Mathematical Methods of Modelling Electronic Structure of Large Systems

Abstract

This thesis focuses on mathematical methods of the quantum chemistry. It consists of several thematic parts. The first part focuses on tensor numerical methods which serve as a~tool for storing and numerical treatment of large multidimensional data. We focus on an efficient numerical representation of several types of basis functions that can be used in electronic structure calculations. In the second part we present our development of an~optimization algorithm intended for solving Kohn-Sham equations. It can be understood as an alternative to standard iterative methods, where problems with the convergence to the ground state energy occur. Finally, our parallel software for electronic structure calculations based on the Hartree-Fock approximation and the density functional theory together with achieved results is presented.