Vibrational Energy Transfer in High-Energy Collisions

Time-dependent wavefunctions are used to evaluate the exact transition probabilities for a forced harmonic oscillator. The forcing is represented by a time-dependent potential, where this potential has a linear dependence on the oscillator coordinate. The results are compared with available numerical solutions for a harmonic oscillator forced with a potential which has an exponential dependence on the oscillator coordinate. The comparison is made for the collision of an N2 molecule with another particle, and it is found that although the results for the two cases are similar, the linear potential gives higher values for the multiquantum transitions. It is then shown that time-dependent wavefunctions which contain the corresponding classical motion as a parameter provide a good set of functions for a perturbation calculation. The energy transfer to these oscillating wavefunctions is always identical to the energy transfer to the classical oscillator. Thus the perturbation value of the energy transfer represents the difference between the classical and the quantum-mechanical result. It is shown that this value, which is zero for the linear forcing potential, is very small for higher-order potentials, even at high velocity of impact. This demonstrates that classical calculations can be used to obtain the energy transfer in molecular collisions at high temperature.