Interaction of two singlet carbene molecules

We continue to limit ourselves to pure rotations, neglecting centrifugal distortion. S. footnote 19 of Chapter 3. 

It may be somewhat puzzling that Fig. 4.7, which appears to disregard the unoccupied orbitals completely, leads to the same conclusion as Fig. 4.8, which explicitly invokes HOMO-LUMO interaction. The frontier orbital interaction is implicit in Fig. 4.7, even though the big component of the reaction coordinate was chosen without direct reference to it. As in any correlation diagram, we must consider the HOMO and LUMO of the reacting system as a whole, rather than of the individual reactants. It is evidently the big displacement which allows ht to interact with after desymmetrization to C /, both have the same irrep, so the non-crossing rule keeps them apart, obliging the former - which bears the frontier electrons - to correlate with tt, and the latter to follow the dashed two-headed arrow to a.  

Consideration of the reverse reaction, fragmentation of ethylene (or better, si-lene) to two methylene (silylene) molecules in their singlet state, suggests that HOMO-LUMO interactions are not always the dominant factor. The energetically costly rupture of a double bond in a single step must nevertheless be formally allowed to retrace the big pathway in reverse. 7r-bond rupture is facilitated by interaction of the HOMO, 7t(62u) with the superjacent (T (63u), while the LUMO, 7t (6i ), assists a-bond rupture by interacting with the subjacent MO, (r ag). 

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  

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Figure 4.9a, b. Interaction of two singlet carbene molecules (a) perpendicular copla-nar approach (CJ ) (b) approach. 

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