Wavelets for electronic structure calculations

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.