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 H-2-trapping are also computed. The stability of the H-2-clathrate hydrate complexes increases upon the subsequent addition of hydrogen molecules to the clathrate hydrates. The efficacy of trapping hydrogen molecules inside the cages of clathrate hydrates in an endohedral fashion depends upon the cavity sizes and shapes of the clathrate hydrates. Computational studies reveal that 5(12) and 5(12)6(2) structures are able to accommodate up to two H-2 molecules whereas 5(12)6(8) can accommodate up to six hydrogen molecules. Adsorption and desorption rates conform to that of a good hydrogen storage material.