Forbidden reactions formal frontier orbitals

Consider the electrocyclic ring-opening reaction of cyclobutene. The molecule is formally divided into two fragments the double bond and the single 0 bond which is cleaved.9 The frontier orbital interactions (0,7t ) and (0, it) relevant to the conrota-tory and disrotatory reactions are given in diagrams 4, 5, 6 and 7, respectively. The net overlap is positive for 4 and 5, but zero for 6 and 7. The conrotatory process is therefore allowed, and the disrotatory process forbidden. 

A characteristic feature of [2 + 2] cycloaddition reactions is that the symmetry properties of the frontier orbitals of the reactants make them formally symmetry forbidden [4] through a symmetric pathway. As a result, the reactants must overcome an activation barrier which makes the process very slow for homogeneous reactants. In organic chemistry, photoexcitation can be used to change the nature of the frontier orbital occupation, breaking the 7r bond and hence facilitating the reaction, but otherwise high heat and other extreme conditions are required in order to make this type of reaction proceed. For reactions with silicon(lOO), chemisorption is observed to be facile for most alkenes even at room temperature [16], contrary to naive expectations based on the cycloaddition model. 

All theoretical studies which analyzed the reaction course of the addition of metal oxides to olefins which were claimed by experimentahsts [111, 117] to yield metalla-2-oxetanes via [2-1-2] addition showed that the [3-1-2] pathway has a lower activation barrier than the [2-1-2] addition [127-136]. This made some theoreticians search for oxidation reactions where the [2-1-2] addition of an oxide to an olefin has a lower barrier than the [3-1-2] addition. The first success albeit nor for a metal oxide was reported by Houk et al. [137]. They reported about ab initio and DFT calculations which show that the [3-1-2] addition of SO3 to ethylene yielding ethylensulfite has a higher barrier than the [2-1-2] addition giving the four-membered cycHc sulfone. It follows that the formally symmetry-forbidden [2-1-2] addition can become more favorable than the [3-1-2] addition. An explanation for the reversal of the activation barriers was given in terms of the strongly polarized frontier orbitals of SO3, which has the LUMO essentially localized at sulfur and the HOMO locahzed at the oxygen atoms. 

Although [2 + 2] and [4 + 4] cycloadditions bear a formal relationship to the Diels-Alder reaction, neither, in fact, takes place under the thermal conditions required for Diels-Alder reactions (see Section 20.4) because they are forbidden as determined by the frontier molecular orbital analysis. 

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