  "title": "Bounds to second\u2010order perturbation energies (particularly dispersion) for excited states",
  "prefix": "10.1002",
  "volume": "5",
  "author": [
    {
      "given": "Suheil F.",
      "family": "Abdulnur",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "311",
  "published-online": {
    "date-parts": [
      [
        2004,
        10,
        12
      ]
    ]
  },
  "reference": [
    {
      "key": "e_1_2_1_2_2",
      "doi-asserted-by": "crossref",
      "first-page": "161",
      "DOI": "10.1002/qua.560020717",
      "volume": "2",
      "author": "Lindner P.",
      "year": "1968",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "e_1_2_1_3_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BF01397633"
    },
    {
      "key": "e_1_2_1_4_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BF01397032"
    },
    {
      "key": "e_1_2_1_5_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/S0065-3276(08)60381-0"
    },
    {
      "key": "e_1_2_1_6_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1734192"
    },
    {
      "key": "e_1_2_1_7_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/qua.560040208"
    },
    {
      "key": "e_1_2_1_8_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/qua.560020604"
    },
    {
      "key": "e_1_2_1_9_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1669717"
    },
    {
      "key": "e_1_2_1_10_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/S0076-5392(08)62673-9"
    },
    {
      "key": "e_1_2_1_11_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1673771"
    },
    {
      "key": "e_1_2_1_12_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0009-2614(70)85204-6"
    },
    {
      "key": "e_1_2_1_13_2",
      "first-page": "255",
      "volume-title": "Perturbation Theory and its Applications in Quantum Mechanics",
      "author": "L\u00f6wdin P. O.",
      "year": "1966"
    },
    {
      "key": "e_1_2_1_14_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/qua.560020612"
    },
    {
      "key": "e_1_2_1_15_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRev.139.A357"
    },
    {
      "key": "e_1_2_1_16_2",
      "unstructured": "J. H.Choi University of Florida Quantum Theory Project Preprint No. 89 (1966)."
    },
    {
      "key": "e_1_2_1_17_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/qua.560030517"
    },
    {
      "key": "e_1_2_1_18_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1664814"
    },
    {
      "key": "e_1_2_1_19_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1724312"
    },
    {
      "key": "e_1_2_1_20_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1701554"
    },
    {
      "key": "e_1_2_1_21_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/9780470143582.ch1"
    },
    {
      "key": "e_1_2_1_22_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.1742296"
    },
    {
      "key": "e_1_2_1_23_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/9780470143582.ch3"
    },
    {
      "key": "e_1_2_1_24_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1364/JOSA.59.000863"
    },
    {
      "key": "e_1_2_1_25_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.13.127"
    },
    {
      "key": "e_1_2_1_26_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1098/rspa.1960.0237"
    },
    {
      "key": "e_1_2_1_27_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1088/0370-1328/86/1/303"
    },
    {
      "key": "e_1_2_1_28_2",
      "first-page": "299",
      "volume": "4",
      "author": "Dutta N. C.",
      "year": "1970",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "e_1_2_1_29_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRev.40.387"
    },
    {
      "key": "e_1_2_1_30_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1080/00268975900100231"
    }
  ],
  "container-title": "International Journal of Quantum Chemistry",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fqua.560050506",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560050506",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        10,
        15
      ]
    ],
    "date-time": "2023-10-15T13:20:56Z",
    "timestamp": 1697376056000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://onlinelibrary.wiley.com/doi/10.1002/qua.560050506"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1971,
        9
      ]
    ]
  },
  "references-count": 29,
  "journal-issue": {
    "issue": "5",
    "published-print": {
      "date-parts": [
        [
          1971,
          9
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1002/qua.560050506"
  ],
  "URL": "http://dx.doi.org/10.1002/qua.560050506",
  "relation": {},
  "ISSN": [
    "0020-7608",
    "1097-461X"
  ],
  "subject": [],
  "container-title-short": "Int J of Quantum Chemistry",
  "published": {
    "date-parts": [
      [
        1971,
        9
      ]
    ]
  }
}