## Abstract

Excited-state calculations, notably for quasiparticle band structures, are nowadays routinely performed within the GW approximation for the electronic self-energy. Nevertheless, certain numerical approximations and simplifications are still employed in practice to make the computations feasible. An important aspect for periodic systems is the proper treatment of the singularity of the screened Coulomb interaction in reciprocal space, which results from the slow 1/r decay in real space. This must be done without introducing artificial interactions between the quasiparticles and their periodic images in repeated cells, which occur when integrals of the screened Coulomb interaction are discretised in reciprocal space. An adequate treatment of both aspects is crucial for a numerically stable computation of the self-energy. In this article we build on existing schemes for isotropic screening and present an extension for anisotropic systems. We also show how the contributions to the dielectric function arising from the non-local part of the pseudopotentials can be computed efficiently. These improvements are crucial for obtaining a fast convergence with respect to the number of points used for the Brillouin zone integration and prove to be essential to make GW calculations for strongly anisotropic systems, such as slabs or multilayers, efficient. (C) 2006 Elsevier B.V. All rights reserved.

Original language | English |
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Pages (from-to) | 1-13 |

Number of pages | 12 |

Journal | Computer Physics Communications |

Volume | 176 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2007 |

### Bibliographical note

© 2006 Elsevier B.V. This is an author produced version of a paper published in Computer Physics Communications and uploaded in accordance with the publisher's self archiving policy.## Keywords

- GW approximation
- anisotropic screening
- Coulomb singularity
- dielectric function
- ELECTRONIC-STRUCTURE CALCULATIONS
- BAND-STRUCTURE CALCULATIONS
- DENSITY-FUNCTIONAL THEORY
- AB-INITIO CALCULATION
- SELF-ENERGY
- SEMICONDUCTORS
- EXCHANGE
- APPROXIMATION
- CONSTANT
- SOLIDS