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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2019017
Keywords: Eigenvalue problem, error analysis, electronic structure calculations, projector augmented-wave method
@article{M2AN_2020__54_1_25_0,
author = {Dupuy, Mi-Song},
title = {Projector augmented-wave method: an analysis in a one-dimensional setting},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {25--58},
year = {2020},
publisher = {EDP Sciences},
volume = {54},
number = {1},
doi = {10.1051/m2an/2019017},
mrnumber = {4051841},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2019017/}
}
TY - JOUR AU - Dupuy, Mi-Song TI - Projector augmented-wave method: an analysis in a one-dimensional setting JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 25 EP - 58 VL - 54 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2019017/ DO - 10.1051/m2an/2019017 LA - en ID - M2AN_2020__54_1_25_0 ER -
%0 Journal Article %A Dupuy, Mi-Song %T Projector augmented-wave method: an analysis in a one-dimensional setting %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 25-58 %V 54 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2019017/ %R 10.1051/m2an/2019017 %G en %F M2AN_2020__54_1_25_0
Dupuy, Mi-Song. Projector augmented-wave method: an analysis in a one-dimensional setting. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 1, pp. 25-58. doi: 10.1051/m2an/2019017
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