Degeneracy, large molecule levels

Notice how the near degeneracy of levels in a large molecule resembles the situation encountered in the treatment of the pseudo Jahn-Teller effect. However, in the present case the coupling between many quasidegenerate... 

Electronic spectra rarely give direct information about molecular structures. Because a typical molecule has many electrons in different energy levels, together with a large number of unoccupied levels, and excitation can occur from each of the occupied levels to many or all of the unoccupied levels, the spectra are in principle complicated, so that assignment can sometimes be difficult or impossible. But symmetry, degeneracy of energy levels and selection rules aU simplify matters, and if we understand all of these, then we will usually be able to extract very useful information. 

Here, we are using the summation index i as the index on the quantum number v. Although a real molecule will fall apart if v, gets too large, we can assume that the summation goes to infinity. We also know that the degeneracies of vibrational levels are 1 as long as they are counted individually—a circumstance we shall meet in polyatomic molecules. 

There is a large class of molecules for which all three rotational constants are dilTerent, although such molecules do not necessarily lack all symmetry. The rotational energy levels and the spectra of such molecules are rather complex. As a consequence of the asymmetry, the K degeneracy of the symmetric top levels is lifted, so that (2/ + 1) levels of different energy for each J value exist. The degree of asymmetry can be expressed by different parameters, a common one is defined by... 

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