Structure II clathrate hydrates of pure hydrogen and binary hydrates of THF + H2 are studied using ab initio calculations to determine the stable occupancies of small cavities. Ab initio calculations are carried out for a double cavity consisting of one dodecahedron (small cavity) and one hexakaidecahedron (large cavity). These two cavities are attached to each other as in sIIhydrates to forma double cavity. One or twoH2 molecules are placed in the small cavity and one THF (or 4H2 molecules) molecule is placed in the large cavity.We have determined the binding energies of the double cavities at the MP2 level using various basis sets (3-21G, 3-21G(2p), 3-21++G(2p), 6-31G, 6-31G(2p), and 6-31++G(2p)). Different basis sets yield different stable occupancies of the small cavity. The results from the highest basis set (6-31++G(2p) with zero point energy corrections) indicate that the single occupancy is slightly more favorable than the double occupancy in both the cases of pure H2 hydrates and THF + H2 double hydrates.