Ring polymer molecular dynamics
This thesis presents the ring polymer molecular dynamics (RPMD) approximation to the Kubo-transformed time correlation function and shows how it may be used as the basis of an approximate quantum-mechanical method for determining the dynamical properties of condensed-phase molecular systems. The performance of the RPMD method is initially investigated by calculating the position (qˆ), and position-cubed (qˆ3), autocorrelation functions of a series of onedimensional potential wells of varying anharmonicity. It is then applied to the evaluation of the incoherent dynamic structure factors of liquid para-hydrogen at 14 K. Finally, the RPMD method is used to determine canonical rate coefficients for two onedimensional models of bimolecular chemical reactions and a multidimensional model of a solution-phase proton transfer reaction. For each application, the accuracy of the RPMD method is established by comparison with exact quantum-mechanical results and/or with experiment. Throughout this work, an emphasis is placed upon identifying the situations in which the RPMD approximation breaks down. It is found that the RPMD method is capable of providing an accurate approximation to the time correlation functions of a variety of condensed-phase molecular systems. Situations for which it is inaccurate include correlation functions which correlate highly nonlinear operators and those involving significant quantum interference effects in the real-time dynamics.