Rotation vibration in diatomic

As the vibrational quantum number increases, the vibrational energy of the molecule increases as well as the average distance between the nuclei. The increase in $R_{meas}$ produces an increase in the moment of inertia $I=\mu R_{meas}^{2}$. Rotational energy decreases as it is inversely proportional to the moment of inertia. To consider this effect, the term $-h\alpha_e(v+1/2)J(J+1)$ is added to the energy, where $\alpha_e$ is the rotation-vibration coupling constant.