Influence of step errors (truncation errors) on results of molecular dynamics simulations

Step errors (local errors, called also truncation errors) of the algorithms used in molecular dynamics simulations may result in non-physical correlations between particle velocities, as well as in errors of thermodynamic properties of simulated systems (energy, pressure). The simulations of the Lennard-Jones liquid showed, that the influence is especially high for the Verlet velocity algorithm. Beeman's technique decreases the correlations between the velocities, but at high densities the values of the errors of general averages are close to that of the Verlet method. The influence of step errors can be decreased by about two orders of magnitude by applying the Cowell-Numerov 4-th order implicit method (equivalent to the Gear 4-th order method treated as an implicit one). The method is very stable (more stable than the Verlet one), and can be highly optimized by restricting iteration to the closest neighbors of a given particle. As a result, the method becomes more efficient than the higher order explicit symplectic methods.