Statistical methods are used increasingly in theoretical chemistry. Applications range from the use of stochastic relaxation techniques in determining minimum energy molecular configurations to dynamical Monte Carlo simulations of molecular motion in liquids. This paper focuses on diffusion-controlled reactions in radiation chemistry. Here the interest is in describing the evolution of isolated clusters, containing a few chemically active particles, resulting from the passage of ionising radiation through a liquid. The subsequent chemistry is determined by the rate at which these particles can encounter each other, pairwise, in the course of their random motion. Classically the trajectories of the particles are described as sample paths of a continuous stochastic process, which in many cases can be assumed to be a diffusion. We have devised an approximate theory based on the approximation that pair distances evolve independently. The effect of this geometric distortion has been studied for small systems by simulation. The extension of this work to a wider class of realistic chemical processes poses many problems. Analytical progress is difficult and methods of simulating large spatial systems are not well developed. Problems which remain to be solved relate to the random geometry of the cluster as its constituent particles diffuse, the development of good approximations to first passage time distributions for diffusions with inhomogeneous drift and methods for the analysis of random motion in a liquid on the basis of detailed non-Markovian models of molecular movement.

A computational Monte Carlo simulation approach for modeling the thermalization of low-energy electrons is presented. The simulation methods rely on, and use, experimentally based cross sections for elastic and inelastic collisions. To demonstrate the different simulation options, average numbers of interactions and the range of low-energy electrons with initial energies ranging from 1 to 20 eV are calculated for density normalized gaseous water. Experimental gas-phase cross sections for (subexcitation) electrons of energies in the range of 1-20 eV were taken from the compilation of Hayashi. The ballistic collision-by-collision simulations provide information on the intricacies of the thermalization processes not available experimentally.