Frontier-orbital method

In chemistry, frontier molecular orbital theory is an application of MO theory describing HOMO / LUMO interactions.

In 1952, Kenichi Fukui published a paper in the Journal of Chemical Physics titled "A molecular theory of reactivity in aromatic hydrocarbons." Though widely criticized at the time, he later shared the Nobel Prize in Chemistry with Roald Hoffmann for his work on reaction mechanisms. Hoffman's work focused on creating a set of four pericyclic reactions in organic chemistry, based on orbital symmetry, which he coauthored with Robert Burns Woodward, entitled "The Conservation of Orbital Symmetry."

Fukui's own work looked at the frontier orbitals, and in particular the effects of the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) on reaction mechanisms, which led to it being called Frontier Molecular Orbital Theory (FMO Theory). He used these interactions to better understand the conclusions of the Woodward–Hoffmann rules.

Fukui realized that a good approximation for reactivity could be found by looking at the frontier orbitals (HOMO/LUMO). This was based on three main observations of molecular orbital theory as two molecules interact:

From these observations, frontier molecular orbital (FMO) theory simplifies reactivity to interactions between the HOMO of one species and the LUMO of the other. This helps to explain the predictions of the Woodward–Hoffmann rules for thermal pericyclic reactions, which are summarized in the following statement:

"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. It can be shown that if the total number of these systems is odd then the reaction is thermally allowed.

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