We present a detailed theoretical characterization of the structure and interactions in dichlorine clathrate hydrate cages. In the case of the dodecahedral cage there is clear evidence of the presence of halogen bonding whereas in the tetrakaidecahedral the expected signatures are there but in a weaker form. Comparison is made with the available structural data from X-ray experiments, where the rotational motion of the dichlorine has been taken into account through Monte Carlo simulations illustrating delocalization effects associated with sampling multiple minima, specifically for the larger cage. Finally, the intermolecular potentials have been calculated with local correlation methods and energy decomposition analysis has been applied to shed light on the nature of the interactions.