Quantum dynamics of small H₂ and D₂ clusters in the large cage of structure II clathrate hydrate: Energetics, occupancy, and vibrationally averaged cluster structures

We report diffusion Monte Carlo (DMC) calculations of the quantum translation-rotation (T-R) dynamics of one to five para- H₂(p-H ₂) and ortho- D₂ (o-D₂) molecules inside the large hexakaidecahedral (5₁₂₆₄) cage of the structure II clathrate hydrate, which was taken to be rigid. These calculations provide a quantitative description of the size evolution of the ground-state properties, energetics, and the vibrationally averaged geometries, of small (p-H ₂)_n and (o-D₂)_n clusters, n=1-5, in nanoconfinement. The zero-point energy (ZPE) of the T-R motions rises steeply with the cluster size, reaching 74% of the potential well depth for the caged (p-H₂)₄. At low temperatures, the rapid increase of the cluster ZPE as a function of n is the main factor that limits the occupancy of the large cage to at most four H₂ or D₂ molecules, in agreement with experiments. Our DMC results concerning the vibrationally averaged spatial distribution of four D₂ molecules, their mean distance from the cage center, the D₂ - D₂ separation, and the specific orientation and localization of the tetrahedral (D ₂)₄ cluster relative to the framework of the large cage, agree very well with the low-temperature neutron diffraction experiments involving the large cage with the quadruple D₂ occupancy.