Energy Exchange in Molecular Collisions

A theory was developed for computing the probability of transition, upon molecular collision, between vibrational states, involving corresponding conversion of translational energy. A spherically symmetric Lennard-Jones 6–12 potential for interaction between the colliding molecules was introduced; their relative translational motion was described classically. Further, the theory was symmetrized to permit inclusion of collisions with nonzero impact parameters. As an example, the theory was applied to the CO2–H2O system. The effective collision diameter for an inelastic event was found to be of the observed order of magnitude, demonstrating not only the selective relaxation effect of water, but also its somewhat unusual temperature dependence. Zener's solution of the problem for a head-on collision was generalized to three-dimensional collisions, assuming a spherically symmetric interaction potential; but the complete solution of this model, including a quantum-mechanical description of the relative translational motion, was not obtained. However, for such a potential it was possible to demonstrate that the semiclassical theory is an adequate approximation to the quantum theory result, whenever the relative translational energies are much greater than the energy of exchange.