This thesis is concerned with the development of a quantum dynamical description of large amplitude vibrations in molecules. The evolution of wavepackets are studied and often reconciled with the frequency domain description of such vibrations. Boltzmann wavepackets possessing thermodynamic ensemble average characteristics are introduced and their behaviour analyzed in terms of transitions between thermally populated stationary states of the system. Quantum mechanical tunnelling associated with large a mplitude vibrations is a well known phenomenon and is studied in this thesis by, a) an alyzing the propagation of Boltzmann wavepackets, and b) analysis of an ensemble of quantum trajectories associated with a Gaussian distribution of initial positional coordinates on the periodic and non-periodic potential functions that describe large amplitude vibrations.