| This thesis comprises two projects that investigate vibrational energy relaxation (VER), and symmetric proton tunneling.;In the first project, we investigate the pathways of VER in the molecule iso-chloroiodomethane embedded in a matrix of argon at 12K, motivated by the experimental studies of Crim and coworkers. We study this relaxation theoretically using molecular dynamics by considering two and three dimensional models. Multiple decay rate constants of the same order of magnitude as the experiment are observed. These decay rate constants are interpreted within the context of the Landau-Teller theory. Sensitivity of the decay rate constants on the bath and system parameters shed more light into the mechanism of VER.;The second project focuses on proton tunneling, which plays a central role in many biological reactions. We investigate a three dimensional model Hamiltonian coupled to a harmonic bath that describes concerted proton transfer in formic acid dimer. The three modes provide a paradigm for the symmetric and anti-symmetric coupled tunneling pathways. The effects of temperature and coupling to the bath on the rates are presented. We compare three methods that have been shown previously to provide good results for the tunneling dynamics -- surface hopping, ring polymer molecular dynamics, and the Makri-Miller method. We find that surface hopping and ring polymer molecular dynamics do not describe some aspects of the dynamics in the deep tunneling regime due to neglect of the coherence effects. Certain modifications in the surface hopping algorithm are suggested to partially include these coherences. The Makri-Miller method predicts the correct trends for the tunneling splittings, which govern the dynamics.;In addition, we also develop a new method to compute tunneling splittings for highly excited states. This method is based on making an adiabatic approximation to the Herring estimate, and is in excellent agreement with the exact results. |
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