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

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Abstract

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.

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Acknowledgments

The research for this paper has been enabled by the Alexander von Humboldt Foundation, whose support for the long term visit of H. Chen at Technische Universität Berlin is gratefully acknowledged.

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Authors and Affiliations

  1. Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 , Aachen, Germany

    Markus Bachmayr

  2. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 , Berlin, Germany

    Huajie Chen & Reinhold Schneider

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  1. Markus Bachmayr
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  2. Huajie Chen
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Correspondence to Reinhold Schneider.

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Bachmayr, M., Chen, H. & Schneider, R. Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry. Numer. Math. 128, 137–165 (2014). https://doi.org/10.1007/s00211-014-0605-5

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