Vibrational–Vibrational–Translational Energy Transfer between Two Diatomic Molecules

A semiclassical calculation of transition probabilities for vibrational–vibrational–translational energy transfer in a collision of two diatomic molecules is presented. The collision model is approximate, utilizing a collinear collision of harmonic oscillators with an exponential repulsion between center atoms. The method of Kerner and Treanor is used to solve the Schrödinger equation with linearized potential in the oscillator coordinates. Our procedure is a logical extension of the Treanor method to diatomic–diatomic collisions. Closed form analytical results are obtained for this model. The general magnitudes and trends of the probabilities are expected to be indicative of the behavior of real molecules. General formulas for the probabilities of processes of the type $$\mathrm{AB}{\mathrm{(n}}_1\mathrm{)\hspace{0.17em}+\hspace{0.17em}}\mathrm{BA}{\mathrm{(n}}_2\mathrm{)\hspace{0.17em}\to \hspace{0.17em}}\mathrm{AB}{\mathrm{(n}}_1\mathrm{\prime )\hspace{0.17em}+\hspace{0.17em}}\mathrm{BA}{\mathrm{(n}}_2\mathrm{\prime )}$$ as a function of collision velocity are presented. Special attention is given to “resonant” energy transfer where $n_1{\mathrm{\prime \hspace{0.17em}+\hspace{0.17em}n}}_2{\mathrm{\prime \hspace{0.17em}=\hspace{0.17em}n}}_1{\mathrm{\hspace{0.17em}+\hspace{0.17em}n}}_2$ .