Quantum vibrational transition probabilities from real classical trajectories: Symmetric diatom–diatom collisions

Our previous theory of vibrationally inelastic atom–diatom collisions, which is based on an approximate correspondence between the classical and quantal equations of motion, is extended here to the problem of translational–vibrational and vibrational–vibrational energy transfer in collisions of two identical diatoms. Parameters describing the quantal motion of harmonic oscillators subject to an interaction potential which includes only terms linear and bilinear in the two oscillator coordinates are evaluated from exact classical trajectories for the full potential. The formalism makes it possible to distinguish between the vibrational–vibrational and translational–vibrational energy transfer modes and to isolate the intermode coupling terms. The validity of approximations based on a reduced state basis is easily evaluated. The model results are in generally excellent agreement with exact fully quantal calculations, and they reproduce well the dependence of the transition probabilities for collinear H2+H2 collisions on the assumed form of the interaction potential.