Hydrogen clathrates have garnered increased interest as economically safe materials for hydrogen storage, but understanding the gas diffusion process continues to be unresolved. This is attributed to limited experimental evidence elucidating cage occupancy, insufficient descriptions of the molecular interactions, and conflicting theoretical evidence for rates of diffusion. Given the encapsulation of hydrogen gas in confined cages coupled with the low temperatures needed to study the frameworks, a quantum description of the molecules is required.

In this thesis, a fully quantum statistical-mechanical study of hydrogen gas diffusion in the structure type II (sII) clathrate hydrate is presented using molecular simulation. To address many of the above concerns, this dissertation details new techniques in quantum statistical mechanics. The complex molecular environment is described by a machine-learned potential energy surface based on high-level quantum calculations. Quantum rate theory, using exact quantum statistics and approximate quantum dynamics, is applied in calculating diffusion rates. Finally, chemical potentials and free energy barriers of varying cage occupancies are determined using enhanced sampling path integral methodologies.