Generalized Langevin dynamics method

Molecular Dynamics simulation is one of many methods to study the macroscopic behavior of systems by following the evolution at the molecular scale. One way of categorizing these methods is by the degree of determinism used in generating molecular positions [134], On the scale from the completely stochastic method of Metropolis Monte Carlo to the pure deterministic method of Molecular Dynamics, we find a multitude and increasingly diverse number of methods to name just a few examples Force-Biased Monte Carlo, Brownian Dynamics, General Langevin Dynamics [135], Dissipative Particle Dynamics [136,137], Colli-sional Dynamics [138] and Reduced Variable Molecular Dynamics [139]. 

The authors proceed to calculate the reaction rates by the flux correlation method. They find that the molecular dynamics results are well described by the Grote-Hynes theory [221] of activated reactions in solutions, which is based on the generalized Langevin equation, but that the simpler Kramers model [222] is inadequate and overestimates the solvent effect. Quite expectedly, the observed deviations from transition state theory increase with increasing values of T. 

It appears that the generalized-Langevin-equation approach is a useful one for gas-surface dynamical studies. The approach provides a useful conceptual framework and offers inherent efficiency. The exact nature of the numerical details must await further studies. However, currently available model calculations suggest that the present method is a useful one. 

Brownian Dynamics (BD) methods treat the short-term behavior of particles influenced by Brownian motion stochastically. The requirement must be met that time scales in these simulations are sufficiently long so that the random walk approximation is valid. Simultaneously, time steps must be sufficiently small such that external force fields can be considered constant (e.g., hydrodynamic forces and interfacial forces). Due to the inclusion of random elements, BD methods are not reversible as are the MD methods (i.e., a reverse trajectory will not, in general, be the same as the forward using BD methods). BD methods typically proceed by discretization and integration of the equation for motion in the Langevin form... 

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