On Molecular Dynamics Algorithms

Abstract

The step errors (the local errors, called also the truncation errors) of algorithms used in molecular dynamics simulations result in errors of thermodynamic properties of simulated systems. The simulations on the Lennard-Jones (L-J) liquid showed that in the case of the Verlet algorithm the values of the errors are noticeable even if we apply Beeman's technique. For the time step j t =0.01 at the temperature k B T , 1.26 and the density =0.75, Beeman's technique "shifts" the pressure by about 0.009 (all in L-J units). The "shift" is proportional to j t 2 and strongly decreases with a decrease of . For the Gear 4th order predictor-corrector method, the shift, at j t =0.0125, is only a few times lower than that for Beeman's technique. The effect is due to scaling of velocity (necessary to eliminate the energy drift), but not to the step errors and quickly vanishes with j t M 0. In order to eliminate the effect, the Cowell-Numerov implicit method in which the nonlinear equations for space variables (equivalent to the equations of the Gear 4th order implicit method) are approximately solved by iteration applied only to the subset of the most rapidly varying forces is proposed. The method is stable, accurate, and efficient. At the given state point for j t =0.0125 the "shift" of pressure, for momentums evaluated from the 5th order formula, amounts to about 0.0002. This value is approximately equal to the result for Calvo and Sanz-Serena's 4th order method (CSS). The proposed method is more efficient than CSS, especially at a high cut-off distance ( R C ). For R C M X, the time of performing single time step approaches to that of the Verlet method.