Already today, it is possible to extract a large amount of interesting information about chemical substances and chemical reactions using molecular dynamics computations based on theoretical models. Several factors contribute to the rapid progress of this discipline: Models are becoming more and more accurate, computers more and more powerful, and computational algorithms more and more efficient.

Molecular dynamics (MD) simulations are widely used in chemistry and molecular biology. In classical MD, Newton's equations of motion are integrated for an ensemble of particles (often atomic nuclei), where each particle moves in a force field generated by all the other particles. The results of MD computations can give both molecular (structure, etc.) and macroscopic (diffusion coefficients, enthalpy, etc.) information. However, accurate computations require accurate force field models, many particles, and long simulation times. It is usually computationally demanding to evaluate the force acting on the particles at a given time instant. For a long time, developers of numerical methods have been trying to reduce the number of force field evaluations as much as possible, and for classical MD problems much progress has been made. Recently, very accurate force field models based on quantum mechanics have been developed. The computational costs of these quantum-classical MD (QCMD) models are extensive, and furthermore very small time steps must be used. Numerical algorithms for these problems have not yet been studied much.

At the Division of Scientific Computing, we have an ongoing project project on simulations of the time-dependent Schrödinger equation (TDSE). The group collaborates with research groups at the Department of Materials Chemistry and the Department of Physical Chemistry. Within this project a modern class of numerical integrators (geometrical integration), massively parallel software based on high-order finite difference discretizations, and accurate boundary treatment are currently analyzed and implemented for the TDSE. The goal of the PhD project is to further develop these methods for use in QCMD simulations. A contact with Vasile Gradinaru at ETH Zürich gives the opportunity to take part in the development of semi-classical methods. Gradinaru and his coworkers have developed a novel method for semi-classical QCMD simulations which is based on Hagedorn wave packets. An alternative way to persue is to couple molecular dynamics with quantum dynamical computations. Our group is currently establishing a contact to Anders Szepezzy, KTH, to explore the potential of such a hybrid approach. In the PhD project these methods will be enhanced for application problems in chemistry and molecular biology. If new and improved computational schemes can be found, the impact to those applications will be very large.

For more information contact Sverker Holmgren (Prof.) or Katharina Kormann (PhD student within the project).