Hamiltonian based resonance-free approach for enabling very large time steps in multiple time-scale molecular dynamics

Extended phase-space isokinetic methods in their deterministic [Minary et al., Phys. Rev. Lett. 93, 150201 (2004)] and stochastic forms [Leimkuhler et al., Mol. Phys. 111, 3579 (2013)] have proved tremendously successful in allowing multiple time-scale molecular dynamics simulations to be performed with very large time steps. These methods work by coupling the physical degrees of freedom to a set of Nose-Hoover chain or Nose-Hoover Langevin thermostats via an isokinetic constraint, which has the effect of avoiding resonance artifacts that plague multiple time-step algorithms. In this paper, we introduce a new resonance-free approach that achieves the same gains in time step but without the imposition of isokinetic constraints or the introduction of extended phase-space variables. Rather, we modify the physical Hamiltonian that effects the same regulation of resonances achieved by the isokinetic constraints. In so doing, we show that sampling errors can be controlled and performance improvements are possible within a simpler Hamiltonian framework. The method is demonstrated in simulations of the structure of liquid water and, in conjunction with enhanced sampling, in generation of the Ramachandran free-energy surface of the solvated alanine dipeptide.