## 1 Introduction  
A clathrate hydrate is a crystalline inclusion compound with a structure consisting of \"big\" and \"small\" cavities formed from polyhedra. A host lattice is composed of water molecules which are hydrogen bonded, joining the cavities by connections to each cage's vertex [1]. The cavities can, and do, entrap guest atoms and molecules. Type II (also termed \"sII\") hydrates comprise a series of big cavities of type 5\({}^{12}6^{4}\) (featuring 12 faces formed by pentagons, and 6 by hexagons) and small-cavity 5\({}^{12}\) dodecahedra, each featuring 12 water pentamers. In the case of hydrogen hydrates, cavities may hold differing numbers of H\({}_{2}\) molecules [1]. Although on short timescales H\({}_{2}\) guests appear to be trapped permanently in particular cages, it is possible for them to hop between cavities on longer timescales, such that they diffuse throughout the lattice [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. H\({}_{2}\) hydrates are of much practical interest as they display many interesting properties as an attractive material for the storage of hydrogen [13; 14; 15; 16; 17; 18; 19; 20; 21]. At 0.2 GPa, it was determined by [PERSON] et al. that mixtures of hydrogen and water form crystals as sII clathrates with a hydrogen accommodation level of 5.3 wt.% at 0.3 GPa and -23 \({}^{\circ}\)C--not far at all from the ambition of 5.5 wt.% expressed by the United States Department of Energy [21]. In any event, the intra-cage environment of hydrates constitutes an intriguing playground for dissecting the vagaries of caged H\({}_{2}\) behavior, especially spectroscopic and dynamical, which can be strongly quantal in nature, arising from nuclear quantum effects (NQEs) from various possible backgrounds. For instance, the center of mass (c.m.) of the guest molecule(s) is quantized in its translational degrees of freedom (DOFs) as a result of being trapped at the nanoscale in hydrate cavities, whether large or small (i.e., the \"particle-in-a-box\" phenomenon). The rotational DOFs of the hydrogen molecule(s) are quantized as well: these are connected with the potential of the cavities which serve to confine the quantized translational DOFs. This gives rise to sparsity in energy levels in translation-rotation (TR) due to the low mass of H\({}_{2}\), its substantial rotational constant, and the hydrate cages' small size. On the theoretical side, TR eigenstates depict notable properties for a single hydrogen molecule in the ground vibrational state in the cages of sII clathrate hydrate (treated as rigid), and this has been characterized by [PERSON] and co-workers via quantum five-dimensional computations in the bound state [22; 23; 24; 25], alongside calculation to a rigorous standard of the associated inelastic neutron-scattering spectra [26; 27; 28; 29; 30; 31]. For a small-cage-confined H\({}_{2}\) molecule, the sII hydrate theoretical results' key aspects are in quantitative agreement with the inelastic neutron scattering (INS) [32] and rotational Raman spectra [33; 34] of these systems. For up to four vibrational-ground-state hydrogen molecules in the \(5^{12}6^{4}\) cages, their quantum TR dynamics have been probed at T = 0 K via diffusion Monte Carlo [35] and path integral molecular dynamics approaches [2; 36; 3; 4] over a range of temperatures, alongside computations employing full coupling and resolution of eigenstates for two [37; 38] and four caged H\({}_{2}\) molecules [39]. Another spectroscopic manifestation of hydrogen molecule entrapment in clathrate cages is the frequency shift of their H-H stretch vibration vis-a-vis the in vacuo result. This is obvious from Raman-mode analysis for mixed sII tetrahydrofuran/H\({}_{2}\) clathrate, in which the \(5^{12}6^{4}\) cavities are occupied fully by THF whilst single H\({}_{2}\) occupancy of \(5^{12}\) cages is obtained, and also for the case of \"pure\" sII clathrates, wherein H\({}_{2}\) molecules are the sole guests [34; 40].