U.S. Department of Energy Office of Scientific and Technical Information
Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians
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.
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." Journal of Chemical Physics, vol. 152, no. 9, Mar. 2020. https://doi.org/10.1063/1.5143318
Pokhilko, Pavel, & Krylov, Anna I. (2020). Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians. Journal of Chemical Physics, 152(9). https://doi.org/10.1063/1.5143318
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," Journal of Chemical Physics 152, no. 9 (2020), https://doi.org/10.1063/1.5143318
@article{osti_1602647,
author = {Pokhilko, Pavel and Krylov, Anna I.},
title = {Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians},
annote = {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},
url = {https://www.osti.gov/biblio/1602647},
journal = {Journal of Chemical Physics},
issn = {ISSN 0021-9606},
number = {9},
volume = {152},
place = {United States},
publisher = {American Institute of Physics (AIP)},
year = {2020},
month = {03}}
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 214, Issue 1119, p. 451-465https://doi.org/10.1098/rspa.1952.0181
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 276, Issue 1365, p. 238-257https://doi.org/10.1098/rspa.1963.0204