DOI: 10.1063/1.453655. Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application

Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application

10.1063/1.453655

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The theory for the analytic evaluation of energy gradients for coupled cluster (CC) wave functions is presented. In particular, explicit expressions for the analytic energy gradient of the CC singles and doubles (CCSD) wave function for a closed-shell restricted Hartree–Fock reference determinant are presented and shown to scale as N6 where N is the one-electron number of atomic basis functions for the molecular system. Thus analytic CCSD gradients are found to be of the same magnitude in computational cost as is the evaluation of analytic gradients for the configuration interaction singles and doubles (CISD) wave function. Applications of this method are presented for the water molecule and the formaldehyde molecule using a double-ζ plus polarization (DZ+P) basis set. The CCSD equilibrium geometries, dipole moments, and, via finite differences of gradients, CCSD harmonic vibrational frequencies and infrared intensities are reported. For H2O these results are compared to analogous CISD, CISDT, CISDTQ, and experimental results, and it is found that the CCSD predictions are most comparable to those of CISDTQ for this particular system. For the case of H2CO, the CCSD results are compared to CISD and experimental predictions. In general, the CCSD results and timings are encouraging.

Bibliography

Scheiner, A. C., Scuseria, G. E., Rice, J. E., Lee, T. J., & Schaefer, H. F. (1987). Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application. The Journal of Chemical Physics, 87(9), 5361â5373.

Authors 5

Andrew C. Scheiner (first)
Gustavo E. Scuseria (additional)
Julia E. Rice (additional)
Timothy J. Lee (additional)
Henry F. Schaefer (additional)

References 88 Referenced 385

10.1016/0166-1280(86)80070-7 / J. Mol. Struct. (Theochem) (1986)
{'key': '2024021005202250200_r2'}
{'key': '2024021005202250200_r3'}
10.1063/1.439707 / J. Chem. Phys. (1980)
10.1063/1.439708 / J. Chem. Phys. (1980)
10.1063/1.443617 / J. Chem. Phys. (1982)
10.1063/1.451253 / J. Chem. Phys. (1986)
10.1016/0009-2614(79)80117-7 / Chem. Phys. Lett. (1979)
10.1063/1.438494 / J. Chem. Phys. (1979)
10.1016/0009-2614(82)83410-6 / Chem. Phys. Lett. (1982)
10.1016/0301-0104(82)85131-8 / Chem. Phys. (1982)
10.1002/jcc.540050613 / J. Comput. Chem. (1984)
10.1063/1.447321 / J. Chem. Phys. (1984)
{'key': '2024021005202250200_r14'}
{'key': '2024021005202250200_r15', 'first-page': '225', 'volume': '13', 'year': '1979', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1979)
10.1063/1.448832 / J. Chem. Phys. (1985)
10.1063/1.445528 / J. Chem. Phys. (1983)
{'key': '2024021005202250200_r18', 'first-page': '245', 'volume': '18', 'year': '1984', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1984)
10.1063/1.447489 / J. Chem. Phys. (1984)
10.1016/0009-2614(85)80278-5 / Chem. Phys. Lett. (1985)
{'key': '2024021005202250200_r21'}
10.1063/1.451823 / J. Chem. Phys. (1986)
10.1016/0166-1280(83)85009-X / J. Mol. Struct. (Theochem) (1983)
10.1063/1.1727484 / J. Chem. Phys. (1966)
{'key': '2024021005202250200_r24a', 'first-page': '32', 'volume': '14', 'year': '1969', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1969)
10.1002/qua.560050402 / Int. J. Quantum Chem. (1971)
10.1103/PhysRevA.5.50 / Phys. Rev. A (1972)
10.1016/S0065-3276(08)60040-4 / Adv. Quantum Chem. (1975)
{'key': '2024021005202250200_r28'}
{'key': '2024021005202250200_r28a', 'first-page': '1971', 'volume': '69', 'year': '1977', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1977)
{'key': '2024021005202250200_r29', 'first-page': '403', 'volume': '11', 'year': '1977', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1977)
{'key': '2024021005202250200_r29a'}
{'key': '2024021005202250200_r30', 'first-page': '421', 'volume': '11', 'year': '1977', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1977)
10.1002/qua.560140503 / Int. J. Quantum Chem. (1978)
10.1002/qua.560140504 / Int. J. Quantum Chem. (1978)
{'key': '2024021005202250200_r33', 'first-page': '33', 'volume': '12', 'year': '1978', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1978)
10.1103/PhysRevA.17.805 / Phys. Rev. A (1978)
10.1002/qua.560150503 / Int. J. Quantum Chem. (1979)
10.1016/0009-2614(78)89113-1 / Chem. Phys. Lett. (1978)
10.1016/0009-2614(79)85172-6 / Chem. Phys. Lett. (1979)
10.1016/0301-0104(79)80153-6 / Chem. Phys. (1979)
10.1016/0009-2614(79)80379-6 / Chem. Phys. Lett. (1979)
{'key': '2024021005202250200_r37a', 'first-page': '3081', 'volume': '77', 'year': '1981', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1981)
10.1063/1.446736 / J. Chem. Phys. (1984)
10.1063/1.441643 / J. Chem. Phys. (1981)
10.1016/0009-2614(82)83368-X / Chem. Phys. Lett. (1982)
{'key': '2024021005202250200_r38b', 'first-page': '289', 'volume': '17', 'year': '1983', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1983)
10.1002/qua.560190203 / Int. J. Quantum Chem. (1981)
{'key': '2024021005202250200_r40'}
10.1146/annurev.pc.32.100181.002043 / Annu. Rev. Phys. Chem. (1981)
10.1063/1.443164 / J. Chem. Phys. (1982)
{'key': '2024021005202250200_r43'}
10.1002/qua.560230307 / Int. J. Quantum Chem. (1983)
10.1063/1.447591 / J. Chem. Phys. (1984)
{'key': '2024021005202250200_r46'}
10.1063/1.446574 / J. Chem. Phys. (1984)
10.1063/1.449067 / J. Chem. Phys. (1985)
10.1021/j100257a007 / J. Phys. Chem. (1985)
10.1016/0009-2614(85)80257-8 / Chem. Phys. Lett. (1985)
10.1063/1.449484 / J. Chem. Phys. (1985)
10.1063/1.451156 / J. Chem. Phys. (1986)
10.1002/qua.560290316 / Int. J. Quantum Chem. (1986)
10.1063/1.451164 / J. Chem. Phys. (1986)
10.1016/0009-2614(87)85169-2 / Chem. Phys. Lett. (1987)
10.1063/1.452289 / J. Chem. Phys. (1987)
10.1063/1.452039 / J. Chem. Phys. (1987)
{'key': '2024021005202250200_r58'}
{'key': '2024021005202250200_r59', 'first-page': '165', 'volume': '11', 'year': '1977', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1977)
{'key': '2024021005202250200_r60', 'first-page': '585', 'volume': '122', 'year': '1986', 'journal-title': 'Chem. Phys. Lett.'} / Chem. Phys. Lett. (1986)
10.1016/0009-2614(86)80461-4 / Chem. Phys. Lett. (1986)
10.1016/0009-2614(80)80396-4 / Chem. Phys. Lett. (1980)
10.1063/1.1670299 / J. Chem. Phys. (1968)
{'key': '2024021005202250200_r64'}
10.1016/0009-2614(87)85168-0 / Chem. Phys. Lett. (1987)
10.1080/00268977200102361 / Mol. Phys. (1972)
10.1080/00268977400102131 / Mol. Phys. (1974)
10.1063/1.445515 / J. Chem. Phys. (1983)
10.1063/1.1680328 / J. Chem. Phys. (1973)
{'key': '2024021005202250200_r70'}
10.1063/1.449931 / J. Chem. Phys. (1986)
10.1063/1.450389 / J. Chem. Phys. (1986)
{'key': '2024021005202250200_r73'}
10.1063/1.440381 / J. Chem. Phys. (1980)
10.1016/0022-2852(71)90094-4 / J. Mol. Spectrosc. (1971)
10.1016/0009-2614(73)89037-2 / Chem. Phys. Lett. (1973)
10.1063/1.443527 / J. Chem. Phys. (1982)
{'key': '2024021005202250200_r78'}
10.1016/0009-2614(87)80165-3 / Chem. Phys. Lett. (1987)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 9:10 a.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 1:51 a.m.)
Indexed	3 weeks, 6 days ago (Aug. 2, 2025, 12:10 a.m.)
Issued	37 years, 9 months ago (Nov. 1, 1987)
Published	37 years, 9 months ago (Nov. 1, 1987)
Published Print	37 years, 9 months ago (Nov. 1, 1987)

Funders 0

None

BibTeX

@article{Scheiner_1987, title={Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application}, volume={87}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.453655}, DOI={10.1063/1.453655}, number={9}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Scheiner, Andrew C. and Scuseria, Gustavo E. and Rice, Julia E. and Lee, Timothy J. and Schaefer, Henry F.}, year={1987}, month=nov, pages={5361–5373} }

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      "first-page": "19",
      "DOI": "10.1016/0009-2614(79)80117-7",
      "volume": "65",
      "year": "1979",
      "journal-title": "Chem. Phys. Lett."
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    {
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      "first-page": "1525",
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    {
      "key": "2024021005202250200_r11",
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      "DOI": "10.1016/0301-0104(82)85131-8",
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    {
      "key": "2024021005202250200_r12",
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    {
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      "first-page": "434",
      "DOI": "10.1063/1.447321",
      "volume": "81",
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      "journal-title": "J. Chem. Phys."
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      "key": "2024021005202250200_r14"
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    {
      "key": "2024021005202250200_r15",
      "first-page": "225",
      "volume": "13",
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      "journal-title": "Int. J. Quantum Chem. Symp."
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      "doi-asserted-by": "crossref",
      "first-page": "4379",
      "DOI": "10.1063/1.448832",
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      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021005202250200_r17",
      "doi-asserted-by": "crossref",
      "first-page": "334",
      "DOI": "10.1063/1.445528",
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      "key": "2024021005202250200_r18",
      "first-page": "245",
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      "journal-title": "J. Chem. Phys."
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    {
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      "DOI": "10.1016/0009-2614(85)80278-5",
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    {
      "key": "2024021005202250200_r21"
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      "key": "2024021005202250200_r22",
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      "key": "2024021005202250200_r23",
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      "key": "2024021005202250200_r24a",
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      "volume": "14",
      "year": "1969",
      "journal-title": "Adv. Chem. Phys."
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      "DOI": "10.1002/qua.560050402",
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    {
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      "key": "2024021005202250200_r28a",
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      "key": "2024021005202250200_r33",
      "first-page": "33",
      "volume": "12",
      "year": "1978",
      "journal-title": "Int. J. Quantum Chem. Symp."
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      "key": "2024021005202250200_r34",
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      "first-page": "805",
      "DOI": "10.1103/PhysRevA.17.805",
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      "year": "1978",
      "journal-title": "Phys. Rev. A"
    },
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      "first-page": "463",
      "DOI": "10.1002/qua.560150503",
      "volume": "15",
      "year": "1979",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "2024021005202250200_r35",
      "doi-asserted-by": "crossref",
      "first-page": "362",
      "DOI": "10.1016/0009-2614(78)89113-1",
      "volume": "59",
      "year": "1978",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024021005202250200_r35a",
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      "first-page": "329",
      "DOI": "10.1016/0009-2614(79)85172-6",
      "volume": "67",
      "year": "1979",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024021005202250200_r36",
      "doi-asserted-by": "crossref",
      "first-page": "325",
      "DOI": "10.1016/0301-0104(79)80153-6",
      "volume": "39",
      "year": "1979",
      "journal-title": "Chem. Phys."
    },
    {
      "key": "2024021005202250200_r37",
      "doi-asserted-by": "crossref",
      "first-page": "111",
      "DOI": "10.1016/0009-2614(79)80379-6",
      "volume": "66",
      "year": "1979",
      "journal-title": "Chem. Phys. Lett."
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      "key": "2024021005202250200_r37a",
      "first-page": "3081",
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      "year": "1981",
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      "DOI": "10.1016/0009-2614(82)83368-X",
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      "journal-title": "Chem. Phys. Lett."
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    {
      "key": "2024021005202250200_r38b",
      "first-page": "289",
      "volume": "17",
      "year": "1983",
      "journal-title": "Int. J. Quantum Chem. Symp."
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    {
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      "first-page": "1910",
      "DOI": "10.1063/1.443164",
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      "key": "2024021005202250200_r43"
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    {
      "key": "2024021005202250200_r45",
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    {
      "key": "2024021005202250200_r46"
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    {
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      "DOI": "10.1063/1.452289",
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    {
      "key": "2024021005202250200_r59",
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    {
      "key": "2024021005202250200_r60",
      "first-page": "585",
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      "year": "1986",
      "journal-title": "Chem. Phys. Lett."
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      "DOI": "10.1016/0009-2614(86)80461-4",
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      "journal-title": "Chem. Phys. Lett."
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    {
      "key": "2024021005202250200_r62",
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      "first-page": "393",
      "DOI": "10.1016/0009-2614(80)80396-4",
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      "year": "1980",
      "journal-title": "Chem. Phys. Lett."
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    {
      "key": "2024021005202250200_r63",
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      "first-page": "1719",
      "DOI": "10.1063/1.1670299",
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    {
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      "first-page": "1265",
      "DOI": "10.1080/00268977200102361",
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