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

Abstract

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

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
  1. Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
  2. Northwestern Univ., Evanston, IL (United States). Dept. of Chemistry
  3. Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy, and Dept. of Chemistry
Publication Date:
Research Org.:
Rice Univ., Houston, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1512944
Alternate Identifier(s):
OSTI ID: 1417782
Grant/Contract Number:  
SC0001474; FG02-09ER16053
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 4; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Harsha, Gaurav, Shiozaki, Toru, and Scuseria, Gustavo E. On the difference between variational and unitary coupled cluster theories. United States: N. p., 2018. Web. doi:10.1063/1.5011033.
Harsha, Gaurav, Shiozaki, Toru, & Scuseria, Gustavo E. On the difference between variational and unitary coupled cluster theories. United States. https://doi.org/10.1063/1.5011033
Harsha, Gaurav, Shiozaki, Toru, and Scuseria, Gustavo E. Sun . "On the difference between variational and unitary coupled cluster theories". United States. https://doi.org/10.1063/1.5011033. https://www.osti.gov/servlets/purl/1512944.
@article{osti_1512944,
title = {On the difference between variational and unitary coupled cluster theories},
author = {Harsha, Gaurav and Shiozaki, Toru and Scuseria, Gustavo E.},
abstractNote = {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},
doi = {10.1063/1.5011033},
journal = {Journal of Chemical Physics},
number = 4,
volume = 148,
place = {United States},
year = {Sun Jan 28 00:00:00 EST 2018},
month = {Sun Jan 28 00:00:00 EST 2018}
}

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Free Publicly Available Full Text
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Cited by: 57 works
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Figures / Tables:

FIG. 1 FIG. 1: Typical configurations with even and odd parity for the N = 8 site Lipkin model. (a) Even parity. (b) Odd parity.

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