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No description available.

In this work, we wish to determine the free energy landscape and the nucleation rate associated with the process of homogeneous ice nucleation. To do this, we simulate the homogeneous nucleation of ice with the mW monatomic model of water and with all-atom models of water using primarily the umbrella sampling rare event method. We find that the use of the mW model of water, which has simpler dynamics compared to all-atom models of water, but is nevertheless surprisingly good at reproducing experimental data, results in very reasonable agreement with classical nucleation theory, in contrast to some previous simulations of homogeneous ice nucleation. We suggest that previous simulations did not observe the lowest free energy pathway in order parameter space because of their use of global order parameters, leading to a deviation from classical nucleation theory predictions. Whilst monatomic water can nucleate reasonably quickly, all-atom models of water are considerably more difficult to simulate, primarily because of their slow dynamics of ice growth and the fact that standard order parameters do not work well in driving nucleation when such models are being used. In this thesis, we describe a local, rotationally invariant order parameter that is capable of growing ice homogeneously in a biassed simulation without the unnatural effects introduced by global order parameters, and without leading to non-physical chain-like growth of 'ice' clusters that results from a naïve implementation of the standard Steinhardt-Ten Wolde order parameter. We have successfully used this order parameter to force the growth of ice clusters in simulations of all-atom models of water. However, although ice growth can be achieved, equilibrating simulations with all-atom models of water is extremely difficult. We describe several approaches to speeding up the equilibration in all-atom models of water to enable the computation of free energy profiles for homogeneous ice nucleation.