Velocity jump processes: An alternative to multi-timestep methods for faster and accurate molecular dynamics simulations.

We propose a new route to accelerate molecular dynamics through the use of velocity jump processes allowing for an adaptive time step specific to each atom-atom pair (two-body) interactions. We start by introducing the formalism of the new velocity jump molecular dynamics, ergodic with respect to the canonical measure. We then introduce the new BOUNCE integrator that allows for long-range forces to be evaluated at random and optimal time steps, leading to strong savings in direct space. The accuracy and computational performances of a first BOUNCE implementation dedicated to classical (non-polarizable) force fields are tested in the cases of pure direct-space droplet-like simulations and of periodic boundary conditions (PBC) simulations using Smooth Particle Mesh Ewald method. An analysis of the capability of BOUNCE to reproduce several condensed-phase properties is provided. Since electrostatics and van der Waals two-body contributions are evaluated much less often than with standard integrators using a 1 fs time step, up to a 400% direct-space acceleration is observed. Applying the reversible reference system propagator algorithms [RESPA(1)] to reciprocal-space (many-body) interactions allows BOUNCE-RESPA(1) to maintain large speedups in PBC while maintaining precision. Overall, we show that replacing the BAOAB standard Langevin integrator by the BOUNCE adaptive framework preserves a similar accuracy and leads to significant computational savings.