## Centrifugal Distortion

In our calculations so far, we have been treating molecules as rigid rotors – assuming that they do not distort under the stress associated with rotation. However, the forces that act on the atoms in rotating molecules are sufficient to cause some distortion of the molecular geometry, which in turn will alter the moment of inertia of the molecule

For example, in a diatomic molecule the effect of the distortion is to stretch the bond, lengthening it and increasing the moment of inertia. This reduces the rotational constant of the molecule, making its rotational energy levels slightly closer together together than the rigid rotor expression would predict. The effect of centrifugal distortions is usually taken into account by writing the expression for the energy as follows:

The quantity D_{J} is a factor which depends upon the identity of the bond undergoing the distortion. It is called the centrifugal distortion constant. When D_{J} is large a bond is easily stretched (distorts greatly under a centrifugal force).

For a diatomic molecule, the centrifugal distortion constant is related to the vibrational wavenumber of the bond. (This is a value which provides a measure of the stiffness of the bond.) Though the relationship is only approximate, it is still of use to provide an estimation of either quantity from the other:

where is the vibrational wavenumber of the bond.