DOI: 10.1063/1.1316037. The higher-order Douglas

The higher-order Douglas–Kroll transformation

10.1063/1.1316037

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The higher-order Douglas–Kroll (DK) Hamiltonians in an external potential are explicitly derived. Application of an exponential-type unitary operator with the 2n+1 rule significantly simplifies the formulations of the high-order DK Hamiltonians. The third-order DK method has been implemented practically. Numerical results for one- and many-electron systems show that good accuracy can be obtained even with the DK Hamiltonian correct to third order in the external potential.

Bibliography

Nakajima, T., & Hirao, K. (2000). The higher-order DouglasâKroll transformation. The Journal of Chemical Physics, 113(18), 7786â7789.

Authors 2

Takahito Nakajima (first)
Kimihiko Hirao (additional)

References 18 Referenced 281

10.1016/0003-4916(74)90333-9 / Ann. Phys. (N.Y.) (1974)
10.1103/PhysRevA.33.3742 / Phys. Rev. A (1986)
10.1103/PhysRevA.39.6016 / Phys. Rev. A (1989)
10.1103/PhysRev.78.29 / Phys. Rev. (1950)
10.1063/1.466059 / J. Chem. Phys. (1993)
10.1007/BF01436580 / Z. Phys. D: At., Mol. Clusters (1989)
10.1007/BF01436910 / Z. Phys. D: At., Mol. Clusters (1990)
10.1002/(SICI)1097-461X(1997)65:3<225::AID-QUA4>3.0.CO;2-Y / Int. J. Quantum Chem. (1997)
10.1016/S0009-2614(99)00150-5 / Chem. Phys. Lett. (1999)
10.1016/S0009-2614(99)00304-8 / Chem. Phys. Lett. (1999)
10.1007/BF00186443 / Theor. Chim. Acta (1996)
10.1103/PhysRevA.22.348 / Phys. Rev. A (1980)
{'key': '2024020706361554700_r12'}
10.1016/0301-0104(84)80001-4 / Chem. Phys. (1984)
{'key': '2024020706361554700_r14'}
{'key': '2024020706361554700_r15'}
10.1103/PhysRevA.47.143 / Phys. Rev. A (1993)
10.1063/1.462210 / J. Chem. Phys. (1992)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 10:14 a.m.)
Deposited	1 year, 6 months ago (Feb. 7, 2024, 5:58 a.m.)
Indexed	5 days, 8 hours ago (Aug. 29, 2025, 5:46 a.m.)
Issued	24 years, 9 months ago (Nov. 8, 2000)
Published	24 years, 9 months ago (Nov. 8, 2000)
Published Print	24 years, 9 months ago (Nov. 8, 2000)

Funders 0

None

BibTeX

@article{Nakajima_2000, title={The higher-order Douglas–Kroll transformation}, volume={113}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1316037}, DOI={10.1063/1.1316037}, number={18}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Nakajima, Takahito and Hirao, Kimihiko}, year={2000}, month=nov, pages={7786–7789} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        29
      ]
    ],
    "date-time": "2025-08-29T09:46:53Z",
    "timestamp": 1756460813410
  },
  "reference-count": 18,
  "publisher": "AIP Publishing",
  "issue": "18",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2000,
        11,
        8
      ]
    ]
  },
  "abstract": "<jats:p>The higher-order Douglas\u2013Kroll (DK) Hamiltonians in an external potential are explicitly derived. Application of an exponential-type unitary operator with the 2n+1 rule significantly simplifies the formulations of the high-order DK Hamiltonians. The third-order DK method has been implemented practically. Numerical results for one- and many-electron systems show that good accuracy can be obtained even with the DK Hamiltonian correct to third order in the external potential.</jats:p>",
  "DOI": "10.1063/1.1316037",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T14:14:52Z",
    "timestamp": 1027692892000
  },
  "page": "7786-7789",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 281,
  "title": "The higher-order Douglas\u2013Kroll transformation",
  "prefix": "10.1063",
  "volume": "113",
  "author": [
    {
      "given": "Takahito",
      "family": "Nakajima",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Hongo, Tokyo, 113-8656, Japan"
        }
      ]
    },
    {
      "given": "Kimihiko",
      "family": "Hirao",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Hongo, Tokyo, 113-8656, Japan"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020706361554700_r1",
      "doi-asserted-by": "crossref",
      "first-page": "89",
      "DOI": "10.1016/0003-4916(74)90333-9",
      "volume": "82",
      "year": "1974",
      "journal-title": "Ann. Phys. (N.Y.)"
    },
    {
      "key": "2024020706361554700_r2",
      "doi-asserted-by": "crossref",
      "first-page": "3742",
      "DOI": "10.1103/PhysRevA.33.3742",
      "volume": "33",
      "year": "1986",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024020706361554700_r3",
      "doi-asserted-by": "crossref",
      "first-page": "6016",
      "DOI": "10.1103/PhysRevA.39.6016",
      "volume": "39",
      "year": "1989",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024020706361554700_r4",
      "doi-asserted-by": "crossref",
      "first-page": "29",
      "DOI": "10.1103/PhysRev.78.29",
      "volume": "78",
      "year": "1950",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020706361554700_r5",
      "doi-asserted-by": "crossref",
      "first-page": "4597",
      "DOI": "10.1063/1.466059",
      "volume": "99",
      "year": "1993",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706361554700_r6",
      "doi-asserted-by": "crossref",
      "first-page": "15",
      "DOI": "10.1007/BF01436580",
      "volume": "11",
      "year": "1989",
      "journal-title": "Z. Phys. D: At., Mol. Clusters"
    },
    {
      "key": "2024020706361554700_r6a",
      "doi-asserted-by": "crossref",
      "first-page": "27",
      "DOI": "10.1007/BF01436910",
      "volume": "15",
      "year": "1990",
      "journal-title": "Z. Phys. D: At., Mol. Clusters"
    },
    {
      "key": "2024020706361554700_r7",
      "doi-asserted-by": "crossref",
      "first-page": "225",
      "DOI": "10.1002/(SICI)1097-461X(1997)65:3<225::AID-QUA4>3.0.CO;2-Y",
      "volume": "65",
      "year": "1997",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "2024020706361554700_r8",
      "doi-asserted-by": "crossref",
      "first-page": "383",
      "DOI": "10.1016/S0009-2614(99)00150-5",
      "volume": "302",
      "year": "1999",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020706361554700_r9",
      "doi-asserted-by": "crossref",
      "first-page": "271",
      "DOI": "10.1016/S0009-2614(99)00304-8",
      "volume": "304",
      "year": "1999",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020706361554700_r10",
      "doi-asserted-by": "crossref",
      "first-page": "213",
      "DOI": "10.1007/BF00186443",
      "volume": "94",
      "year": "1996",
      "journal-title": "Theor. Chim. Acta"
    },
    {
      "key": "2024020706361554700_r11",
      "doi-asserted-by": "crossref",
      "first-page": "348",
      "DOI": "10.1103/PhysRevA.22.348",
      "volume": "22",
      "year": "1980",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024020706361554700_r12"
    },
    {
      "key": "2024020706361554700_r13",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1016/0301-0104(84)80001-4",
      "volume": "84",
      "year": "1984",
      "journal-title": "Chem. Phys."
    },
    {
      "key": "2024020706361554700_r14"
    },
    {
      "key": "2024020706361554700_r15"
    },
    {
      "key": "2024020706361554700_r16",
      "doi-asserted-by": "crossref",
      "first-page": "143",
      "DOI": "10.1103/PhysRevA.47.143",
      "volume": "47",
      "year": "1993",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024020706361554700_r17",
      "doi-asserted-by": "crossref",
      "first-page": "1227",
      "DOI": "10.1063/1.462210",
      "volume": "96",
      "year": "1992",
      "journal-title": "J. Chem. Phys."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/113/18/7786/19288853/7786_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/113/18/7786/19288853/7786_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        7
      ]
    ],
    "date-time": "2024-02-07T10:58:07Z",
    "timestamp": 1707303487000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/113/18/7786/458704/The-higher-order-Douglas-Kroll-transformation"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2000,
        11,
        8
      ]
    ]
  },
  "references-count": 18,
  "journal-issue": {
    "issue": "18",
    "published-print": {
      "date-parts": [
        [
          2000,
          11,
          8
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1316037",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2000,
        11,
        8
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2000,
        11,
        8
      ]
    ]
  }
}