NMR Evidence of Cage-to-Cage Diffusion of H$_{2}$ in H$_{2}$-Clathrates

H$_{2}$ and heavy-ice at P$>$1 kbar and T $\sim $250 K form H$_{2}$-D$_{2}$O clathrate; four and one H$_{2}$ may occupy each large (L) and small (S) cage, respectively. In H$_{2}$-THF-H$_{2}$O clathrate, H$_{2}$ occupies singly and only S cages. Previous electronic-structure calculations estimate the barriers for H$_{2}$ passage though hexagonal and pentagonal faces of cages as $\sim $6 and $\sim $25 kcal/mol, respectively. Our H$_{2}$ NMR linewidth data reflect random crystal fields from frozen cage-wall D$_{2}$O orientations. We find dramatic reductions in linewidth starting at 120 K (175 K) for H$_{2}$-D$_{2}$O (H$_{2}$-TDF-D$_{2}$O) indicating time-averaging of the crystal fields. Assuming Arrhenius behavior, our data imply energies for escape from L (S) cages of about $\sim $4 ($\sim $6) kcal/mol. For L cages, the agreement with the calculated (cages were treated as rigid) barrier is reasonable. For H$_{2}$ in S cages, in H$_{2}$-TDF-D$_{2}$O, the extreme disagreement with theory points to another mechanism of time-averaging, reorientations of the cage-wall D$_{2}$O molecules, as suggested by previous work in TDH-H$_{2}$O clathrate. Our limited NMR spectra at high T $\sim $145 K in H$_{2}$-D$_{2}$O show evidence of distinct resonances from diffusionally mobile and immobile H$_{2}$ molecules, as expected.