Effect of surface nodes on the six-dimensional molecule–surface scattering dynamics of H₂–Cu(100) and D₂–Cu(111) systems

Abstract

We include the phonon modes originating from the three layers of Cu(100)/Cu(111) surface atoms on the dynamics of molecular [H₂(v,j)/D₂(v,j)] degrees of freedom (DOFs) through a mean field approach, where the surface temperature is incorporated into the effective Hamiltonian (potential) either by considering Boltzmann probability (BP) or by including the Bose–Einstein probability (BEP) factor for the initial state distribution of the surface modes. The formulation of effective potential has been carried out by invoking the expression of transition probabilities for phonon modes known from the “stochastic” treatment of linearly forced harmonic oscillator (LFHO). We perform four-dimensional (4D⊗2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time and temperature-dependent effective Hamiltonian to calculate elastic/inelastic scattering cross-section of the scattered molecule for the H₂(v,j)–Cu(100) system, and dissociative chemisorption–physisorption for both H₂(v,j)–Cu(100) and D₂(v,j)–Cu(111) systems. Calculated sticking probabilities by either 4D⊗2D or 6D quantum dynamics on an effective potential constructed by using BP factor for the initial state distribution of the phonon modes could not show any surface temperature dependence. In the BEP case, (a) both 4D⊗2D and 6D quantum dynamics demonstrate that the phonon modes of the Cu(100) surface affect the state-to-state transition probabilities of the scattered H2 molecule substantially, and (b) the sticking probabilities due to the collision of H₂ on Cu(100) and D₂ on Cu(111) surfaces show noticeable and substantial change, respectively, as function of surface temperature only when the quantum dynamics of all six molecular DOFs are treated in a fully correlated manner (6D).