  Mixed-quantum classical (MQC) methods for simulating the dynamics of
molecules at metal surfaces have the potential to accurately and efficiently
provide mechanistic insight into reactive processes. Here, we introduce simple
two-dimensional models for the scattering of diatomic molecules at metal
surfaces based on recently published electronic structure data. We apply
several MQC methods to investigate their ability to capture how nonadiabatic
effects influence molecule-metal energy transfer during the scattering process.
Specifically, we compare molecular dynamics with electronic friction, Ehrenfest
dynamics, Independent Electron Surface Hopping, and the Broadened Classical
Master Equation approach. In the case of Independent Electron Surface Hopping,
we implement a simple decoherence correction approach and assess its impact on
vibrationally-inelastic scattering. Our results show that simple,
low-dimensional models can be used to qualitatively capture experimentally
observed vibrational energy transfer and provide insight into the relative
performance of different MQC schemes. We observe that all approaches predict
similar kinetic energy dependence, but return different vibrational energy
distributions. Finally, by varying the molecule-metal coupling, we can assess
the coupling regime in which some MQC methods become unsuitable.
