Classical equilibrium molecular dynamics simulations have been performed to investigate dynamical properties of cage radial breathing modes and intra- and inter-cage hydrogen migration in both pure hydrogen and mixed hydrogen-tetrahydrofuran sII hydrates at 0.05 kbar and up to 250 K. For the mixed H_2-THF system in which there is single H_2 occupation of the small cage (labelled "1SC 1LC"), we find that no H_2 migration occurs, and this is also the case for pure H_2 hydrate with single small-cavity occupation and quadruple occupancy for large cages (dubbed "1SC 4LC"). However, for the more densely filled H_2-THF and pure-H_2 systems, in which there is double H_2 occupation in the small cage (dubbed "2SC 1LC" and "2SC 4LC," respectively), there is an onset of inter-cage H2 migration events from the small cages to neighbouring cavities at around 200 K, with an approximate Arrhenius temperature-dependence for the migration rate from 200 to 250 K. It was found that these "cage hopping" events are facilitated by temporary openings of pentagonal small-cage faces with the relaxation and reformation of key stabilising hydrogen bonds during and following passage. The cages remain essentially intact up to 250 K, save for transient hydrogen bond weakening and reformation during and after inter-cage hydrogen diffusion events in the 200-250 K range. The "breathing modes," or underlying frequencies governing the variation in the cavities' radii, exhibit a certain overlap with THF rattling motion in the case of large cavities, while there is some overlap of small cages' radial breathing modes with lattice acoustic modes.
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