This proposal deals with the clathrate hydrates in which guest methane molecule is trapped inside the polyhedral cages formed by the network of hydrogen-bonded water molecules. The interest in these systems arises from the possibility that methane hydrate may be a major energy resource in the future and the role it could play in past and future climate changes. This project proposes a first rigorous and thorough theoretical investigation of the quantum dynamics of methane molecule confined inside the clathrate hydrate. Therefore, full dimensional quantum calculations of the translation-rotational energy levels and wave functions will be performed for the methane molecule trapped inside the small and medium cages of the clathrate hydrate. The results will be incorporated in the statistical mechanics models which will lead in more reliable predictions of the macroscopic properties of methane hydrates such is thermodynamic stability under wide range of conditions. The results of the proposed research stay will contribute to a detailed interpretation of the available experimental results and enhance the understanding of some key aspects of methane hydrates as potential energy resources.