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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
23/2009

The tensor product approximation to single-electron systems

Sambasiva Rao Chinnamsetty, Wolfgang Hackbusch and Heinz-Jürgen Flad

Abstract

We study tensor product (TP) approximation to single-electron systems. TP approximation with optimal tensor rank provides an interesting alternative to the traditional Gaussian-type orbital (GTO) basis functions in electronic structure calculations. The GTO basis functions are commonly used in electronic structure calculations for approximation of single-electron wavefunctions the so-called orbitals. The rigorous results are available only for the H atom concerning the approximation errors of GTO bases for the solution of the single-electron Schr\"odinger equation. In this paper, we apply the TP approximation to the H atom for computation of the kinetic energy and potential energy. We then apply the TP approximation to the single-electron systems with several nuclei and study the accuracy of the approximation. We also study the sparse wavelet representation of univariate components of the TP approximation which paves the way for the fast computation of various integrals involving the orbitals and orbital products in electronic structure methods.

Received:
Apr 30, 2009
Published:
Apr 30, 2009
Keywords:
Tensor product approximation, Tensor rank, Electronic structure calculations, Single-electron Schrödinger equation, Gaussian-type orbitals, Kinetic energy, Potential energy

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Preprint
2009 Repository Open Access
Sambasiva Rao Chinnamsetty, Wolfgang Hackbusch and Heinz-Jürgen Flad

The tensor product approximation to single-electron systems