Transition state wave packet study of hydrogen diffusion on Cu(100) surface

Abstract

The transition state wave packet (TSWP) approach to the thermal rate constant based on the flux-flux autocorrelation function is used to investigate the diffusion dynamics of an H atom on the Cu(100) surface in the uncorrelated hopping regime. The high efficiency of the approach makes it feasible to include up to eight Cu modes explicitly in the time dependent quantum simulation. This is necessary since on the rigid surface the flux-flux autocorrelation function never decays to a negligibly small value to give a converged rate constant. For short times, the Cu modes included dynamically merely have a zero-point-energy effect on the flux-flux autocorrelation function. For longer times, however, the Cu modes absorb the activation energy of the H atom and effectively suppress recrossing of the transition state surface, resulting in convergence of the autocorrelation function and the hopping rate. For this system, recrossing of the transition state surface is minimal with the medium damping present, and the converged hopping rate can be well approximated by the short time behavior of the correlation function on the rigid surface. In addition, we find that the contributions of the excited Cu modes to the hopping rate may be accurately modeled by thermal “transition state” factors. Based on this, a new quantum transition state theory (QTST) is derived. The new theory provides a general way to calculate the approximate quantum correction to the traditional TST. It also provides a systematic and flexible tool to calculate the rate constant at any desired level of accuracy between the traditional TST level and the exact result. Finally, since the surface relaxation due to the presence of the H atom lowers both the energies of H atom in the binding well and on the saddle point almost equally, it only minimally affects the hopping rate, provided the configuration of the surface atoms is fully relaxed initially.