Relationship between Noncommuting Terms in H and the Most Appropriate Hunds Case

6 Relationship between Noncommuting Terms in H and the Most Appropriate Hund s Case 

The reason there are so many Hund s cases is that each Hund s case corresponds to an arrangement of terms in H in order of relative importance. For each arrangement there is a different Hund s case. Since each Hund s case is associated with a complete set of commuting angular momentum operators, explicitly defined transformations between any two Hund s case basis sets may be specified independent of the details of a particular molecular example. 

It is instructive to list the terms in H, the specific orderings of which lead to various familiar and unfamiliar Hund s cases (Nikitin and Zare, 1994 Watson, 1999). It is important to note that any two incompatible (i.e., non-commuting) terms in H always express their antagonism in the same way. Suppose H1 and H are two such non-commuting terms. (More specifically, HJ comprises all terms in H that do not commute with H , and vice versa.) Then, if H is included in H, H generates differences in the energies, e[0 and E 1, that are connected by non-zero off-diagonal matrix elements of HJ, H 2, and vice versa — e[0 — E vs. H 2. Whether H or HJ wins and 

This operator antagonism is also manifest in dynamics through the equation of motion for expectation values (see Section 9.1.7) 

There is no unique way of specifying the potentially antagonistic terms in H. 

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