Department of Mathematics

Numerical Methods for Molecular Quantum Dynamics

    For the understanding of chemical reactions and the interactions with ultrashort laser pulses one has to treat molecules as quantum mechanical objects. The challenge with this very accurate theory is the curse of dimensionality which comes along with the concept of the wave function. The goal of this project is to develop methods for treating larger molecular systems in quantum dynamical calculations. Two approaches are in the focus of this project - systematic reduction of dimensions and the introduction of semi-classical approximations. Moreover these methods are applied to current problems in physics and chemistry together with groups form these research areas. 

Left pic: Visualization of a wave packet propagation of the nucleophilic substitution reaction between Chloride and Methyliodine. The molecular system has 15 degrees of freedom and can thus not be treated with quantum dynamics in a straight forward manner. A coordinate transform based on the reactive coordinates combined with a reduction to the most relevant dimensions preserves the main features of the reaction.

Right pic: shows the probability density of an atom which gets ionized by an intense and ultra-short laser pulse. Such processes can be used for the generation of xray light pulses or to gain insight into the electronic structure of molecules. An accurate theoretical description of such processes involves a multi-electron model which requires advanced computational methods.