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Wavelets for electronic structure calculations

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Abstract

Molecular electronic structure calculations have a multi‐scale character through the presence of a set of singularities corresponding to atomic nuclei, and thus there exists a potential to improve the efficiency of these calculations using fast wavelet transform techniques. We report on the development of a one dimensional prototype benchmark problem of sufficient complexity to capture the features of 3‐D problems that are being solved today in quantum electronics calculations. Theoretical estimates of decay across scales and spatial distribution of wavelet coefficients for the solutions of the 1‐D and 3‐D problems are derived and verified experimentally. Equivalence in a multi‐resolution context of the solutions of the 1‐D prototype and the 3‐D problem is established.

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Authors and Affiliations

  1. Environmental Molecular Sciences Laboratory, K1‐96, Pacific Northwest National Laboratory, Richland, WA, 99352, USA

    M.E. Brewster, George I. Fann & Zhiyun Yang

Authors
  1. M.E. Brewster
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  2. George I. Fann
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  3. Zhiyun Yang
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Brewster, M., Fann, G.I. & Yang, Z. Wavelets for electronic structure calculations. Journal of Mathematical Chemistry 22, 117–142 (1997). https://doi.org/10.1023/A:1019171830287

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  • DOI: https://doi.org/10.1023/A:1019171830287

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