DOI: 10.1063/1.456070. Analytic energy derivatives in many-body methods. II. Second derivatives

Analytic energy derivatives in many-body methods. II. Second derivatives

10.1063/1.456070

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Second derivatives of the energy correspond to second-order response properties and molecular force constants. Currently, both the theory and application of analytic second derivatives in many-body methods are limited to second-order perturbation theory. The general theory of analytic second derivatives for the coupled-cluster (CC) model is presented. The analytic expressions for the second derivative of the energy are given in terms of the response (or ‘‘relaxed’’) density, discussed in part I, and the first-derivative t amplitudes for efficient evaluation. Explicit expressions for the second derivatives of the coupled-cluster singles, doubles, and linearized triples model (CCSDT-1) are presented. Analytic derivatives for the finite-order MBPT(3) and MBPT(4) models are derived as special cases of the theory.

Bibliography

Salter, E. A., & Bartlett, R. J. (1989). Analytic energy derivatives in many-body methods. II. Second derivatives. The Journal of Chemical Physics, 90(3), 1767â1773.

Authors 2

E. A. Salter (first)
Rodney J. Bartlett (additional)

References 49 Referenced 70

{'key': '2024021007163352800_r1', 'first-page': '225', 'volume': '13', 'year': '1979', 'journal-title': 'Int. J. Quantum Chem. Symp.'} / Int. J. Quantum Chem. Symp. (1979)
10.1063/1.445528 / J. Chem. Phys. (1983)
10.1063/1.445835 / J. Chem. Phys. (1983)
10.1063/1.447061 / J. Chem. Phys. (1984)
10.1016/0009-2614(83)80648-4 / Chem. Phys. Lett. (1983)
{'key': '2024021007163352800_r4'}
10.1016/0009-2614(86)87048-8 / Chem. Phys. Lett. (1986)
{'key': '2024021007163352800_r4b'}
10.1063/1.450259 / J. Chem. Phys. (1986)
10.1063/1.451164 / J. Chem. Phys. (1986)
10.1021/ja00219a016 / J. Am. Chem. Soc. (1988)
10.1016/0009-2614(87)87076-8 / Chem. Phys. Lett. (1987)
{'key': '2024021007163352800_r6', 'first-page': '421', 'volume': '1', 'year': '1958', 'journal-title': 'Nucl. Phys.'} / Nucl. Phys. (1958)
10.1016/0029-5582(60)90140-1 / Nucl. Phys. (1960)
10.1063/1.1727484 / J. Chem. Phys. (1966)
{'key': '2024021007163352800_r7a', 'first-page': '35', 'volume': '14', 'year': '1969', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1969)
10.1103/PhysRevA.5.50 / Phys. Rev. A (1972)
{'key': '2024021007163352800_r7c'}
{'key': '2024021007163352800_r7d', 'first-page': '35', 'volume': '14', 'year': '1969', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1969)
10.1002/qua.560140504 / Int. J. Quantum Chem. (1978)
10.1088/0031-8949/21/3-4/007 / Phys. Scripta. (1980)
10.1002/qua.560140503 / Int. J. Quantum Chem. (1978)
10.1063/1.442131 / J. Chem. Phys. (1981)
10.1063/1.443164 / J. Chem. Phys. (1982)
10.1063/1.438069 / J. Chem. Phys. (1979)
10.1146/annurev.pc.32.100181.002043 / Annu. Rev. Phys. Chem. (1981)
{'key': '2024021007163352800_r12a'}
10.1063/1.447591 / J. Chem. Phys. (1984)
10.1063/1.452353 / J. Chem. Phys. (1987)
10.1063/1.455742 / J. Chem. Phys. (1988)
10.1103/PhysRevA.10.1927 / Phys. Rev. A (1974)
10.1016/0009-2614(77)80161-9 / Chem. Phys. Lett. (1977)
{'key': '2024021007163352800_r16a', 'first-page': '157', 'volume': '59', 'year': '1978', 'journal-title': 'Chem. Phys. Lett.'} / Chem. Phys. Lett. (1978)
10.1016/0009-2614(80)80465-9 / Chem. Phys. Lett. (1980)
10.1063/1.439657 / J. Chem. Phys. (1980)
10.1016/0009-2614(80)80728-7 / Chem. Phys. Lett. (1980)
10.1016/0009-2614(83)80204-8 / Chem. Phys. Lett. (1983)
10.1007/BF00557930 / Theor. Chem. Acta (1983)
{'key': '2024021007163352800_r18'}
10.1063/1.451823 / J. Chem. Phys. (1986)
10.1016/0009-2614(87)80093-3 / Chem. Phys. Lett. (1987)
{'key': '2024021007163352800_r20a'}
10.1063/1.453655 / J. Chem. Phys. (1987)
{'key': '2024021007163352800_r22'}
{'key': '2024021007163352800_r22a', 'first-page': '29', 'volume': '150', 'year': '1988', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1988)
See AIP document no. PAPS JCPSA-90-1752-43 for 43 pages of detailed coupled-cluster first and second derivative expressions. Order by PAPS number and journal reference from American Institute of Physics, Physics Auxiliary Publication Service, 335 East 45th Street, New York, NY 10017. The price is $1.50 for each microfiche (98 pages) or $5.00 for photocopies of up to 30 pages, and $0.15 for each additional page over 30 pages. Airmail additional. Make checks payable to the American Institute of Physics.
10.1063/1.447550 / J. Chem. Phys. (1984)
10.1016/0009-2614(85)80278-5 / Chem. Phys. Lett. (1985)
10.1063/1.453520 / J. Chem. Phys. (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, 4:11 a.m.)
Indexed	2 months, 4 weeks ago (June 2, 2025, 8:25 a.m.)
Issued	36 years, 6 months ago (Feb. 1, 1989)
Published	36 years, 6 months ago (Feb. 1, 1989)
Published Print	36 years, 6 months ago (Feb. 1, 1989)

Funders 0

None

BibTeX

@article{Salter_1989, title={Analytic energy derivatives in many-body methods. II. Second derivatives}, volume={90}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.456070}, DOI={10.1063/1.456070}, number={3}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Salter, E. A. and Bartlett, Rodney J.}, year={1989}, month=feb, pages={1767–1773} }

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