Comparison of Approximate Translational—Vibrational Energy-Transfer Formulas with Exact Classical Calculations

Abstract

The Hamiltonian equations of motion for collinear‐colliding diatomic‐molecule—atom and diatomic‐molecule—diatomic‐molecule systems are numerically integrated to obtain vibrational energy‐transfer data. The diatomic molecules are taken to be either harmonic or Morse‐type oscillators, and the collision potential is either an exponentially repulsive potential or a Lennard‐Jones 6–12 potential. The results of the exact classical three‐body calculations are compared to results predicted by classical and semiclassical approximations. The ratios of approximate to exact energy‐transfer values are related to the value of a parameter which depends only upon the masses of the particles involved in the collision; this correlation is found to be relatively insensitive to the values of the collision energy and of the potential parameters over wide ranges. The exact classical energy‐transfer data for the four‐body systems are compared to the approximate and exact three‐body data. The validity of using three‐body approximations in treating four‐body collisions is discussed.