From predictors and SHAKE toward unified integration scheme for molecular dynamics

Molecular dynamics (MD) simulations applied to various special tasks such as thermostats, barostats, external volume control, or external magnetic fields often require tailored integration methods, complicating software development. Here, we propose a unified integration scheme for solving the common sets of equations of motion in MD. To achieve this, we adapted the traditional SHAKE method for treating rigid bonds to a predictor-corrector integration scheme and combined it with the existing time-reversible velocity predictor and box predictor. This new approach enables using both the time-honored Verlet method and the recently improved Gear methods. The resulting unified integration scheme was tested on two simple models and two MD systems: SPC/E water and ionic liquid (1-ethyl-3-methylimidazolium tetrafluoridoborate). Trajectories in microcanonical, Nosé-Hoover canonical, and MTK isobaric ensembles were generated. The results for Verlet-based methods were in excellent agreement with those obtained using conventional integration methods. For particular tasks, the use of higher-order methods can be beneficial. Overall, in comparison with standard approaches, our universal scheme provides a significantly simpler route to devising new integrators and maintaining existing simulation software. Furthermore, our family of new integrators can be efficiently deployed in massively parallel MD software.