Real-space all-electron Density Functional Theory with Multiwavelets

Abstract

This thesis presents the implementation of a numerical real-space method for the calculation of the electronic structure of molecular systems within the self-consistent field approximations of quantum chemistry. The code is based on the multi-resolution multiwavelet basis which provide sparse representations of functions and operators, in particular integral operators with Green's function convolution kernels. The mathematical formalism provides efficient (linear-scaling) algorithms for operator application, e.g. for the Coulomb operator for the calculation of electrostatic potentials, as well as rigorous error control.

The Hartree-Fock and Kohn-Sham equations of quantum chemistry are reformulated in integral form and solved to self-consistency using iterative solution techniques. The code is able to attain high-accuracy for many-electron molecular systems, both restricted closed-shell and unrestricted open-shell.

Because of the inherent high demands on computational resources that comes with real-space methods, the code relies on parallel algorithms and data distribution in order to become competitive with conventional methods, and the code has been properly adapted in order to utilize modern massively parallel computing architectures.