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Clathrate hydrates hold considerable promise as safe and economical materialsfor hydrogen storage. Here we present a quantum mechanical study of H$_2$ andD$_2$ diffusion through a hexagonal face shared by two large cages of clathratehydrates over a wide range of temperatures. Path integral molecular dynamicssimulations are used to compute the free-energy profiles for the diffusion ofH$_2$ and D$_2$ as a function of temperature. Ring polymer molecular dynamicsrate theory, incorporating both exact quantum statistics and approximatequantum dynamical effects, is utilized in the calculations of the H$_2$ andD$_2$ diffusion rates in a broad temperature interval. We find that the shapeof the quantum free-energy profiles and their height relative to the classicalfree energy barriers at a given temperature, as well as the rate of diffusion,are profoundly affected by competing quantum effects: above 25 K, zero-pointenergy (ZPE) perpendicular to the reaction path for diffusion between cavitiesdecreases the quantum rate compared to the classical rate, whereas at lowertemperatures tunneling outcompetes the ZPE and as result the quantum rate isgreater than the classical rate.

Competing quantum effects in the free energy profiles and diffusion rates of hydrogen and deuterium molecules through clathrate hydrates