PhD Project: Finite Element Methods in Quantum Chemistry

In January I officially started my PhD in the Theoretical Chemistry group of Prof. Dr. Andreas Dreuw at the Interdisziplinäres Zentrum für wissenschaftliches Rechnen of the Ruprecht-Karls-Universität Heidelberg. The principle aim of the project is to replace the common formalism of using atom-centered basis functions (e.g. Gaussian atomic orbitals) by a finite element basis. The finite element method (FEM), which was originally developed in the engineering community, has been applied to problems all over the physical sciences in recent years. In electronic structure theory, however, it has not really been considered in great depth so far.

Together with Dr. Michael Wormit — a Postdoc in our group — and Prof. Dr. Guido Kanschat from the Mathematical Methods of Simulation group we are currently working on a simple first program that solves the famous Hartree-Fock (HF) equations using finite elements (FEs). Surely this is only the first step towards finite-element based Quantum Chemistry and many things can be done to go beyond HF. We hope. however, that simple calculations will already give us some understanding of the very different properties of FEs compared to an Gaussian basis and how these can be used effectively.

A short presentation, which I compiled for our group's yearly seminar in Hirschegg (Kleinwalsertal, Austria), can be downloaded below. In said talk I give a brief introduction into the mathematical formalism of FEs and how the FEM could be applied in an SCF calculation.

The finite-element method in quantum chemistry