| সংক্ষিপ্ত: | <p>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.</p> <p>The performance of the RPMD method is initially investigated by calculating the position (<em>q<sup>ˆ</sup></em>), and position-cubed (<em>q<sup>ˆ3</sup></em>), 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.</p> <p>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.</p>
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