Frictional effects near a metal surface.

When a classical master equation (CME) is used to describe the nonadiabatic dynamics of a molecule at metal surfaces, we show that in the regime of reasonably strong molecule-metal couplings, the CME can be reduced to a Fokker-Planck equation with an explicit form of electronic friction. For a single metal substrate at thermal equilibrium, the electronic friction and random force satisfy the fluctuation-dissipation theorem. When we investigate the time scale for an electron transfer (ET) event between the molecule and metal surface, we find that the ET rates show a turnover effect (just as in Kramer's theory) as a function of frictional damping.