The primary focus of this thesis is to study the impact of incorporating helium atoms into hydrostructures, spanning from clathrate-like and ice-like clusters up to complete periodic crystalline systems. Noble-gas hydrates are of particular interest, due to their ability to keep trapped such inert gases. The recent synthesis of some noble gas (Ne, He) clathrate hydrates and the previously reported presence of He in ice frameworks, as well as their potential implication in the stabilization and discovery of new low-density ices, combined with the limited information available on such hydrates, serve as strong motivations to expand our understanding of these relatively unexplored systems. One of the main features of these He-filled structures is the stability conferred by the weak van der Waals dispersion forces occurred between the host lattice and the guest atoms (noble gas in our case), in addition to the hydrogen bonds established among the water molecules. Hence, it is crucial to have reliable reference data in order to accurately describe these interactions. As a result, the first part of this thesis is devoted to the systematic examination of the performance and accuracy of various conventional and modern DFT functionals, as well as available analytical model potentials, in comparison with high-level, well-converged wave function-based datasets. In this manner, benchmark reference datasets for He@hydrate frameworks are gathered and utilized to identify the computationally viable, best-performing DFT functionals. Minimum and non-minimun configurations of a selection of clathrate-like and ice-like fundamental units and building blocks are considered in order to ensure a correct characterization of the underlying forces in repulsive, near-equilibrium, and asymptotic/long-range regions of the full potential energy surface. As the quality of the data has profound implications on the development of models, the outcome of such benchmark studies becomes essential guidance for forthcoming new chem-informatics potentials and force-fields models. Enthalpy, Gibbs free energy and entropy are practical and important thermodynamic properties, that provide valuable information about the course of a formation/dissociation reaction. The second part of this thesis involves utilizing first-principles DFT approaches to analyse the variations in H, G, and S under different T-P conditions, specifically focusing on the encapsulation of He atoms within sII clathrate-like cages, both individual or connected to their neighbor cage, and ice II/ice XVII individual channels. Moreover, we investigate the feasibility of including an increased number of He atoms inside the different size cages of the sII structure, assessing structural and energetic properties such as binding or evaporation energies. The idea of this investigation is to determine whether it is viable to obtain a meaningful and orientative initial estimate regarding the thermodynamic feasibility and spontaneous nature of the formation process of He-filled clathrate/ice structures through the analysis of finite-size clathrate-like and ice-like cluster frameworks
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