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A more correct treatment would also include the zero-point energy in the other two degrees of freedom, i.e., the zero-point energy in the bending mode for the [R] branch and vice versa, the zero-point energy in the R mode for the [γ] branch. However, these energies are about a factor of 3 and 6 smaller than the zero-point energy in the HO stretching mode and therefore neglected.
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