## 1 Introduction
have carried out sophisticated Raman-type analysis of hydrogen hydrates with state-of-the-art ab initio molecular-dynamics (AIMD) simulation and Raman experiments--although the AIMD was propagated classically [22]. Very recently, [PERSON] et al. carried out inelastic neutron scattering (INS) measurements of quantum dynamics of D\({}_{2}\) and H\({}_{2}\) molecules confined in pure- and binary-hydrate structures (helium in the latter case), determining [23] and assessing molecular quantal rotation and translations. [PERSON] and co-workers made substantial recent advances in more rigorous 6- and 8-D quantum treatments of singly and doubly occupied sII-hydrate cages [24; 25]. In particular, the INS studies of reference [23] suggest that the large cage in sII hydrogen hydrates is rarely more than doubly occupied, with average occupancies of circa 1.5-1.8 at kilobar pressures (and 0.85-1 for 512 cages), while reference [11] predicted that singly occupied 512 and doubly or triply occupied 51264 cages are more energetically realistic across a range of temperatures and cavity occupancies. These findings more reasonably accord with the subsequently reported INS findings [23]. Given these careful intra-cage phenomena studies of references [11; 19; 20; 21; 22; 23; 24; 25] and others, we concluded that the weight of most recent scientific evidence, from both experiment and theory, supports the view that we can (and probably should) use single- and double-H\({}_{2}\) and D\({}_{2}\) occupations of the small and large sII hydrate cavities, respectively, as being reasonable and ripe for further detailed study. Keeping this mandate in mind (i.e., to study in further detail intra-cage phenomena for singly- and doubly occupied small and large sII-lattice cages, respectively), we noted that the tetrahedral structure of intra-cage'sites' to accommodate guest molecules for various large-cage occupancies within sII-hydrate 51264 cages is less well characterised in the literature. However, reference [11] showed (from AIMD) a range of probable spatial distributions for likely H\({}_{2}\) positions in large cages. Further analysis is warranted for the doubly occupied case, in particular the study of nuclear quantum effects impacting these positions. Moreover, although reference [26] reported some interesting quasielastic neutron scattering (QENS) measurements of classical \"jump-diffusion\" dynamics between these sites, reference [23] examined this from a quantum perspective for lower-temperature behaviour, where assumptions of classical site-site hopping are more questionable. In this study, we sought to investigate further tetrahedral-site distributions for doubly occupied large cages using path-integral dynamics to incorporate nuclear quantum effects at 100 K. Unlike our previous work in references [11; 19; 27], in which occupancy of the 51264 cavities was an important consideration, in this study we emphasised again that the overwhelming (and very recent) consensus of the state-of-the art experiment and molecular simulation is definitively in favour of no more than double occupation of such cages as being routinely feasible. Keeping this in mind, we focused on doubly occupied cavities in the present contribution. Having studied such quantum site structural distributions for such doubly occupied \(5^{12}6^{4}\) cages, we then proceeded to assess further dynamical vibrations and intra-cage diffusive motion between these sites, as well as relaxation of residence time distributions thereat as a function of temperatures (80-125 K) where classical effects are dominant (i.e., above 50 K) [23, 26].