For a linear polyatomic molecule, the first-order polyatomic vibration-rotation interaction is
where is the degeneracy of normal mode . The bending mode has , so the two measured states imply
The two stretching zero-point contributions are not supplied. The true all-mode equilibrium constant is therefore not uniquely determined by this band alone. Neglecting those unknown stretching corrections gives the bend-only estimate
Using and converting inverse centimetres to inverse metres,
If the intended course approximation instead treats the observed vibration as a single nondegenerate oscillator with , its extrapolation gives
That is a useful effective one-coordinate estimate, but it should not be identified with an exact equilibrium constant of the doubly degenerate polyatomic bend. Both estimates give at the accuracy warranted here.