QUANTUM STOCHASTIC APPROACH FOR MOLECULE SURFACE SCATTERING .1. ATOM PHONON INTERACTIONS

We present a general, fully quantum mechanical theory for molecule sur face scattering at finite temperature within the time dependent Hartre e (TDH) factorization. We show the formal manipulations which reduce t he total molecule-surface-bath Schrodinger equation into a form which is computationally convenient to use. Under the TDH factorization, the molecular portion of the wavefunction evolves according to a mean-fie ld Hamiltonian which is dependent upon both time and temperature. The temporal and thermal dependence is due to stochastic and dissipative t erms that appear in the Heisenberg equations of motion for the phonon operators upon averaging over the bath states. The resulting equations of motion are solved in one dimension self consistently using quantum wavepackets and the discrete variable representation. We compute ener gy transfer to the phonons as a function of surface temperature and in itial energy and compare our results to results obtained using other m ean-field models, namely an averaged mean-field model and a fully quan tum model based upon a dissipative form of the quantum Liouville equat ion. It appears that the model presented here provides a better estima tion of energy transfer between the molecule and the surface.