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Projector augmented-wave method: an analysis in a one-dimensional setting
- Publication Year :
- 2017
-
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 $H$ by a pseudo-Hamiltonian $H^{PAW}$ 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 $H^{PAW}$ 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 Schr\"odinger operator with double Dirac potentials.<br />Comment: 31 pages, 4 figures
- Subjects :
- Mathematics - Numerical Analysis
Condensed Matter - Materials Science
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1712.04685
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1051/m2an/2019017