The rotational motion of a linear polyatomic molecule can be treated as an extension of the diatomic molecule case. One obtains the \(Y_{J,M} (\theta,\phi)\) as rotational wavefunctions and, within the approximation in which the centrifugal potential is approximated at the equilibrium geometry of the molecule \((R_e)\), the energy levels are: \[ E^0_J = \hbar^2 \dfrac{J(J+1)}{2I}. \nonumber \] Here the total moment of inertia I of the molecule takes the place of \(\mu R_e^2\) in the diatomic molecule case \[ I = \sum\limits_a m_a (R_a - R_{CofM})^2; \nonumber \] \(m_a\) is the mass of atom a whose distance from the center of mass of the molecule is \((R_a - R_{CofM}).\) The rotational level with quantum number J is (2J+1)-fold degenerate again because there are (2J+1) M- values.