Many biological and physical effects can be traced back to basic chemical processes. To develop a deeper understanding, it is crucial to simulate these fundamental processes efficiently and with good accuracy. The main challenge is to capture the underlying quantum mechanical structures properly. The forces governing the dynamics of molecules, their stable configurations and reaction probabilities are represented by potential energy surfaces (PES), which are hypersurfaces in a typically high-dimensional space. Unfortunately, the evaluation of PES is in general very time-consuming. Since simulations of a chemical process often require thousands or even millions of such force evaluations, it is essential to develop smart discretizations for both the dynamics of a molecule, and the underlying PES. It is a main goal of project B06 to to explore the interplay between simulation methods for molecular quantum dynamics and the discretization of PES. The focus lies on discretizations that preserve the relevant physical and geometric properties of the original system. B06 connects research topics ranging from abstract mathematical physics to the implementation of numerical algorithms for specific molecules. This facilitates new insights into both the theoretical concepts, and practical applications.

# B06

Potential Energy Surfaces

## Discretizing the Forces for Molecular Quantum Dynamics

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Potential energy surfaces are at the origin of the analytic description of molecular quantum dynamics and they give insight in it. B06 explores the accessibility of these high-dimensional structures for simulations of chemical processes which are fundamental for our understanding of basic principles in nature.
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**Group:**B. Dynamics-
**Principal Investigators:** **Universities:****Term:**2012 - 2016