Classical Trajectory and Monte Carlo Techniques

Abstract

The classical trajectory Monte Carlo (CTMC) method originated with Hirschfelder, who studied the H + D2 exchange reaction using a mechanical calculator 1 . With the availability of computers, the CTMC method was actively applied to a large number of chemical systems to determine reaction rates and final state vibrational and rotational populations (e.g., Karplus et al. 2 ). For atomic physics problems, a major step was introduced by Abrines and Percival 3 , who employed Kepler's equations and the Bohr–Sommerfield model for atomic hydrogen to investigate electron capture and ionization for intermediate velocity collisions of H+ + H. An excellent description is given by Percival and Richards 4 . The CTMC method has a wide range of applicability to strongly coupled systems, such as collisions by multiply charged ions 5 . In such systems, perturbation methods fail, and basis set limitations of coupled-channel molecular-orbital and atomic-orbital techniques have difficulty in representing the multitude of active excitation, electron capture, and ionization channels.