Cycloadditions aromatic transition state theory

Another approach to analyzing concerted pericyclic reactions is based on the observation that the forbidden [2+2] cycloaddition involves a cyclic array of four electrons in the transition state, while the allowed [4+2] cycloaddition involves a cyclic array of six electrons. This is a familiar pattern that immediately calls to mind aromaticity, in which the ground states of molecules with four ir electrons in a cycle are destabilized and termed antiaromatic, while molecules with six tt electrons are stabilized and aromatic. Building off an earlier analysis by Evans, Zimmerman developed aromatic transition state theory. Simply put, reactions with a simple cyclic array of 4h + 2 electrons (commonly six) in a pericyclic transition state will be stabilized by aromaticity, making the reactions favorable. Note that the relevant electrons need not be exclusively in it orbitals a mixture of cr and it bonds in a cyclic array is acceptable. 

Occasionally, though, you will run across a more exotic pericyclic process, and will want to decide if it is allowed. In a complex case, a reaction that is not a simple electrocyclic ringopening or cycloaddition, often the basic orbital symmetry rules or FMO analyses are not easily applied. In contrast, aromatic transition state theory and the generalized orbital symmetry rule are easy to apply to any reaction. With aromatic transition state theory, we simply draw the cyclic array of orbitals, establish whether we have a Mobius or Hiickel topology, and then count electrons. Also, the generalized orbital symmetry rule is easy to apply. We simply break the reaction into two or more components and analyze the number of electrons and the ability of the components to react in a suprafacial or antarafacial manner. 

Density functional theory and MC-SCF calculations have been applied to a number of pericyclic reactions including cycloadditions and electrocyclizations. It has been established that the transition states of thermally allowed electrocyclic reactions are aromatic. Apparently they not only have highly delocalized structures and large resonance stabilizations, but also strongly enhanced magnetic susceptibilities and show appreciable nucleus-independent chemical-shift values. 

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