Rotational energies are quantized. For a diatomic molecule like CO or HCl, or a linear polyatomic molecule like OCS in its ground vibrational state, the allowed rotational energies in the rigid rotor approximation are E J rot = J 2 2 I = J ( J + 1 ) ℏ ℏ 2 2 I = J ( J + 1 ) B . J is the quantum number for total rotational angular momentum and takes all integer values starting at zero, i.e., J = 0 , 1 , 2 , … … , B = ℏ ℏ 2 2 I is the rotational constant, and I is the moment of inertia. Here we are using B in energy units. If it is expressed in frequency units, replace B by hB in all the expression that follow, where h is Planck's constant. If B is given in units of c m − − 1 , then replace B by hcB where c is the speed of light in vacuum.