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.