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Title: Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians

Abstract

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’ forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians can be extracted directly from the so-obtained effective Hamiltonians. By establishing a quantitative connection between many-body states and simple models, the approach facilitates the analysis of the correlated wave functions. We propose a simple diagnostic for assessing the validity of the model space choice based on the overlaps between the target- and model-space states. Finally, artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Univ. of Southern California, Los Angeles, CA (United States)
Publication Date:
Research Org.:
Univ. of Southern California, Los Angeles, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1602647
Alternate Identifier(s):
OSTI ID: 1602591
Grant/Contract Number:  
SC0018910
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 152; Journal Issue: 9; Related Information: Supplementary information is available at https://aip.scitation.org/doi/suppl/10.1063/1.5143318; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EOM-CC; Hubbard Hamiltonian; Heisenberg Hamiltonian

Citation Formats

Pokhilko, Pavel, and Krylov, Anna I. Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians. United States: N. p., 2020. Web. doi:10.1063/1.5143318.
Pokhilko, Pavel, & Krylov, Anna I. Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians. United States. doi:https://doi.org/10.1063/1.5143318
Pokhilko, Pavel, and Krylov, Anna I. Tue . "Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians". United States. doi:https://doi.org/10.1063/1.5143318. https://www.osti.gov/servlets/purl/1602647.
@article{osti_1602647,
title = {Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians},
author = {Pokhilko, Pavel and Krylov, Anna I.},
abstractNote = {Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’ forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians can be extracted directly from the so-obtained effective Hamiltonians. By establishing a quantitative connection between many-body states and simple models, the approach facilitates the analysis of the correlated wave functions. We propose a simple diagnostic for assessing the validity of the model space choice based on the overlaps between the target- and model-space states. Finally, artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.},
doi = {10.1063/1.5143318},
journal = {Journal of Chemical Physics},
number = 9,
volume = 152,
place = {United States},
year = {2020},
month = {3}
}

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