This thesis is concerned primarily with the effect of environmental degrees of freedom upon molecular quantum systems. Such systems, when isolated from external influence, evolve according to the Schrodinger equation. However, interaction with an environment alters the dynamics of these systems giving rise to decoherence (and/or dephasing) which destroys the systems quantum coherence. The Redfield approach is adopted to model the effect of such an environment upon both harmonic oscillator systems and systems which are governed by doubleminimum potential functions in Chapters 3 and 4 of this thesis. Here, Boltzmann wavepackets, which possess thermodynamic ensemble average characteristics, are employed to investigate quantum mechanical tunnelling in ammonia and cyanamide systems both isolated from and interacting with an environment. In Chapter 5, the inversion mode vibration of the hydrogen-bonded complex 2,5-DHF· · -HCCH is modelled extensively by ab initio computational methods and is found to exhibit intriguing behaviour. Complexes of the type 2,5-DHF· • -HX are often modelled with a planar 2,5-DHF ring. This assumption is based upon the principle of unperturbed components which states that the hydrogen-bond complexation of two subunits does not effect the geometry of either of the subunits. This principle is questioned by the results of Chapter 5. The vibrational eigenstate structure of 2,5-DHF-• -HCCH is explored in Chapter 6 using three different models for the reduced moment of inertia. Each model yields results which are in good agreement with the experimental studies of Cole, Hughes and Legon. The small o+ -o-splitting of this complex(~ 10-7 cm-1) leads to a slow tunnelling timescale(~ 10-5 s) in which an entire HCCH fragment tunnels between different spatial domains. Redfield theory is applied to the inversion vibration of this complex towards the end of Chapter 6.