Overcoming instabilities in Verlet-I/r-RESPA with the mollified impulse method

Abstract. The primary objective of this paper is to explain the derivation of symplectic mollified Verlet-I/r-RESPA (MOLLY) methods that overcome linear and nonlinear instabilities that arise as numerical artifacts in Verlet-I/r-RESPA. These methods allow for lengthening of the longest time step used in molecular dynamics (MD). We provide evidence that MOLLY methods can take a longest time step that is 50 % greater than that of Verlet-I/r-RESPA, for a given drift, including no drift. A 350 % increase in the timestep is possible using MOLLY with mild Langevin damping while still computing dynamic properties accurately. Furthermore, longer time steps also enhance the scalability of multiple time stepping integrators that use the popular Particle Mesh Ewald method for computing full electrostatics, since the parallel bottleneck of the fast Fourier transform associated with PME is invoked less often. An additional objective of this paper is to give sufficient implementation details for these mollified integrators, so that interested users may implement them into their MD codes, or use the program ProtoMol in which we have implemented these methods