## 3 Results and Discussion  
After examining D\({}_{2}\)-guest structural distributions first [11; 23], isosurface plots for both large and small cages and for both classical and path integral molecular dynamics simulations are plotted below. Because no single isosurface can capture the full extent of the three-dimensional density data, we chose to use two isosurfaces for each case: one at 5% the density maximum (in light transparent grey) and one at 10% the density maximum (in darker grey). Turning to classical results, we observed that for guest D\({}_{2}\) molecules in the singly occupied small 5\({}^{12}\) cages, their centre of masses (COMs) were distributed close to the cage-centres with no discernible anisotropy. The large 5\({}^{12}\)6\({}^{4}\) cages, which were each occupied by two D\({}_{2}\) guest molecules, showed much more structure in their COM positions. The guest molecule COMs were preferentially located in tetrahedrally-oriented sites, one behind the centre of each of the large cage's four hexagonal faces. There was also significant population at off-tetrahedral sites, with the density isosurface taking on a somewhat cubic shape overall. Additionally, there was some population at the centre of each hexagonal face, which were shared by large cage pairs. Turning to the path-integral results, we observed that the guest density in the small cages was practically identical to the classical results, where the guest centre of masses confined to the cage-centre region. Although similar to the classical results, there was a more observable difference for the large cage results (i.e., the off-tetrahedral locations appear more heavily populated, such that the density within the large cages appears almost symmetrically distributed along the eight vertices of a cube). For the reader's closer reference, Gaussian-type 'cube' files are provided as part of Supplementary Material for both classical and PIMD spatial density results. Further details on temperature and occupation effects on the nature of quantum and classical spatial distributions of such D\({}_{2}\) and H\({}_{2}\) guests in the 51264 cages have been outlined (in detail) in reference [11]. In brief, the present results for double occupation are, by and large, compatible with 100 K results in reference [11], sampled from high-fidelity Density-Functional Theory (DFT) calculations; indeed, the H\({}_{2}\)-water potential model, optimised for hydrogen hydrates was developed using such DFT calculations [27]. In essence, for H\({}_{2}\) occupancies of 1 to 5 at 50, 100 and 200 K, the guests' density isosurfaces showed how the density became more or less perfect during the quadruple occupation [11] (which is in accord with the findings of Figure 1 in the present work). When temperature increased, the extent of delocalisation increases (and not just for the guests), serving to'smear' the intra-cage iso-densities more greatly [11]. This resulted in slightly less well-defined adherence to the tetrahedral sites and, to a greater extent, off-site spatial density [11]. In terms of these singly occupied 512 cages, using the orthonormal tetrahedral-vector approach above to identify local-axis systems therein from both classical and path-integral MD, there was no real preferred orientations of the D-D axis in its angular histogram in  
Figure 1: Spatial density isosurface plots (0.1 Å) at 100 K in singly and doubly occupied small and large cages. either case, which indicates no preferred local orientational alignment and relatively free rotational motion. In terms of free energies of the guests, and on related energy barriers (as mentioned previously), our previous work in references [11; 19; 27] established that H\({}_{2}\) occupations of 2 or 3 in 51,264 cages were the most thermodynamically feasible. It was also found that such free energy terms were lower in the classical case than for the quantum case, owing to quantal delocalisation increasing these terms.