Baders Analysis of Molecular Fragmentation

The thermolysis of ethylene to two methylene fragments provides an opportunity for referring to Bader s [19] seminal contribution to our understanding of the relations between symmetry, geometry and energy. His ideas, which were subsequently developed by Pearson [20] and by Salem and Wright [21], are discussed in detail in Pearson s book [22], so they will only be touched upon briefly here.  

The approach is based on the premise that a thermally excited molecule will decompose preferentially along a pathway that incorporates the symmetry coordinate which mixes a low-lying excited state into the ground-state most effectively. In outline, his recipe is similar to our Equation 3.12, except that the configurations are not mixed by an external field, but by a vibrational distortion of the nuclear frame. The requirement can be stated  

We will return to them briefly in Chapter 10, in connection with preferred modes of photofragmentation. 

When the symmetry point group is commutative, all of its irreps are nondegenerate and Equation 4.2 can be rewritten  

as will usually be the case, the ground-state is a closed-shell singlet, and therefore totally symmetric, the requirement reduces to  

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