A Formulation of the Ring Polymer Molecular Dynamics

The exact formulation of the path integral centroid dynamics is extended to include composites of the position and momentum operators. We present the generalized centroid dynamics (GCD), which provides a basis to calculate Kubo-transformed correlation functions by means of classical averages. We define various types of approximate GCD, one of which is equivalent to the ring polymer molecular dynamics (RPMD). The RPMD and another approximate GCD are tested in one-dimensional harmonic system, and it is shown that the RPMD works better in the short time region.