Surface reaction dynamics and the harmonic oscillator

One of the fundamental steps in chemical reaction dynamics involves breaking reactant bonds. This is facilitated by placement of energy into the vibrational degrees of freedom associated with the bond. Here we present a model for vibrational excitation in molecule-surface collisions in which the equilibrium geometry of the (diatomic) molecule varies with distance from the surface. The special feature of this model is that the potential energy surfaces for bound nuclear motion are constructed from quadratic potentials, thus enabling analytic solutions. Comparisons are made between exact results obtained from a purely classical trajectory model and various hybrid models in which the internal vibrational modes are treated quantum mechanically in the harmonic limit.