Symmetry Properties, Integrals, and the Noncrossing Rule

The antisymmetric direct product, which we use to generate the triplet levels of 4.15, is defined by 

we need to identify the operations corresponding to in equations 4.58 and 4.59. For the point group. 

The use of symmetry is extremely powerful in being able to simplify many orbital problems by quickly Identifying those interactions thatare exactly zero. In particular, the rule, which we investigate in this section, requires thatall integrals of the overlap i/fol or interaction type are zero unless fa and transform as the same 

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