# 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. Furthermore, 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:

- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (United States)

- Publication Date:

- OSTI Identifier:
- 22415790

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 19; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CORRELATIONS; DENSITY FUNCTIONAL METHOD; DIAGRAMS; ELECTRONS; ERRORS; GREEN FUNCTION; IMPLEMENTATION; MATHEMATICAL SOLUTIONS; RANDOM PHASE APPROXIMATION; SPIN

### Citation Formats

```
Phillips, Jordan J., E-mail: philljj@umich.edu, 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.

```
Phillips, Jordan J., E-mail: philljj@umich.edu, Kananenka, Alexei A., & Zgid, Dominika.
```*Fractional charge and spin errors in self-consistent Green’s function theory*. United States. doi:10.1063/1.4921259.

```
Phillips, Jordan J., E-mail: philljj@umich.edu, Kananenka, Alexei A., and Zgid, Dominika. Thu .
"Fractional charge and spin errors in self-consistent Green’s function theory". United States. doi:10.1063/1.4921259.
```

```
@article{osti_22415790,
```

title = {Fractional charge and spin errors in self-consistent Green’s function theory},

author = {Phillips, Jordan J., E-mail: philljj@umich.edu 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. Furthermore, 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},

issn = {0021-9606},

number = 19,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}