When a molecule rotates, the centrifugal force pulls the atoms apart. As a result, the moment of inertia of the molecule increases, thus decreasing the value of , when it is calculated using the expression for the rigid rotor. To account for this a centrifugal distortion correction term is added to the rotational energy levels of the diatomic molecule.
where  is the centrifugal distortion constant.
Therefore, the line positions for the rotational mode change to
In consequence, the spacing between lines is not constant, as in the rigid rotor approximation, but decreases with increasing rotational quantum number.
An assumption underlying these expressions is that the molecular vibration follows simple harmonic motion. In the harmonic approximation the centrifugal constant   can be derived as
where k is the vibrational force constant. The relationship between  and  
where  is the harmonic vibration frequency, follows. If anharmonicity is to be taken into account, terms in higher powers of J should be added to the expressions for the energy levels and line positions. A striking example concerns the rotational spectrum of hydrogen fluoride which was fitted to terms up to [J(J+1)].