Classical dynamics in a quantum spirit: a revision of adiabatic trajectory treatment for H₂/Pd(111)

The quasi-classical trajectory method is a standard tool for studying gas-surface interactions. However, its purely classical treatment of molecular motion, particularly the lack of quantization of internal degrees of freedom, may limit its accuracy compared to quantum mechanical descriptions. To address this limitation, semi-classical corrections have been developed over the years, most notably Gaussian binning combined with the adiabaticity correction. This framework introduces non-uniform weighting of trajectories, grounded in semiclassical theory, to better align with quantum results. Recently, this approach was refined for H₂ scattering on W(100), where adiabatic trajectories were more rigorously characterized and assigned appropriate statistical weights. In this work, we extend this analysis to H₂ scattering on Pd(111), a system governed by distinct dynamical features. Our results confirm the validity of the method, providing a theoretical foundation for earlier more empirical studies. By reconciling classical and quantum perspectives, this work establishes a robust framework for investigating gas-surface interactions with improved accuracy.