where an increase in J corresponds to absorption and a decrease in J to emission. The transition energy is the difference in the energy between the two levels. If one level has a rotational quantum number of J then absorption is to the level with quantum number J+1. For the non-rigid rotor, the energy of these levels is:

and

The energy difference is then:

Input a value into the calculator below for the rotational constant and centrifugal constant (both in cm^-1) and press "calculate" to work out the transition energies (in cm^-1). Typically, D is of the order of 0.001. Unlike the rigid rotor where the separation is constant, the separation of the lines decreases as J increases (and the centrifugal distortion increases). Using large values of J actually causes the separation to become negative.

Once you have covered all of the available resources for rotational spectroscopy, you should test your knowledge and understanding with the self test.