Tensor product approximation with optimal rank in quantum chemistry

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

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Submission date: 18. Apr. 2007
Pages: 27
published in: The journal of chemical physics, 127 (2007) 8, art-no. 084110 
DOI number (of the published article): 10.1063/1.2761871
Bibtex
Keywords and phrases: Tensor product approximation, quantum chemistry
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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.