# Rotation of diatomic homonuclear molecule

I know that the rotation energy of a diatomic homonuclear molecule is $E_{Rot}=\frac{\hbar J(J+1)}{R^2 M}$. Does the axis of rotation depend on $J$? With respect to which axis does the molecule for $J=1$ and why is that so?

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The axis of rotation does not depend on $J$, at least in this case. Furthermore, a diatomic homonuclear molecule only has one distinguished axis of rotation: With the atoms at $(-1,0,0)$ and $(1,0,0)$, it is impossible to differentiate between the $y$ and $z$ axis in terms of rotational energy (the $x$ axis does not contribute/it is impossible to decide whether the molecule roates about the $x$ axis).