Efficient multi-scale computation of products of orbitals in electronic structure calculations

Sambasiva Rao Chinnamsetty, Wolfgang Hackbusch, and Heinz-Jürgen Flad

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Submission date: 03. Dec. 2009
Pages: 15
published in: Computing and visualization in science, 13 (2010) 8, p. 397-408 
DOI number (of the published article): 10.1007/s00791-011-0153-9
Bibtex
Keywords and phrases: Standard approach, Non-standard approach, Daubechies wavelet bases, Tensor product approximation, Electronic structure calculations, Products of orbitals, Two-electron integrals
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Abstract:
The computation of two-electron integrals in electronic structure calculations is a major bottleneck in Hartree-Fock, density functional theory and post-Hartree-Fock methods. For large systems, one has to compute a huge number of two-electron integrals for these methods which leads to very high computational costs. The adaptive computation of products of orbitals in wavelet bases provides an important step towards efficient algorithms for the treatment of two-electron integrals in tensor product formats. For this, we use the non-standard approach of Beylkin which avoids explicit coupling between different resolution levels. We tested the efficiency of the algorithm for the products of orbitals in Daubechies wavelet bases and computed the two-electron integrals. This paper contains the detailed procedure and corresponding error analysis.