Three-Dimensional Model of Collision-Induced Vibrational Transitions in Homonuclear Diatomic Molecules

Abstract

The one‐dimensional, semiclassical theory of vibrational transitions in homonuclear diatomic molecules is extended to three dimensions. Small perturbation methods are applied to harmonic‐oscillator, rigidrotator wavefunctions, and the interaction potential is assumed to be a linear superposition of exponential repulsions between atomic centers. This potential is expanded to terms of first‐order influence on the transition probabilities, and the spherically averaged potential is used to determine the collision trajectory and the time‐dependent perturbation. Vibrational transitions (predominantly $\text{Δυ\hspace{0.17em}=\hspace{0.17em}±\hspace{0.17em}1}$ ) are found to be accompanied by simultaneous rotational transitions (predominantly $\text{Δl\hspace{0.17em}=\hspace{0.17em}0, ±\hspace{0.17em}2}$ ). The effect of coupled rotations increases the vibrational transition rates by 50% or more. Analytic approximations are derived for cross sections, rate coefficients, and relaxation rates. The three‐dimensional model permits one to fit both the gradient and the magnitude of an effective exponential repulsion to observed vibrational relaxation data, whereas only the gradient can be determined using one‐dimensional theories. This “effective” interaction potential for vibrational excitation is steeper and of shorter range than potentials normally responsible for pure scattering. We surmise that a multiplicity of interaction potentials exist for molecules, just as for atoms, and that the steeper inner potentials resulting from paired electron spin configurations are responsible for most vibrational transitions, whereas the outer potentials resulting from unpaired spins are responsible for most of the scattering.