A Multisurface Scattering Theory

Abstract

The curve-crossing problems studied in the previous two chapters are one-dimensional cases of more general multisurface scattering. From the chemist’s viewpoint multisurface scattering is of considerable interest, because there are many important chemical reactions that involve more than one potential surface. Such reactions were first studied theoretically by Tully and Preston [10.1] and later studies include the Feynman path integral method by George and collaborators [10.2,3] and others [10.4,5]. The Feynman path integral method contains an attractive feature that appears well suited for studying electronic transitions involving more than one potential surface. Therefore, it is logical that the complex trajectory method is based on this approach. The complex trajectory method as formulated by George and co-workers blends the Schrodinger picture for electronic motion, the Feynman picture for nuclear motion, as well as the WKB approximation for the electronic and nuclear transition probabilities. The WKB approximation for the electronic transition probabilities turns out to be basically a slight generalizatior of the well-known result by Zener [7.1] in the sense that the phase integrals are evaluated numerically by solving the classical equations of motion in the complex time plane. However, we recall that Zener’s theory treats not electronic motion per se, but nuclear motion subject to the effective potentials provided by the electrons in the Born-Oppenheimer approximation.