Projector augmented-wave method: an analysis in a one-dimensional setting - Sorbonne Université
Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2020

Projector augmented-wave method: an analysis in a one-dimensional setting

Mi-Song Dupuy

Abstract

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 by a pseudo-Hamiltonian PAW via the PAW transformation acting in balls around each nuclei. Formally, the new eigenvalue problem has the same eigenvalues as and smoother eigenfunctions. In practice, the pseudo-Hamiltonian PAW 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.
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Dates and versions

hal-02457937 , version 1 (28-01-2020)

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Mi-Song Dupuy. Projector augmented-wave method: an analysis in a one-dimensional setting. ESAIM: Mathematical Modelling and Numerical Analysis, 2020, 54 (1), pp.25-58. ⟨10.1051/m2an/2019017⟩. ⟨hal-02457937⟩
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