Reversible integrators for basic extended system molecular dynamics

Abstract

Starting from a family of equations of motion for the dynamics of extended systems whose trajectories sample constant pressure and temperature ensemble distributions (Ferrario, M., 1993, in Computer Simulation in Chemical Physics, edited by M. P. Allen and D. J. Tildesley (Dordrecht: Kluwer)), explicit time reversible integration schemes are derived through a straightforward Trotter factorization of the dynamic Liouville propagator, along the lines first described by Tuckerman, M., Martyna, G. J., and Berne, B. J., 1992, J. chem. Phys., 97, 1990. The original Andersen's constant-pressure dynamics are recovered in the limit of zero coupling with the Nose thermostat. Reversible integration schemes are derived as a generalization of the velocity Verlet algorithm, with direct handling of the velocity dependent forces in such a way that both predictions and relative iterative corrections are not required. For the sake of clarity both the equations of motion and the Trotter factorization are kept to the basic level. The proposed structure can accommodate easily, when needed, complications such as multiple timesteps and more effective thermostats (Nose-Hoover-chain). Finally, an application is made to a model molecular system subjected to holonomic constraints by means of the SHAKE algorithm. In the constant pressure case it is no longer possible to avoid using a prediction for the constraint contribution to the volume acceleration; however, recourse to a minimal iteration scheme still achieves excellent overall behaviour for the proposed integration algorithm, with no perceptible difference from the unconstrained case.