  Accurate description of nonadiabatic dynamics of molecules at metal surfaces
involving electron transfer has been a longstanding challenge for theory. Here,
we tackle this problem by first constructing high-dimensional neural network
diabatic potentials including state crossings determined by constrained density
functional theory, then applying mixed quantum-classical surface hopping
simulations to evolve coupled electron-nuclear motion. Our approach accurately
describes the nonadiabatic effects in CO scattering from Au(111) without
empirical parameters and yields results agreeing well with experiments under
various conditions for this benchmark system. We find that both adiabatic and
nonadiabatic energy loss channels have important contributions to the
vibrational relaxation of highly vibrationally excited CO(vi = 17), whereas
relaxation of low vibrationally excited states of CO(vi = 2) is weak and
dominated by nonadiabatic energy loss. The presented approach paves the way for
accurate first-principles simulations of electron transfer mediated
nonadiabatic dynamics at metal surfaces.
