Wigner phase-space description above and below the classical threshold for the H+H2 reaction

The Wigner phase-space representation offers a semiclassical way of describing molecular collisions. In this paper the collinear H+H2 exchange reaction is studied using the Wigner phase-space approach. The general behavior of the calculated Wigner reaction probabilities as a function of the collision energy is consistent with that of the exact quantum-mechanical probabilities reported in the past. Quantitative disagreements between the Wigner and quantum-mechanical probabilities arise mainly from the neglect of ‘‘dynamical’’ tunneling in the Wigner approach due to the use of real-valued classical trajectories. Nevertheless, the Wigner approach is capable of describing some aspect of tunneling as the high momentum tail of the initial Wigner distribution function is likely to exhibit tunneling. Thus the approach yields a nonzero reaction probability below the classical threshold energy.