We examined the formation of Intrinsically Localized Modes (ILMs) for a pair of harmonic phonons along the direction [111] of the Sodium Iodide (NaI) crystalline lattice. The tendency for ILMs to form at a certain center-of-mass momentum ▁q and corresponding relative momentum vector ▁k is attributed to the van-Hove singularities condition in the non-interaction two-phonon density of states continuum. We observed that, as ▁q converges to the high-symmetry point L=▁q (π/a,π/a,π/a) of the Brillouin zone, the relative momentum vector ▁k remains invariant at ▁k (π/2,π/2,π/2) for a certain threshold value of ▁q, and coalesces at the upper-edge of the two-phonon density of states spectrum with high degeneracy in the two-phonon critical energy. We conclude that the excitation spectra of the pairs of harmonic phonon excitations become energetically degenerate past the threshold ▁q value towards L at the invariant vector ▁k, announcing the strong presence of ILMs. The calculated ILMs were observed at critical energies of 20.0 meV and 25.0 meV for the spring coupling constants ratios K_2/K_1 ≈0.598 and K_2/K_1 ≈0.202 respectively. Reports of Inelastic Neutron Scattering experiments have identified one-phonon breather excitations energy of 10.2 meV at elevated temperatures of 555 K. The formation of ILMs, or multi-phonon bound states, is expected to arise as a result of the anharmonic interactions that lift these degeneracies to enhance the formation of ILMs. / Physics