Wavelets for electronics structure calculations

ABSTRACT We report on wavelet compression of a 1-D prototype benchmark problem of sufficient complexity to capture the features of 3-D quantum electronics structure calculations. These problems have a multi-scale character through the presence of a set of singularities corresponding to atomic nuclei. Theoretical estimates of asymptotic decay across scales are derived and verified numerically. In addition, we study the effects of the location ofsingularity on the accuracy of the compression and on scaling. 1 INTRODUCTION The methods used in computational chemistry for the determination of molecular electronic structure arefundamentally 3-D, or in some cases, 6-D and higher. These problems have a multi-scale character through thepresence of a set of point singularities corresponding to the atomic nuclei, whose locations are known. There aremany indications both of a physical and mathematical nature to suggest that this problem could be effectively solved within a multiresolution analysis (MRA) framework.