Antarafacial geometry

How can we predict whether a given cycloaddition reaction will occur with suprafacial or with antarafacial geometry According to frontier orbital theory, a cycloaddition reaction takes place when a bonding interaction occurs between the HOMO of one reactant and the LUMO of the other. An intuitive explanation of this rule is to imagine that one reactant donates electrons to the other. As with elec-trocyclic reactions, it s the electrons in the HOMO of the first reactant that are least tightly held and most likely to be donated. But when the second reactant accepts those electrons, they must go into a vacant, unoccupied orbital—the LUMO. 

Figure 30.10 (a) Interaction of a ground-state HOMO and a ground-state LUMO in a potential [2 - 2] cycloaddition does not occur thermally because the antarafacial geometry is too strained, (b) Interaction of an excited-state HOMO and a ground-state LUMO in a photochemical [2 r 2] cycloaddition reaction is less strained, however, and occurs with suprafacial geometry. 

This [1,7] sigmatropic reaction proceeds with antarafacial geometry because four electron pairs are involved in the rearrangement. 

This [2 + 2] reverse cycloaddition is not likely to occur as a concerted process because the antarafacial geometry required for the thermal reaction is not possible for a four n-electron system. 

Interaction of HOMO and LUMO in a potential thermal [2 + 2] cydoaddition. The reaction does not occur because antarafacial geometry is too strained. 

Shown below is the reaction of butadiene with ethylene, except that we have the ethylene collide with the butadiene at a skewed angle. Recall that molecules in a reaction flask are constantly colliding with the solvent and each other in all possible orientations, but only certain orientations lead to chemical reactions. In the antarafacial geometry for the butadiene, there is one contact between the butadiene and ethylene in which the phasing does not match. Hence, this geometry for a collision between the two reactants will not lead to product and is considered forbidden. 

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