Quantum vibrational transition probabilities from real classical trajectories: Collinear atom–diatom collisions

Abstract

Quantum vibrational transition probabilities may be estimated from single, real classical trajectories by exploiting the approximate correspondence between the classical and quantal motions. In this paper we explore the range of validity of several such correspondence methods for collinear atom–diatom collisions by comparing the results with those from rigorous quantum mechanical calculations. The model systems considered here include: (a) a harmonic oscillator with (1) a repulsive exponential, (2) a Landau–Teller, and (3) a Lennard-Jones interaction potential, and (b) a Morse oscillator with a repulsive exponential interaction potential. The range of the dimensionless mass parameter M is 0.00628 to 3.737 and the total system energy ranges from 1.55 to 10.0 in units of h/ωe. For both Morse and harmonic oscillator excitation the semiclassical results are generally more accurate for small M and for small initial and final vibrational quantum numbers. Quantitatively, the results are consistently better for a harmonic oscillator than for a Morse oscillator. The threshold behavior for harmonic oscillator excitation can be predicted quantitatively using a classical trajectory in which the arithmetic mean of the initial and final speeds is equal to the arithmetic mean of the translational speeds for the corresponding quantum transition. By detailed balancing, the probabilities for vibrational de-excitation in slow collisions are also predicted accuretaly.