# Self-interaction in Green's-function theory of the hydrogen atom

## Abstract

Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation theory (MBPT) in Hedin's GW approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the GW self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for GW and show that the self-interaction part of the GW self-energy, while nonzero, is small. The effect of calculating the GW self-energy from exact wave functions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating.

- Authors:

- Department of Physics, University of York, Heslington, York YO10 5DD (United Kingdom)
- Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovicova 3, 841 04 Bratislava (Slovakia)
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin (Germany)

- Publication Date:

- OSTI Identifier:
- 20982302

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032505; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BENCHMARKS; COMPUTER CALCULATIONS; CORRELATIONS; DENSITY; DENSITY FUNCTIONAL METHOD; EIGENFUNCTIONS; EIGENVALUES; ELECTRONIC STRUCTURE; ELECTRONS; EXCITATION; GREEN FUNCTION; HARTREE-FOCK METHOD; HYDROGEN; INTERACTIONS; MANY-BODY PROBLEM; PERTURBATION THEORY; SELF-ENERGY; WAVE FUNCTIONS

### Citation Formats

```
Nelson, W., Bokes, P., Rinke, Patrick, and Godby, R. W.
```*Self-interaction in Green's-function theory of the hydrogen atom*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032505.

```
Nelson, W., Bokes, P., Rinke, Patrick, & Godby, R. W.
```*Self-interaction in Green's-function theory of the hydrogen atom*. United States. doi:10.1103/PHYSREVA.75.032505.

```
Nelson, W., Bokes, P., Rinke, Patrick, and Godby, R. W. Thu .
"Self-interaction in Green's-function theory of the hydrogen atom". United States.
doi:10.1103/PHYSREVA.75.032505.
```

```
@article{osti_20982302,
```

title = {Self-interaction in Green's-function theory of the hydrogen atom},

author = {Nelson, W. and Bokes, P. and Rinke, Patrick and Godby, R. W.},

abstractNote = {Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation theory (MBPT) in Hedin's GW approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the GW self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for GW and show that the self-interaction part of the GW self-energy, while nonzero, is small. The effect of calculating the GW self-energy from exact wave functions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating.},

doi = {10.1103/PHYSREVA.75.032505},

journal = {Physical Review. A},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}