String-plucking model for vibrational excitation of molecules

Abstract

A "string-plucking" model has been developed to describe the translational to vibrational energy transfer between an atom and a harmonic oscillator in terms of the time-dependent force constant and equilibrium distance of the molecule. The model is compared with exact classical trajectory calculations of collinear and "breathing sphere" collisions involving repulsive exponential or Lennard-Jones interaction potentials. In the adiabatic limit for simple collisions (i.e., in the absence of multiple collisions produced by a light middle atom or a deep potential well), the energy transfer predicted by the model is in good agreement with the exact trajectory results. In the case of the Lennard-Jones potential, both model and exact calculations predict that the effect of decreasing the initial kinetics energy is to increase the fractional energy transfer up to 100%. For breathing sphere collisions with a Lennard-Jones potential, the model correctly predicts a sharp decline in energy transfer at a critical impact parameter which is found in the exact trajectory calculations to equal the rainbow impact parameter. For simple collisions with either potential both model and exact calculations show that the effect of increasing the vibrational energy is equivalent to diminishing the initial radial kinetic energy by an equal amount. The model is also compared with the Landau-Teller, Nikitin, and Attermeyer-Marcus theories, and their regions of validity are explored.