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Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations

Journal Article · · Physical Review A
 [1];  [2]
  1. Rice Univ., Houston, TX (United States); DOE/OSTI
  2. Rice Univ., Houston, TX (United States)
+ Show Author Affiliations
The past several years have seen renewed interest in the use of symmetry-projected Hartree-Fock for the description of strong correlations. Unfortunately, these symmetry-projected mean-field methods do not adequately account for dynamic correlation. Presumably, this shortcoming could be addressed if one could combine symmetry-projected Hartree-Fock with a many-body method such as coupled-cluster theory, but this is by no means straightforward because the two techniques are formulated in very different ways. However, we have recently shown that the singlet S2-projected unrestricted Hartree-Fock wave function can in fact be written in a coupled-cluster-like wave function. That is, the spin-projected unrestricted Hartree-Fock wave function can be written as a polynomial of a double-excitation operator acting on some closed-shell reference determinant. Here, we extend this result and show that the spin-projected generalized Hartree-Fock wave function (which has both S2 and Sz projection) is likewise a polynomial of low-order excitation operators acting on a closed-shell determinant and provide a closed-form expression for the resulting polynomial coefficients. The spin projection of the generalized Hartree-Fock wave function introduces connected triple and quadruple excitations which are absent when spin-projecting an unrestricted Hartree-Fock determinant. We include a few preliminary applications of the combination of this spin-projected Hartree-Fock and coupled-cluster theory to the Hubbard Hamiltonian and comment on generalizations of the methodology. Results here are not for production level, but a similarity-transformed theory that combines the two offers the promise of being accurate for both weak and strong correlation, and may offer significant improvements in the intermediate correlation regime where neither projected Hartree-Fock nor coupled cluster is particularly accurate.
Research Organization:
Rice Univ., Houston, TX (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
SC0001474
OSTI ID:
1535748
Alternate ID(s):
OSTI ID: 1374068
Journal Information:
Physical Review A, Journal Name: Physical Review A Journal Issue: 2 Vol. 96; ISSN 2469-9926
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (6)

Projected coupled cluster theory journal August 2017
Open-shell coupled-cluster valence-bond theory augmented with an independent amplitude approximation for three-pair correlations: Application to a model oxygen-evolving complex and single molecular magnet journal December 2018
Projected coupled cluster theory: Optimization of cluster amplitudes in the presence of symmetry projection journal October 2018
Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations journal April 2019
Unrestricted treatment for the direct variational determination of the two-electron reduced density matrix for doubly occupied-configuration-interaction wave functions journal April 2019
Open-Shell Coupled-Cluster Valence-Bond Theory Augmented with an Independent Amplitude Approximation for Three-Pair Correlations: Application to a Model Oxygen-Evolving Complex and Single Molecular Magnet text January 2018

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