PROJECTS

Adaptive solution of coupled cluster equation and tensor product approximation
of two-electron integrals

PRINCIPAL INVESTIGATOR

Prof. Dr. Dr. h.c. Wolfgang Hackbusch Max-Planck-Institut für Mathematik in den Naturwissenschaften Inselstraße 22-26 04103 Leipzig Germany 0341/9959750 0341/9959999 Wolfgang.Hackbusch@mis.mpg.de www: Homepage

TOGETHER WITH

Prof. Dr. Reinhold Schneider Christian-Albrechts-Universität zu Kiel Institut für Informatik Christian-Albrechts-Platz 4 24098 Kiel Germany 0431/8807470 0431/8804464 rs@numerik.uni-kiel.de www: Homepage

PROJECT RESEARCH ASSISTANT

ABSTRACT

In order to achieve optimal computational complexity in electronic structure calculations, i.e. linear scaling concerning system size and more general with respect to the number of degrees of freedom, it is crucial to utilize adaptivity in various places. Within the first part of our project we want to apply recent ideas from multiscale analysis to develop adaptive algorithms for coupled cluster and configuration interaction methods. Here, adaptivity means to select those excitation amplitudes from the full configuration space which contribute most to the energy. Such kind of schemes have been already discussed in the literature, however, we intend to incorporate some new mathematical insights by selecting amplitudes according to appropriate norms, and to apply a posteriori error estimators which enable a quantitative estimate of the remaining approximation error. The second part of our proposal concerns the efficient computation of two-electron integrals which constitutes a major bottleneck of standard quantum chemistry methods. We want to incorporate adaptivity into our previously developed density-fitting scheme based on optimal tensor product approximations. This can be accomplished by means of hierarchical tensor product decompositions as well as adaptive algorithms for convolutions with the Coulomb potential.