Sigmatropic rearrangements frontier orbital theory

In contrast, applying frontier orbital theory to unimolecular reactions like electrocyclic reactions and sigmatropic rearrangements is inherently contrived, since we have artificially to treat a single molecule as having separate components, in order to have any frontier orbitals at all. Furthermore, frontier orbital theory does not explain why the barrier to forbidden reactions is so high—whenever it has been measured, the transition structure for the forbidden pathway has been 40 kJ mol-1 or more above that for the allowed pathway. Frontier orbital theory is much better at dealing with small differences in reactivity. 

Applying frontier orbital theory to unimolecular reactions like electrocyclic ring closures and sigmatropic rearrangements is inherently contrived, since we are looking at only one orbital. To set up an interaction between frontier orbitals, we... 

So far, cycloadditions have been our only examples of pericyclic reactions. There are several other classes of pericyclic reactions, of which the most notable are cheletropic reactions, sigmatropic rearrangements and electrocyclic reactions. In essence, frontier orbital theory treats each of them as a cycloaddition reaction. 

Intermediate 5 is not isolated. It is transformed into the more stable dihydronaphthalene 2 by means of a thermal [1,5] sigmatropic hydrogen shift. This type of sigmatropic rearrangement can be understood in terms of the frontier molecular orbital theory considering the interaction between the H(ls) orbital and the LUMO ( l/3 ) of the diene component in the transition state (Fig. 14.2). A positive overlap between the orbitals where bond breaking and bond making takes place is produced when the H atom slides across the top face of the planar transition state. This kind of shift is called suprafacial. 

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