Perturbation MO Theory and the Frontier Orbital Concept

A qualitative description of chemical reactivity in terms of the molecular orbitals of the reactants is offered by the perturbation molecular orbital (PMO) theory. As per this theory, the spatial shape and the energy aspects of the MOs of each reactant get perturbed due to approach of the other-reactant MOs. In other words, there is a mutual perturbation of the molecular orbitals of the reacting molecules during a reaction, the perturbation continuing until the reaction is over and the products are formed. 

The PMO theory has been successfully used to draw qualitative conclusions about the course of some chemical reactions, worthwhile examples being the familiar applications of the Woodward-Hoffmann rules to organic pericyclic reactions. In pericyclic reactions involving one reactant, the highest-energy occupied MO (HOMO) is of prime importance. Thus for thermal cyclisation of substituted s-cis 1,3-butadiene, it is found that there occurs conrotatory ring closure, as only conrotatory movement of the orbitals would provide a bonding interaction between the two newly overlapping lobes of its HOMO (whereas disrotatory movement would have provided here an antibonding interaction).

For PMO-theory discussions about bimolecular reaction processes, there is used the frontier orbital concept (by Pearson), which states that the most important orbital interactions occur between the highest occupied orbital (HOMO) of one reactant and the lowest unoccupied orbital (LUMO) of the other reactant: These two particular MOs are called the frontier orbitals. As per this concept, as the two reactant molecules approach each other, electron density starts getting transferred from the HOMO frontier orbital in one reactant to the LUMO one in the other. Which reactant would provide the interacting HOMO (or which reactant the corresponding LUMO) gets decided by the spatial symmetry, energy and bonding characteristics of the orbitals: the frontier orbitals are those for which the aforesaid electron-density flow results in weakening of the old intramolecular bonding within each reactant, and strengthening the newly developing intermolecular bonding between the two reactants. Also, for better reactivity (i.e., low activation energy), the initial energy difference between the two frontier orbitals should be low, and the overlap between them should be large (i.e., the overlap integral  ∫f₁f₂dv  have a large positive value). 

Thus for the reaction of H₂ and F₂ forming HF, if one suggests a bimolecular one-step mechanism in which the two reactants would come together broadside to form a four-centre transition state, we would find that flow of electron density from the s_g1s HOMO of H₂ to the s_u*2p LUMO of F₂ would weaken the H--H and the F--F bonds while strengthening the two newly developing H--F bonds, but the overlap between these two MOs would become zero because of their different symmetries (see Figure, case a). 

On the other hand, the p_g*2p HOMO of F₂ and the s_u*1s LUMO of H₂ do have a positive overlap (see Figure, case b), but flow of electron density from this antibonding HOMO of F₂ would strengthen rather than weaken the existing F--F bonding. Thus one would conclude that the above suggested mechanism involves a rather high activation energy, and so is not a favourable one!