In the field of materials modelling, traditional atomistic models seldom achieve high accuracy and speed at the same time. Recent developments using high-dimensional fits to approximate the quantum chemical potential energy surface (PES) have overcome this problem. This thesis presents such models for methane–water mixtures, in particular for methane clathrates. Since the discovery of their existence on Earth about half a century ago, methane clathrates have been subject to numerous studies motivated by industrial and environmental perspectives. This project develops atomistic models that describe methane–water interactions with high accuracy. The model development in this work focuses on the dimer and the trimer PESs, which are fitted to quantum mechanical data. The fitting methods used are the Gaussian Approximation Potentials (GAP) [1, 2] and the permutationally invariant polynomials (PIP) [3] methods, the latter applied in collaboration. The long-range electrostatic interactions are calculated using a classical force field, the modified TTM4F [4]. The resulting models are validated against quantum mechanical and experimental data. A clathrate phase diagram is calculated in the quasi-harmonic approximation using the model based on PIPs. As the fitted level, CCSD(T)-F12, is not applicable to larger systems, we compare the calculations to DMC results for the larger clusters and periodic systems. However, small systematic differences are found between the developed models and DMC; comparing different CCSD(T)-F12 versions against DMC, this inconsistency is confirmed to arise from the differences between the two quantum chemical methods. In another collaboration [5], different potential fitting methods are also compared using the same datasets and found to achieve similar accuracies when applied to only the energy differences.