The vibrational frequency shift of H-2 in the 5(12) cage of the sII clathrate hydrate with and without surrounding water molecules is reported at 0 K, using diffusion Monte Carlo calculations for the ground and first excited vibrational states of H-2. Approximate Id calculations of the frequency shift are also reported with the H-2 at the equilibrium position in the clathrate hydrate. These calculations make use of full-dimensional potential energy surfaces for the H-2-H2O 2-body and H-2-H2O-H2O 3-body interactions. The inclusion of the 3-body interaction is shown to make roughly a 33% contribution to the frequency shift and to bring the calculated value of -40 +/- 4 cm(-1) to within just 3 cm(-1) of the experimental value at 20 K. This level of agreement with experiment may be somewhat fortuitous; however, the importance of the 3-body interaction is firmly established by these calculations. The frequency shift reported here with 2-body interactions does not agree with a previously reported calculation using just 2-body interactions from a different ab initio potential energy surface and with a different method to obtain the frequency shift. A similar Id calculation of the frequency shift using that potential is reported and agrees to within roughly 10% of the one previously reported. Therefore, this suggests that the difference between the present calculations and the previous one using just 2-body interactions is mainly due to differences in the potential energy surfaces.