Quantum theory of energy exchange in direct encounters of polyatomic molecules with nonrigid surfaces

Recently developed effective mass theory of vibrational, rotational and translational energy exchange in molecular collisions is extended naturally to polyatomic molecules colliding with nonrigid surfaces. Considering the processes where the short-range forces are of prevailing importance, we transform the Hamiltonian into the form which enables us to eliminate the coordinates which are cyclic in the limit of zero range forces and can thus be expected to be approximately ignorable when forces are of short, but finite, range. Instead of three rotational and three translational coordinates we are thus left with one only relevant generalized coordinate. The mass corresponding to this coordinate can easily be calculated; it depends on the mass and the moments of inertia of the molecule, and on the segment of the potential surface on which the system evolves. The motion of the only relevant generalized coordinate is then quantized. The inelastic scattering problem is treated within first-order in the distorted wave expansion. In the cases where this may be expected to be inadequate, more advanced approximation schemes developed in scattering theory could be applied as well. The excitations of bulk phonons and also of vibrational modes localized on the surface are included in the theory. As an application, energy transfer in collisions of CO 2 molecules with Pt and Ag surfaces is studied (since this is the experimentally most studied case involving molecules of more than two atoms), and the results are compared with the experiments and with the recent semiclassical stochastic trajectory calculations in which the transfer of vibrational energy to rotations is neglected and the solid's vibrations are treated by a quasiclassical approximation. Excellent agreement was found between the present theory and the trajectory calculations mentioned for all three gas temperatures considered (290, 580 and 1160 K) in the case of small change in vibrational energy and high surface temperature, i.e., under the conditions where the agreement between the two methods could possibly be expected because of the approximations involved.