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Title: Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3];  [3]; ORCiD logo [3];  [3]; ORCiD logo [4];  [2]
  1. Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
  2. Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA, Department of Chemistry, Rice University, Houston, Texas 77005, USA
  3. Department of Chemistry, Rice University, Houston, Texas 77005, USA
  4. Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Spain
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1361758
Grant/Contract Number:
FG02-09ER16053
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 5; Related Information: CHORUS Timestamp: 2018-02-15 02:59:39; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

Citation Formats

Wahlen-Strothman, Jacob M., Henderson, Thomas M., Hermes, Matthew R., Degroote, Matthias, Qiu, Yiheng, Zhao, Jinmo, Dukelsky, Jorge, and Scuseria, Gustavo E.. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian. United States: N. p., 2017. Web. doi:10.1063/1.4974989.
Wahlen-Strothman, Jacob M., Henderson, Thomas M., Hermes, Matthew R., Degroote, Matthias, Qiu, Yiheng, Zhao, Jinmo, Dukelsky, Jorge, & Scuseria, Gustavo E.. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian. United States. doi:10.1063/1.4974989.
Wahlen-Strothman, Jacob M., Henderson, Thomas M., Hermes, Matthew R., Degroote, Matthias, Qiu, Yiheng, Zhao, Jinmo, Dukelsky, Jorge, and Scuseria, Gustavo E.. Tue . "Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian". United States. doi:10.1063/1.4974989.
@article{osti_1361758,
title = {Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian},
author = {Wahlen-Strothman, Jacob M. and Henderson, Thomas M. and Hermes, Matthew R. and Degroote, Matthias and Qiu, Yiheng and Zhao, Jinmo and Dukelsky, Jorge and Scuseria, Gustavo E.},
abstractNote = {},
doi = {10.1063/1.4974989},
journal = {Journal of Chemical Physics},
number = 5,
volume = 146,
place = {United States},
year = {Tue Feb 07 00:00:00 EST 2017},
month = {Tue Feb 07 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1063/1.4974989

Citation Metrics:
Cited by: 8works
Citation information provided by
Web of Science

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  • Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems, but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories.more » We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.« less
  • Cited by 2
  • No abstract prepared.
  • We present a general perturbative method for correcting a singles and doubles coupled-cluster energy. The coupled-cluster wave function is used to define a similarity-transformed Hamiltonian, which is partitioned into a zeroth-order part that the reference problem solves exactly plus a first-order perturbation. Standard perturbation theory through second-order provides the leading correction. Applied to the valence optimized doubles (VOD) approximation to the full-valence complete active space self-consistent field method, the second-order correction, which we call (2), captures dynamical correlation effects through external single, double, and semi-internal triple and quadruple substitutions. A factorization approximation reduces the cost of the quadruple substitutions tomore » only sixth order in the size of the molecule. A series of numerical tests are presented showing that VOD(2) is stable and well-behaved provided that the VOD reference is also stable. The second-order correction is also general to standard unwindowed coupled-cluster energies such as the coupled-cluster singles and doubles (CCSD) method itself, and the equations presented here fully define the corresponding CCSD(2) energy. (c) 2000 American Institute of Physics.« less
  • We analyze the ability of a restricted variation after projection method to achieve the full variation after projection solution in a pairing Hamiltonian. The study of the projected potential energy surfaces defined along the fluctuations of the particle number ({delta}N){sup 2} and ({delta}N){sup 4} allows the enlargement of the variational space to take into account more correlations within the projection after the variation framework. The results show the equivalence of the full variational projected solution to a restricted projected solution with an educated choice of the restricted variational space. Finally, we show that the Lipkin-Nogami approach can be derived, undermore » certain conditions, in an variational context and that the projected Lipkin-Nogami approach represents an approximation to a restricted variation after projection method with the ({delta}N){sup 2} as degree of freedom.« less