Computationally efficient molecular dynamics integrators with improved sampling accuracy

The design of numerical integrators for particle simulations with arbitrary potentials entails fundamental trade-offs between the accuracy achieved and the amount of computation required. Here we introduce a class of explicit variational integrators designed to achieve high accuracy for quadratic potentials, with little additional computation relative to traditional integrators. We show that, in practice, these new integrators also improve accuracy for classical biomolecular simulations, since the potential in the vicinity of a typical trajectory point in such a simulation is generally well modelled by a quadratic well. In particular, these integrators provide better sampling accuracy for biomolecular simulation than the commonly used Verlet integrators, as indicated by a weaker dependence of simulated ensemble properties on the time step. They also reduce short-timescale energy fluctuations, thus substantially improving the efficiency of Hybrid Monte Carlo methods, and are easy to implement through straightforward modification of codes based on Verlet integrators.