Mathematical and Numerical Methods for Complex Quantum Systems

Chemical Dimensions of Quantum Dynamics

Paul Zimmerman

University of Michigan


Exact solutions to the time-dependent Schrodinger equation come at high computational cost. With techniques such as the Multi-Configurational Time-Dependent Hartree (MCTDH) method, efficient simulations of electronic-nuclear dynamics can be performed when a suitable—sufficiently compact—basis of nuclear degrees of freedom is available. This presentation discusses how mathematical and chemical means can be used to identify the vital degrees of freedom in interesting molecular systems undergoing ultrafast electronic transitions. The goal of this identification is to achieve accurate model systems that are computationally tractable through dimensionality reduction. Examples from gas phase photo physics and next-generation organic solar cells will suggest how close interplay between chemical and mathematical reasoning can lead to new methods and insights.