Structure, stability and reactivity of clathrate hydrates with or without hydrogen encapsulation are studied using standard density functional calculations. Conceptual density functional theory based reactivity descriptors and the associated electronic structure principles are used to explain the hydrogen storage properties of clathrate hydrates. Different thermodynamic quantities associated with H2-trapping are also computed. The stability of the H2-clathrate hydrate complexes increases upon the subsequent addition of hydrogen molecules to the clathrate hydrates. The efficacy of trapping of hydrogen molecules inside the cages of clathrate hydrates depends upon the cavity sizes and shapes of the clathrate hydrates. Computational studies reveal that 512 and 51262 structures are able to accommodate up to two H2 molecules whereas 51268 can accommodate up to six hydrogen molecules.