PROJECTS

Operator calculus of density matrices and sparse wavelet representations

PRINCIPAL INVESTIGATOR

TOGETHER WITH

Prof. Dr. Reinhold Schneider Christian-Albrechts-Universität zu Kiel Informatik und Praktische Mathematik Christian-Albrechts-Platz 4 D-24098 Kiel +49 431 880-7470 +49 431 880-4464 rs@numerik.uni-kiel.de

ABSTRACT

The multiscale character of the electronic structure of molecules expresses itself in the energy and length-scales to be encountered, which extend over several orders of magnitude. Multiresolution analysis, a central topic of applied mathematics, proved to be a useful tool for applications in quantum chemistry. We suggest a multiresolution approach to linear scaling methods for Hartree-Fock (HF) and Kohn-Sham (KS) equations based on wavelet representations of density matrices and Fock operators. The unifying framework of pseudo-differential operators provides the basis for our mathematical analysis. A peculiar new feature of our approach is the use of Gaussian-type wavelets which enables a combination of various useful concepts from standard Gaussian-type basis sets with multiresolution analysis. Furthermore we want to apply hierarchical Kronecker tensor product approximations to electron densities for an efficient evaluation of Hartree potentials and exchange operators. The self-consistent solution of HF or KS equations requires an adaptive operator calculus that enables to control the sparsity of matrices during the iterative solution process. Multiresolution methods become competitive to conventional quantum chemistry methods for systems where high numerical accuracy is required.