A statistical theory of reactivity based on molecular orbitals participation and its application to organic reactions

The FMO theory considers the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) as drivers of chemical reactivity. This theory has been successfully applied in many fields, but there are some cases where the reactivity is not well described by FMO even if orbitally controlled. In order to consider the participation of the molecular orbitals (MOs) beyond the frontier ones in the reactivity and also to explain the different reactivity possibilities that a same reagent can have (which can be correlated to experimental products <i>e.g.</i>, major and minor products), we propose a theory that is based on two fundamental principles: the first one states that the participation/contribution of the MOs in the reactivity is not absolutely defined, therefore there are many possibilities involving just the reagent <b>R1</b>, that are related to many possibilities of reactivity. The second one states that the interaction between <b>R1</b> and the second reagent <b>R2</b> reduces these many possibilities of participation/contribution to a final option, which is related to just one type of reactivity, that can be correlated with experimental data. The search for these many possibilities of participation of MOs in the reactivity is based on an extension of the three-state grand canonical ensemble model and then because our theory focuses on non-ionization reactions, nucleophilic and electrophilic probabilities are derived. Electron densities are directly evaluated from the MOs, together with their orbital energies related to a microstate, and at the end an ensemble average electron density (average Fukui function) depending on the respective microstate probabilities at a constant <i>kT</i>_p value is calculated. Upon varying <i>kT</i>_p three reactivity zones: the FMO zone, the many-state zone (<i>kT</i>_p ≈ Δ<i>E</i>_<i>ij</i>) and the no information zone appear in a natural way, each of them linked to their reactivity information content. We study the reactivity in electrophilic aromatic substitutions in substituted benzenes, hetero aromatic molecules and in polycyclic aromatic hydrocarbons. Furthermore, the nucleophilic addition reaction on acrolein and benzaldehyde, and the nucleophilic substitution on quinoline is scrutinized. With our theory it was possible to describe the reactivity correctly when the FMO theory is incomplete or incorrect, and also when FMO is correct according to experiment.