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:
-
- 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. 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. 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 = {Tue Mar 03 00:00:00 EST 2020},
month = {Tue Mar 03 00:00:00 EST 2020}
}
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