The effect of phonon modes on the D₂(v=0,j=0)–Cu(111) scattering processes

Abstract

We include the phonon modes originating from the three layers of Cu(111) surface atoms on the dynamics of incoming molecular [D₂(v, j)] degrees of freedom (DOFs) through a mean-field approach, where the surface temperature is incorporated into the effective potential by considering the Bose–Einstein probability factor for the initial state distribution of the surface modes calculated within the harmonic approximation. Such a time- and temperature-dependent effective Hamiltonian is further subdivided assuming a weak coupling between two sets of molecular DOFs, namely (x, y, z, Z) and (X, Y), respectively, in particular, to reduce the computational cost, and the corresponding coupled quantum dynamical equations of motion have been formulated in terms of the time-dependent discrete variable representation (TDDVR) approach. We demonstrate the applicability of the TDDVR method to investigate the collision of H₂(v, j) on the Cu(100) surface by calculating the reaction probabilities and scattering cross-sections. Calculated results for the D₂(v=0, j=0)–Cu(111) system show that the phonon modes affect the state-to-state transition probabilities of the scattered D₂ molecule substantially and chemisorption–physisorption processes noticeably.