## 3 Result and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Cage Type**} & \multirow{2}{*}{**Structure**} & \multicolumn{3}{c}{**Travel Possibility/Cage**} & \multirow{2}{*}{**Cage Number/Unit Cell**} & \multicolumn{3}{c}{**Travel Possibility/Unit Cell**} \\ \cline{3-4}  & & **LL** & **SL/LS** & **SS** & & **LL** & **SL/LS** & **SS** \\ \hline Large & 5\({}^{12}6^{4}\) & 4 & \multirow{2}{*}{12} & - & 8 & 14.28\% & 42.85\% & 42.85\% \\ \cline{1-1} \cline{5-7} Small & 5\({}^{12}\) & - & & 6 & 16 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hydrate type II structural information and hopping-path possibilities. The diffusion between two large cages or between two small cages is labelled as LL and SS, respectively. Diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled as LS and SL, respectively. Figure 3: Averaged cage radius with respect to the temperature for (**a**) hydrogen (**b**) deuterium large cage occupancies, and (**c,d**) are for small cage occupancies for hydrogen and deuterium, respectively. Figure 4: Cage occupancy averages vs temperature for large-cage occupancies (**a**) and small-cage occupancies (**b**) for hydrogen and deuterium. Figure 5: Schematic of a Markov model for internal cage hopping in clathrate hydrate. The diffusion between two large cages or between small cages is labelled as LL and SS, respectively. Diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled LS and SL, respectively. The inter-cage hopping also depends upon the number of guest molecules present in the large cage, as well as their underlying (cage-hopping-dominated) [36] self-diffusivity. SL and LS showed almost the same probability in inter-cage hopping. The results of the inter cage hopping are illustrated in Figure 6, and the detailed tables are given in Tables S1 and S2 in the SI Section for H\({}_{2}\) and D\({}_{2}\), respectively. As discussed previously (Figure 4) in the systems with one or two occupancies, the cage radius is quite similar; therefore, lowering the number of molecules in the larger cages in the double-occupancy case will result in the lower flexibility of the cage structure, and serves to limit small-to-small (SS) cage-hop transitions in the case of higher-occupancy models. However, at a higher occupancy, the larger cage size (i.e., subject to cage deformation), owing to the larger number of guest molecules in the large cages, serves to rationalise the higher level of SL and LS migrations observed in Figure 6c,d. Figure 6: The inter-cage hopping with respect to the temperature. The results of the different systems—1-occupancy (**a**), 2-occupancy (**b**), 3-occupancy (**c**) and 4-occupancy (**d**)—for the model with H\({}_{2}\) molecules as the guests are reported with solid colours, and hashed colours were used to present the results for the D\({}_{2}\)-containing model. The diffusion between two large cages or between small cages is labelled as LL and SS, respectively. The diffusion from a large cage to a small cage, and from a small cage to a large cage is labelled as LS and SL, respectively.