A transition-rate investigation by molecular dynamics with the Langevin/implicit-Euler scheme

We report results from molecular dynamics simulations for a bistable piecewise-harmonic potential. A new method for molecular dynamics-the Langevin/implicit-Euler scheme-is investigated here and compared to the common Verlet integration algorithm. The implicit scheme introduces new computational and physical features since it (1) does not restrict integration time step to a very small value, and (2) effectively damps vibrational modes ω≫ω_c, where ω_c is a chosen cutoff frequency. The main issue we explore in this study is how different choices of time steps and cutoff frequencies affect computed transition rates. The one-dimensional, double-well model offers a simple visual and computational opportunity for observing the two different damping forces introduced by the scheme-frictional and intrinsic-and for characterizing the dominating force at a given parameter combination. Another question we examine here is the choice of time step below which the Langevin/implicit-Euler scheme produces "correct" transition rates for a model potential whose energy distribution is "well-described" classically.