Kinetic lattice model for long-time chemical phenomena: Introduction of time-scale into Monte Carlo simulation

The kinetic lattice model (KLM) has been proposed, as a model of the slow d ynamics in chemical systems, where the molecular diffusion can be treated a nd the time notion can be introduced within the Monte Carlo (MC) simulation scheme by combining Stokes-Einstein relation and Einstein's formula for th e diffusion coefficient D of the solute molecule. Then, its mean square dis placement calculated via MC simulations, brings about directly a time-scale per 1 MC step. For a model chemical system consisting of a spherical molec ule with a radius of 10 Angstrom in such a solvent with the coefficient of viscosity eta of toluene, 1 MC step was found to correspond to the order of 100 ps for both 2-dimensional and 3-dimensional KLM. At the same time, the temperature dependence and the dimensionality were discussed within the pr esent KLM. It was established that the KLM should be a plausible and unique tool to understand the long-time chemical phenomena which have been, for a long time, difficult problems that can not be dealt by any direct microsco pic methods.