Polyatomic Molecules Method of Calculation

The relation of the anharmonic force field to the spectroscopic observables for a polyatomic molecule is similar to the calculation described above for a 

Spectroscopic Data Relative to Diatomic Molecules , International Tables of Selected Constants, Pergamon Press, Oxford, 1971, Vol. 17. 

The final stage is to relate the coefficients in the effective hamiltonian to the observed spectrum this is essentially the problem of assignment and analysis of an observed spectrum, and is already discussed in many places in the spectroscopic literature. 

The vibration-rotation hamiltonian of a polyatomic molecule is more complicated than that of a diatomic molecule, both because of the increased number of co-ordinates, and because of the presence of Coriolis terms which are absent from the diatomic hamiltonian. These differences lead to many more terms in the formulae for a and x values obtained from the contact transformation, and they also lead to various kinds of vibrational and rotational resonance situations in which two or more vibrational levels are separated by so small an energy that interaction terms in the hamiltonian between these levels cannot easily be handled by perturbation theory. It is then necessary to obtain an effective hamiltonian over these two or more vibrational levels, and to use special techniques to relate the coefficients in this hamiltonian to the observed spectrum. 

These various aspects of the calculation will now be discussed in more detail, and the whole calculation is reviewed on pp. 140—142. 

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