Hydrogen molecules in the small dodecahedral cage of a clathrate hydrate: Quantum translation-rotation dynamics of the confined molecules

We report the results of a rigorous theoretical study of the quantum translation-rotation (T-R) dynamics of one, two, and three H₂ and D₂ molecules confined inside the small dodecahedral (H ₂O)₂₀ cage of the sII clathrate hydrate. For a single D₂ molecule, o- and p-D₂, in the small cage, accurate quantum five-dimensional (5D) calculations of the T-R energy levels and wave functions are performed by diagonalizing the 5D Hamiltonian which includes explicitly, as fully coupled, all three translational and the two rotational degrees of freedom of D₂, while the cage is taken to be rigid. These calculations provide a quantitative description of the quantum dynamics of D₂ inside the small cage and enable comparison with our quantum 5D results for the encapsulated H₂, p- and o-H₂, published very recently. The ground-state properties of one, two, and three p-H ₂ and o-D₂ molecules in the small cage are calculated rigorously using the diffusion Monte Carlo method, with the emphasis on the quantum dynamics of two confined hydrogen molecules. The guest molecules are found to be effectively excluded from the sizable central region of the cage; they reside within a shell less than 2 bohrs wide and are additionally localized by the corrugation of the H₂-cage interaction potential. The two H₂ molecules are compressed, their mean distance inside the cage being much smaller than in the free H₂ dimer.