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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 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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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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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).

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Mathematics Subject Classification

  • 41A25
  • 65N35
  • 65Z05