Knowledge Bank

Analytical expressions for the splitting of the $A1$ and the $A2$ rovibrational states in symmetric top molecules are derived with emphasis on the symmetry properties of the Hamiltonian and the wavefunctions. A perturbation technique employing interaction diagrams is used instead of the contact transformation which has been used by previous $workers.1,2,3$ Also a few revisions on the existing theory of vibration rotation interaction are made. It is stressed that the observed l-type doubling constants in symmetric top molecules provide information about those anharmonicity potential constants which are not involved in the expression for $\alpha$. A numerical example is given for the ammonia molecule and the magnitude of the anharmonicity term is estimated. The possibility of observing the direct transition between the split levels is discussed.