Rotational energy ($E_J={\hslash }^{2}J(J+1)/(2I)$)

For a linear rigid rotor with moment of inertia $I$, the energy eigenvalue at angular momentum quantum number $J$ is ${\hslash }^{2}J(J+1)/(2I)$. Each level has statistical weight $2J+1$ before additional symmetry or nuclear-spin restrictions.

The angular momentum associated with end-over-end molecular rotation. In an open-shell diatomic molecule it is useful to distinguish $\mathbf{N}$ from the total $\mathbf{J}=\mathbf{N}+\mathbf{S}$, which also contains the electronic spin angular momentum.