This project, supported by the NSF Theoretical and Computational Chemistry Program, extends the principal investigator's recent development of semiclassical approximations to treat the time evolution of quantum mechanical systems such as tunneling and other classically forbidden processes. A large sample of classical trajectories is generated and used to compute the Van Vleck-Gutwiller propagator by integrating over initial momenta by the cellular method. Four specific topics will be studied: (1) fundamental aspects of the theory, (2) applications to atomic and molecular scattering, spectroscopy, and reactive scattering, (3) processes governed by small Franck-Condon factors, and (4) multiple scattering of electrons off surfaces with applications to the theory of scanning tunneling microscopy. This fundamental theoretical research project attempts to incorporate the essential quantum mechanical features of molecular dynamics into a simpler classical mechanical formalism. The theory, still in the early stages of development, has a very wide range of potential application. This project further develops fundamental aspects of the theory, and explores applications to molecular spectroscopy, elementary chemical reactions, and to the theory of scanning tunneling microscopy.
