A comparative study of the centroid and ring-polymer molecular dynamics methods for approximating quantum time correlation functions from path integrals

The problems of ergodicity and internal consistency in the centroid and ring-polymer molecular dynamics methods are addressed in the context of a comparative study of the two methods. Enhanced sampling in ring-polymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations. It is shown that this approach converges more rapidly than periodic resampling of velocities from a single long RPMD run. Dynamical quantities obtained from RPMD and centroid molecular dynamics (CMD) are compared to exact results for a variety of model systems. Fully converged results for correlations functions are presented for several one dimensional systems and para-hydrogen near its triple point using an improved sampling technique. Our results indicate that CMD shows very similar performance to RPMD. The quality of each method is further assessed via a new 2 descriptor constructed by transforming approximate real-time correlation functions from CMD and RPMD trajectories to imaginary time and comparing these to numerically exact imaginary time correlation functions. For para-hydrogen near its triple point, it is found that adiabatic CMD and RPMD both have similar 2 error.