Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry

Atomic-like basis functions provide a natural, physically motivated description of electronic states, among which Gaussian-type orbitals are the most widely used basis functions in molecular simulations. This paper aims at developing a systematic analysis of numerical approximations based on linear...

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Bibliographic Details
Published inNumerische Mathematik Vol. 128; no. 1; pp. 137 - 165
Main Authors Bachmayr, Markus, Chen, Huajie, Schneider, Reinhold
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2014
Subjects
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
65Z05
41A25
65N35
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Summary:Atomic-like basis functions provide a natural, physically motivated description of electronic states, among which Gaussian-type orbitals are the most widely used basis functions in molecular simulations. This paper aims at developing a systematic analysis of numerical approximations based on linear combinations of Gaussian-type orbitals. We derive a priori error estimates for Hermite-type Gaussian bases as well as for even-tempered Gaussian bases. Numerical results are presented to support the theory.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-014-0605-5