On the difference between variational and unitary coupled cluster theories

Harsha, Gaurav; Shiozaki, Toru; Scuseria, Gustavo E.

doi:10.1063/1.5011033

Title: On the difference between variational and unitary coupled cluster theories

Journal Article · 28 January 2018 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5011033 · OSTI ID:1512944

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Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
Northwestern Univ., Evanston, IL (United States). Dept. of Chemistry
Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy, and Dept. of Chemistry

There have been assertions in the literature that the variational and unitary forms of coupled cluster theory lead to the same energy functional. Numerical evidence from previous authors was inconsistent with this claim, yet the small energy differences found between the two methods and the relatively large number of variational parameters precluded an unequivocal conclusion. Using the Lipkin Hamiltonian, we here present conclusive numerical evidence that the two theories yield different energies. The ambiguities arising from the size of the cluster parameter space are absent in the Lipkin model, particularly when truncating to double excitations. We show that in the symmetry adapted basis under strong correlation, the differences between the variational and unitary models are large, whereas they yield quite similar energies in the weakly correlated regime previously explored. We also provide a qualitative argument rationalizing why these two models cannot be the same. Additionally, we study a generalized non-unitary and non-hermitian variant that contains excitation, de-excitation, and mixed operators with different amplitudes and show that it works best when compared to the traditional, variational, unitary, and extended forms of coupled cluster doubles theories

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Research Organization:: Rice Univ., Houston, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0001474; FG02-09ER16053

OSTI ID:: 1512944

Alternate ID(s):: OSTI ID: 1417782

Journal Information:: Journal of Chemical Physics, Vol. 148, Issue 4; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 59 works

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