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**joining the two atoms**(also the axis of symetry) and make a quantum argument involving the energy levels of a rigid rotator to conclude that kT<<[itex]\Delta E[/itex] for this particular degree of freedom.

But isn't this kind of rotation impossible to begin with in QM? One of my HW problem in QM last year was to show that the energy needed to put a totally smooth cylinder in rotation about it's axis of symetry is infinite. This follows a principle like "it is not possible to put in motion an object that you cannot tell is in motion". And this is precisely what we have here with the diatomic molecule so I find it peculiar that we are even considering such rotations.