Dynamics of molecules with internal degrees of freedom by multiple time-step methods

Abstract

In molecular dynamics simulations of flexible molecules, the treatment of motions that take place on different time scales (e.g., bond stretching and bond angle bending vs dihedral angle librations and overall translation and rotation) or of forces that vary differently with distance (e.g., bonding forces vs electrostatic forces) is a major consideration. The most rapidly varying quantity limits the integration time step, while the most slowly varying quantity usually determines the simulation time required. The reversible multiple time-step methods introduced by Tuckerman, Berne, and Martyna [J. Chem. Phys. 97, 1990 (1992)] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast motions most effectively. As a first step toward extending multiple time-step methods to macromolecules, we investigate their utility for determining the dynamics of n-alkanes as neat liquids and in aqueous solution. Because the dynamics is done in Cartesian rather than internal coordinates, the different time steps are implemented in terms of hard and soft forces acting on individual atoms; e.g., hard forces are contributed by bond stretching (and bond angle bending) terms and soft forces by the remaining intramolecular and intermolecular (van der Waals and electrostatic) terms in the additive empirical potential function used to describe these systems. Integrations with and without a Nose–Hoover thermostat are performed. Comparisons are made with ordinary single time step molecular dynamics and dynamics with constraints applied to the bonds. The stability of the integration methods and the dynamic properties are considered. It is shown that stable integrations that yield agreement with standard dynamics can be achieved with a saving of up to a factor of 5 in computer time.