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We perform the lattice dynamical simulation studies of hydrate host lattice interacting with Xe, Ar, and N,2 atoms/molecules. The calculated results show that the well-defined peaks (2.0meV and 3.8meV) and another peak (6.2meV) are assigned to the vibrations of N,2 molecules in large and small cages, respectively. It is confirmed that the double N,2 molecule occupancies of large cage lead to filling of the mode gap between the small cage and the large cage.