Classical Model for Vibrational and Rotational Excitation of Diatomic Molecules by Collision. II. Interaction with Arbitrary Potential Functions

Publisher Website
Google Scholar
Abstract
Two classical models for vibrational energy transfer between a diatomic harmonic oscillator A-B and an atom C are examined in detail. The first model corresponds to a harmonic repulsion between B and C with a smooth cutoff at zero interaction. It can be solved exactly. The second corresponds to a Morse-like potential between B and C. In this case, the orbits for colinear collisions are followed on a digital computer, and ΔEv the inelastic energy transfer is ``measured'' from this numerical solution for the equation of motion. The results can be transformed into probabilities by defining excitation as the condition: 2hν>ΔEv≥hν. ΔEv is a strong function of the phase angle of the oscillator. The probability function for excitation is transformed into a rate constant by averaging over the temperature-dependent distribution functions for energies. In contrast to other ``classical'' solutions, it is found that P, the probability of excitation (or de-excitation), has a nearly Arrhenius type of dependence on temperature. The activation energy of P is quadratically sensitive to the range of the repulsive interaction between B and C. This arises from the result that the excitation probability P(ER) goes very sharply to zero as ER, the relative collisional energy, approaches some small limiting value. This is in marked contrast to present theories for which P(ER) goes asymptotically to zero with ER. Features of the classical model are discussed in some detail and comparisons are made with experimental data from shock tubes. Because of the extreme sensitivity of the model to the value for the range parameters, no absolute predictions of de-excitation probabilities are possible. However, it is possible to fit the temperature dependence reasonably well with physically acceptable Morse parameters.

This publication has 2 references indexed in Scilit: