Efficient multiple-time-step integrators with distance-based force splitting for particle-mesh-Ewald molecular dynamics simulations

Abstract

We develop an efficient multiple-time-step force splitting scheme for particle-mesh-Ewald molecular dynamics simulations. Our method exploits smooth switch functions effectively to regulate direct and reciprocal space terms for the electrostatic interactions. The reciprocal term with the near field contributions removed is assigned to the slow class; the van der Waals and regulated particle-mesh-Ewald direct-space terms, each associated with a tailored switch function, are assigned to the medium class. All other bonded terms are assigned to the fast class. This versatile protocol yields good stability and accuracy for Newtonian algorithms, with temperature and pressure coupling, as well as for Langevin dynamics. Since the van der Waals interactions need not be cut at short distances to achieve moderate speedup, this integrator represents an enhancement of our prior multiple-time-step implementation for microcanonical ensembles. Our work also tests more rigorously the stability of such splitting schemes, in combination with switching methodology. Performance of the algorithms is optimized and tested on liquid water, solvated DNA, and solvated protein systems over 400 ps or longer simulations. With a 6 fs outer time step, we find computational speedup ratios of over 6.5 for Newtonian dynamics, compared with 0.5 fs single-time-step simulations. With modest Langevin damping, an outer time step of up to 16 fs can be used with a speedup ratio of 7.5. Theoretical analyses in our appendices produce guidelines for choosing the Langevin damping constant and show the close relationship among the leapfrog Verlet, velocity Verlet, and position Verlet variants.