Applied and Interdisciplinary Mathematics Seminar

University of Michigan

Winter 2008
Friday, 7 March, 3:10-4:00pm, 1084 East Hall

Numerical Methods for Multidimensional Tunneling Transitions: A Quantum Transition State Theory

Jing Shi

Wayne State University


Abstract

Quantum tunneling plays crucial roles in some physical and chemical processes, ranging from quantum cosmology to enzymatic reactions. The quantum nature of the motion often comes along with multidimensionality, namely the coupled motion of many degrees of freedom. The high dimensionality of the potential energy surface poses a great challenge in both theoretical and numerical descriptions of tunneling. Numerical simulation based on the Schrodinger equation is often prohibitively expensive. We develop an efficient and accurate numerical method to calculate the tunneling transition, based on the path integral formulation ('instanton') of quantum transition state theory. It is free from any further ad hoc assumptions ('adiabatic' or 'sudden') and does not require pre-defined reaction coordinates. The application to hydrogen tunneling transfer in polyatomic molecules will also be demonstrated.