In order to study computationally increasingly complex systems using theoretical methods model Hamiltonians are required to accurately describe the potential energy surface they represent. Also ab-initio methods improve the calculation of the excited states of these complex systems becomes increasingly feasible. One such model Hamiltonian described herein, the Vibronic Coupling Hamiltonian, has previously shown its versitility and ability to describe a variety of non-adiabatic problems. This thesis describes a new method, a genetic algorithm, for the parameterisation of the Vibronic Coupling Hamiltonian to describe both previously calculated potential energy surfaces (allene and pentatetraene) and newly calculated (cyclo-butadiene and toluene) potential energy surfaces. In order to test this genetic algorithm quantum nuclear dynamics calculations were performed using the multi-configurational time dependent hartree method and the results compared to experiment
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