We propose an approximate method for calculating Kubo-transformed real-time correlation functions involving position-dependent operators, based on path integral (Parrinello-Rahman) molecular dynamics. The method gives the exact quantum mechanical correlation function at time zero, exactly satisfies the quantum mechanical detailed balance condition, and for correlation functions of the form C(Ax)(t) and C(xB)(t) it gives the exact result for a harmonic potential. It also works reasonably well at short times for more general potentials and correlation functions, as we illustrate with some example calculations. The method provides a consistent improvement over purely classical molecular dynamics that is most apparent in the low-temperature regime.

Numerous studies have identified large quantum mechanical effects in the dynamics of liquid water. In this paper, we suggest that these effects may have been overestimated due to the use of rigid water models and flexible models in which the intramolecular interactions were described using simple harmonic functions. To demonstrate this, we introduce a new simple point charge model for liquid water, q-TIP4P/F, in which the O-H stretches are described by Morse-type functions.We have parameterized this model to give the correct liquid structure, diffusion coefficient, and infra-red absorption frequencies in quantum (path integral-based) simulations. The model also reproduces the experimental temperature-variation of the liquid density and affords reasonable agreement with the experimental melting temperature of hexagonal ice at atmospheric pressure.By comparing classical and quantum simulations of the liquid, we find that quantum mechanical fluctuations increase the rates of translational diffusion and orientational relaxation in our model by a factor of around 1.15. This effect is much smaller than that observed in all previous simulations of simple empirical water models, which have found a quantum effect of at least 1.4 regardless of the quantum simulation method or the water model employed. The small quantum effect in our model is a result of two competing phenomena. Intermolecular zero point energy and tunneling effects destabilize the hydrogen bonding network, leading to a less viscous liquid with a larger diffusion coefficient. However this is offset by intramolecular zero point motion, which changes the average water monomer geometry resulting in a larger dipole moment, stronger intermolecular interactions, and slower diffusion. We end by suggesting, on the basis of simulations of other potential energy models, that the small quantum effect we find in the diffusion coefficient is associated with the ability of our model to produce a single broad O-H stretching band in the infra-red absorption spectrum.

This article reviews the ring-polymer molecular dynamics model for condensed-phase quantum dynamics. This model, which involves classical evolution in an extended ring-polymer phase space, provides a practical approach to approximating the effects of quantum fluctuations on the dynamics of condensed-phase systems. The review covers the theory, implementation, applications, and limitations of the approximation.

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We further develop the ring polymer molecular dynamics (RPMD) method for calculating chemical reaction rates [I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 122, 084106 (2005)]. We begin by showing how the rate coefficient we obtained before can be calculated in a more efficient way by considering the side functions of the ring-polymer centroids, rather than averaging over the side functions of the individual ring-polymer beads. This has two distinct advantages. First, the statistics of the phase-space average over the ring-polymer coordinates and momenta are greatly improved. Second, the resulting flux-side correlation function converges to its long-time limit much more rapidly. Indeed the short-time limit of this flux-side correlation function already provides a "quantum transition state theory" approximation to the final rate coefficient. In cases where transition state recrossing effects are negligible, and the transition state dividing surface is put in the right place, the RPMD rate is therefore obtained almost instantly. We then go on to show that the long-time limit of the new flux-side correlation function, and hence the fully converged RPMD reaction rate, is rigorously independent of the choice of the transition state dividing surface. This is especially significant because the optimum dividing surface can often be very difficult to determine for reactions in complex chemical systems.