| Issue |
ESAIM: M2AN
Volume 54, Number 1, January-February 2020
|
|
|---|---|---|
| Page(s) | 25 - 58 | |
| DOI | https://doi.org/10.1051/m2an/2019017 | |
| Published online | 14 January 2020 | |
Projector augmented-wave method: an analysis in a one-dimensional setting
Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS, 75205 Paris, France
* Corresponding author: dupuy@math.univ-paris-diderot.fr
Received:
13
December
2017
Accepted:
18
February
2019
In this article, a numerical analysis of the projector augmented-wave (PAW) method is presented, restricted to the case of dimension one with Dirac potentials modeling the nuclei in a periodic setting. The PAW method is widely used in electronic ab initio calculations, in conjunction with pseudopotentials. It consists in replacing the original electronic Hamiltonian H by a pseudo-Hamiltonian HPAW via the PAW transformation acting in balls around each nuclei. Formally, the new eigenvalue problem has the same eigenvalues as H and smoother eigenfunctions. In practice, the pseudo-Hamiltonian HPAW has to be truncated, introducing an error that is rarely analyzed. In this paper, error estimates on the lowest PAW eigenvalue are proved for the one-dimensional periodic Schrödinger operator with double Dirac potentials.
Mathematics Subject Classification: 65N15 / 65G99 / 35P15
Key words: Eigenvalue problem / error analysis / electronic structure calculations / projector augmented-wave method
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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