A Stochastic, Resonance-Free Multiple Time-Step Algorithm for Polarizable Models That Permits Very Large Time Steps.

Molecular dynamics remains one of the most widely used computational tools in the theoretical molecular sciences to sample an equilibrium ensemble distribution and/or to study the dynamical properties of a system. The efficiency of a molecular dynamics calculation is limited by the size of the time step that can be employed, which is dictated by the highest frequencies in the system. However, many properties of interest are connected to low-frequency, long time-scale phenomena, requiring many small time steps to capture. This ubiquitous problem can be ameliorated by employing multiple time-step algorithms, which assign different time steps to forces acting on different time scales. In such a scheme, fast forces are evaluated more frequently than slow forces, and as the former are often computationally much cheaper to evaluate, the savings can be significant. Standard multiple time-step approaches are limited, however, by resonance phenomena, wherein motion on the fastest time scales limits the step sizes that can be chosen for the slower time scales. In atomistic models of biomolecular systems, for example, the largest time step is typically limited to around 5 fs. Previously, we introduced an isokinetic extended phase-space algorithm (Minary et al. Phys. Rev. Lett. 2004, 93, 150201) and its stochastic analog (Leimkuhler et al. Mol. Phys. 2013, 111, 3579) that eliminate resonance phenomena through a set of kinetic energy constraints. In simulations of a fixed-charge flexible model of liquid water, for example, the time step that could be assigned to the slow forces approached 100 fs. In this paper, we develop a stochastic isokinetic algorithm for multiple time-step molecular dynamics calculations using a polarizable model based on fluctuating dipoles. The scheme developed here employs two sets of induced dipole moments, specifically, those associated with short-range interactions and those associated with a full set of interactions. The scheme is demonstrated on the polarizable AMOEBA water model. As was seen with fixed-charge models, we are able to obtain large time steps exceeding 100 fs, allowing calculations to be performed 10 to 20 times faster than standard thermostated molecular dynamics.