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MiS Preprint
41/2007

Tensor product approximation with optimal rank in quantum chemistry

Sambasiva Rao Chinnamsetty, Mike Espig, Boris N. Khoromskij, Wolfgang Hackbusch and Heinz-Jürgen Flad

Abstract

Tensor product decompositions with optimal rank provide an interesting alternative to traditional Gaussian-type basis functions in electronic structure calculations. We discuss various applications for a new compression algorithm, based on the Newton method, which provides for a given tensor the optimal tensor product or so-called best separable approximation for fixed Kronecker rank. In combination with a stable quadrature scheme for the Coulomb interaction, tensor product formats enable an efficient evaluation of Coulomb integrals.

This is demonstrated by means of best separable approximations for the electron density and Hartree potential of small molecules, where individual components of the tensor product can be efficiently represented in a wavelet basis. We present a fairly detailed numerical analysis, which provides the basis for further improvements of this novel approach.

Our results suggest a broad range of applications within density fitting schemes, which have been recently successfully applied in quantum chemistry.

Received:
Apr 18, 2007
Published:
Apr 18, 2007
Keywords:
Tensor product approximation, quantum chemistry

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inJournal
2007 Repository Open Access
Sambasiva Rao Chinnamsetty, Mike Espig, Boris N. Khoromskij, Wolfgang Hackbusch and Heinz-Jürgen Flad

Tensor product approximation with optimal rank in quantum chemistry

In: The journal of chemical physics, 127 (2007) 8, p. 084110