  In this thesis, we use classical, semi-classical and quantum-mechanical
methods to simulate chemical reaction dynamics inside of an optical cavity.
Within such a cavity, by selectively coupling vibrational modes of the
reactants to the vacuum state of light, recent experiments have observed
significant changes in reaction rates and equilibrium constants - all without
any external input of energy. We investigate the dynamics of both a single
reaction and an ensemble of N identical reactions coupled to the cavity. In our
single reactant studies, we find significant modification to the rate of
reaction and to its quantum-mechanical equilibrium constant. All of the effects
observed in our single molecule studies are however found to diminish as the
number of reactants is increased. For any experimentally relevant number of
molecules, the cavity effects on the reaction rate and the equilibrium constant
are therefore shown to be negligible within all theories considered in this
thesis. This thesis therefore does not offer any explanation for the
experimental observations. It does however highlight issues with all current
theoretical work on this topic, and provides suggestions - in light of the
results presented here and in recent literature - as to what might be required
to explain these effects.
