Molecular Dynamics and Transition State Theory: The Simulation of Infrequent Events

Abstract

Before the advent of the high speed digital computer, the theoretical treatment of atomic motion was limited to systems whose dynamics admitted an approximate separation of the many-body problem into analytically tractable one- or two-body problems. Two approximations were the most useful in making this separation: 1) Stochastic approximations such as 'random walk' or 'molecular chaos', which treat the motion as a succession of simple one- or two-body events, neglecting the correlations between these events implied by the over-all deterministic dynamics. The analytical theory of gases, for example, is based on the molecular chaos assumption, i.e. the neglect of correlations betweeen consecutive collision partners of the same molecule. Another example is the random walk theory of diffusion in solids, which neglects the dynamical correlations between consecutive jumps of a diffusing lattice vacancy or interstitial. 2) the harmonic approximation, which treats atomic vibrations as a superposition of independent normal modes. This