Vibrational Relaxation at a Metal Surface: Electronic Friction Versus Classical Master Equations

Within a 2-D scattering model, we investigate the vibrational relaxation of an idealized molecule colliding with a metal surface. Two perturbative nonadiabatic dynamics schemes are compared: $(i)$ electronic friction (EF) and $(ii)$ classical master equations (CME). In addition, we also study a third approach, $(iii)$ a broadened classical master equation (BCME) that interpolates between approaches $(i)$ and $(ii)$. Two conclusions emerge. First, even though we do not have exact data to compare against, we find there is strong evidence suggesting that EF results may be spurious for scattering problems with more than one nuclear dimension. Second, we find that there is an optimal molecule-metal coupling that maximizes vibrational relaxation rates by inducing large nonadiabatic interactions.