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Title: Fractional charge and spin errors in self-consistent Green’s function theory

Abstract

We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Here, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.

Authors:
 [1];  [1];  [1]
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  1. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
Research Org.:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1843751
Alternate Identifier(s):
OSTI ID: 1228202
Grant/Contract Number:  
SC0010381; ER16391
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 19; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Hybrid density functional calculations; Self consistent field methods; Perturbation theory; Random phase approximation; Becke; Three-parameter; Lee-Yang-Parr; Dyson-Schwinger equation; Free electron model; Correlation energy; Density functional theory

Citation Formats

Phillips, Jordan J., Kananenka, Alexei A., and Zgid, Dominika. Fractional charge and spin errors in self-consistent Green’s function theory. United States: N. p., 2015. Web. doi:10.1063/1.4921259.
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Phillips, Jordan J., Kananenka, Alexei A., & Zgid, Dominika. Fractional charge and spin errors in self-consistent Green’s function theory. United States. https://doi.org/10.1063/1.4921259
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Phillips, Jordan J., Kananenka, Alexei A., and Zgid, Dominika. Tue . "Fractional charge and spin errors in self-consistent Green’s function theory". United States. https://doi.org/10.1063/1.4921259. https://www.osti.gov/servlets/purl/1843751.
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@article{osti_1843751,
title = {Fractional charge and spin errors in self-consistent Green’s function theory},
author = {Phillips, Jordan J. and Kananenka, Alexei A. and Zgid, Dominika},
abstractNote = {We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Here, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.},
doi = {10.1063/1.4921259},
journal = {Journal of Chemical Physics},
number = 19,
volume = 142,
place = {United States},
year = {Tue May 19 00:00:00 EDT 2015},
month = {Tue May 19 00:00:00 EDT 2015}
}
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https://doi.org/10.1063/1.4921259
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