The tensor product approximation to single-electron systems
Sambasiva Rao Chinnamsetty, Wolfgang Hackbusch, and Heinz-Jürgen Flad
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Submission date: 30. Apr. 2009
paper prepared for: J. Chem . Phys.
Keywords and phrases: Tensor product approximation, Tensor rank, Electronic structure calculations, Single-electron Schr\"odinger equation, Gaussian-type orbitals, Kinetic energy, Potential energy
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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 Schrödinger 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.