Hongzhi Cheng

The dynamics of atomic and molecular motion at metal surfaces govern a host of important processes. To successfully simulate those processes, we often need to treat them as nonadiabatic dynamics. The huge number of electronic states, a continuum, presented in metal surfaces poses a serious problem. To overcome this difficulty, we introduce the wide-band diabatic dynamics method to greatly simplify the problem by decoupling the equations of motions of the atoms on different electronic states.

A further approximation can be achieved by introducing a semiclassical Gaussian wavepacket method. Due to the fact that the continuum of potential energy surfaces are approximately parallel to each other, a substantial simplification can be made. The combination of those approximations produces a method that is practical to apply to multidimensional processes involving several atoms or molecules and a metal surface.

Another topic in this dissertation is an analysis of stratified sampling method applied to estimating probabilities in non-equilibrium physical processes. A low-probability chemical reaction at a metal surface is one example, so the sampling method can be applied in conjunction with the nonadiabatic dynamics approach described above. Different from most other schemes whose accuracy is not guaranteed, the method proposed here can ensure accuracy by carefully estimating upper bounds of variance.