Statistical mechanics in rotationally inelastic scattering of molecules from surface within the dynamical Lie algebraic method

The dynamical Lie algebraic (DLA) method of Alhassid and Levine Phys. Rev. A 18 (1978) 89] is applied to statistical mechanics in rotationally inelastic scattering of molecules from surfaces. Specifically, the method is generalized to include the motion of surface atoms, i.e., phonons. For given Hamiltonian and initial state, the set of constraints required to obtain the solution of the motion equations is determined by an algebraic procedure. It is furthermore found possible to derive the motion equations for the mean values of the constraints. Application of the method to the scattering of NO molecules from a Pt(1 1 1) surface is made. The mean values of the final energies of NO molecules scattered from the surface obtained using the DLA method are in good agreement with experimental results in qualitative trends. The DLA method thus appears to have a wide range of validity for describing the statistical mechanics of the gas-surface scattering.