Vibrationally inelastic scattering of NO from metal surfaces: A partial mean-field approach

Vibrationally inelastic scattering of NO from metal surfaces probes electronically nonadiabatic molecule-surface dynamics. Experiments have reported multi-quantum relaxation and a work function dependence associated with transient charge transfer. In this work, we develop a partial mean-field approach for a Newns-Anderson model of NO scattering. The molecule-surface distance is treated classically using the mean-field approach, whereas the NO stretch, molecular electronic states, and metal electron bath are treated quantum mechanically with fermionic hierarchical equations of motion (HEOM). Benchmarks against fully quantum HEOM simulations show that the new approach reproduces transient electron transfer and mean vibrational-translational trajectories. It also reproduces the final vibrational distributions over a range of initial vibrational states, incident energies, hybridization widths, and coupling strengths. We then apply the method to NO(ν = 2) scattering from ultrathin Ag/Au(111) films. Both shifted and interpolated potential models reproduce the main work function dependence: lower work function increases transient NO- population and enhances relaxation, especially in the ν = 2 → 0 channel. Together, these results show that the partial mean-field approach can accurately describe direct NO scattering with a classical translational coordinate, provided that the NO vibration and electronic degrees of freedom are treated quantum mechanically.