Test of approximations to surface motion in gas-surface dynamics:: Linear versus quadratic coupling for Ts=0 K

A coupled wave vector formalism is applied to compute the reduced density matrix for dissociation and inelastic scattering of D-2 molecules on Cu surfaces at finite temperature. The effect of lattice recoil at 0 K is utilized to test different levels of approximation to the molecule-lattice coupling in the Hamiltonian. Although the first order, linear coupling term is found adequate to account for the surface recoil effect in D-2 scattering with rotational transitions, the quadratic term is required for an adequate description of the recoil accompanying dissociation, a process characterized by a stronger interaction between the incident molecule and the activation barrier present in the D-2/Cu potential energy surface (PES). A detailed analysis is carried out using a low-dimensional model PES, changing the location of the dissociation barrier. This reveals that the necessity of the quadratic term for dissociation can be attributed to a late barrier. For an early barrier, in the entrance channel, the linear coupling approximation is sufficient to describe dissociation.