Frontier molecular orbital theory

In 1952, Kenichi Fukui published a paper in the Journal of Chemical Physics titled "A molecular theory of reactivity in aromatic hydrocarbons.

"[1] Though widely criticized at the time, he later shared the Nobel Prize in Chemistry with Roald Hoffmann for his work on reaction mechanisms.

[2] From these observations, frontier molecular orbital (FMO) theory simplifies prediction of reactivity to analysis of the interaction between the more energetically matched HOMO–LUMO pairing of the two reactants.

In addition to providing a unified explanation of diverse aspects of chemical reactivity and selectivity, it agrees with the predictions of the Woodward–Hoffmann orbital symmetry and Dewar–Zimmerman aromatic transition state treatments of thermal pericyclic reactions, which are summarized in the following selection rule: "A ground-state pericyclic change is symmetry-allowed when the total number of (4q+2)s and (4r)a components is odd" (4q+2)s refers to the number of aromatic, suprafacial electron systems; likewise, (4r)a refers to antiaromatic, antarafacial systems.

FMO theory also finds that this reaction is allowed and goes even further by predicting its stereoselectivity, which is unknown under the Woodward-Hoffmann rules.

The HOMO of butadiene and the LUMO of ethene are both antisymmetric (rotationally symmetric), meaning the reaction is allowed.

* In terms of the stereoselectivity of the reaction between maleic anhydride and cyclopentadiene, the endo-product is favored, a result best explained through FMO theory.

The maleic anhydride is an electron-withdrawing species that makes the dieneophile electron deficient, forcing the regular Diels–Alder reaction.

Assuming the reaction happens suprafacially, the shift results with the HOMO of butadiene on the four carbons that are not involved in the sigma bond of the product.