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.

Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges

“…The latter problem can be mitigated by attaching thermostats to the internal modes of the ring polymer, a technique that can be seen as being half-way between RPMD and CMD (236). In fact, one can see that as long as one avoids stepping outside of each method's comfort zone, CMD and thermostated RPMD give results that are consistent with each other and with methods based on a quantum description of a subset of the degrees of freedom (236).…”

“…The latter problem can be mitigated by attaching thermostats to the internal modes of the ring polymer, a technique that can be seen as being half-way between RPMD and CMD (236). In fact, one can see that as long as one avoids stepping outside of each method's comfort zone, CMD and thermostated RPMD give results that are consistent with each other and with methods based on a quantum description of a subset of the degrees of freedom (236). NQEs are indispensable if one wants to achieve a quantitatively-accurate description of the dynamical properties of water, but the differences between the various methods are comparable to those one should expect from performing simulations on an imperfect potential energy surface.…”

Hydrogen dynamics in solid formic acid: insights from simulations with quantum colored-noise thermostats

“…A natural extension of this methodology would employ more advanced and accurate approaches, e.g. thermostatted ringpolymer molecular dynamics (TRPMD) [74,75]. A way of reducing the computational cost of TRPMD has been proposed by Kapil et.…”

Competing quantum effects in the free energy profiles and diffusion rates of hydrogen and deuterium molecules through clathrate hydrates

“…In particular, the computation of realistic diffusion rates which can be compared to experimental results will require calculation of the quantum free-energy barriers and diffusion rates for a wide range of H 2 and D 2 occupancies of clathrate cages, and averaging over them. Computation of transmission coefficients may require advanced thermostatting techniques [75][76][77] in order to enhance statistical sampling. Diffusion through the pentagonal faces connecting small and large clathrate cages will also be investigated, as will be the effect of nuclear spin statistics…”