How to remove the spurious resonances from ring polymer molecular dynamics

Abstract

Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the desirable features of RPMD: thermostatted RPMD (TRPMD) is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.

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Cited by in corpus (10)

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• Boltzmann-conserving classical dynamics in quantum time-correlation functions: Matsubara dynamics
• Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics
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• Simultaneous Deep Tunneling and Classical Hopping for Hydrogen Diffusion on Metals
• Stability of Complex Biomolecular Structures: Vander Waals, Hydrogen Bond Cooperativity, and Nuclear Quantum Effects
• Nuclear quantum effects in water exchange around lithium and fluoride ions
• "Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems
• State Dependent Ring Polymer Molecular Dynamics for Investigating Excited Nonadiabatic Dynamics
• From Classical to Quantum and Back: Hamiltonian Adaptive Resolution Path Integral, Ring Polymer, and Centroid Molecular Dynamics