Why and When Is Electrophilicity Minimized? New Theorems and Guiding Rules†

We investigate the physical basis, validity, and limitations of the minimum electrophilicity principle, MEP, which postulates that the sum of the electrophilicity indices, ∑ω, of the reaction products will be smaller than that of the reactants, Δω < 0. We present a much-improved understanding of the conditions for minimizing electrophilicity indices. Two indices, ω₁ = (I + A)²/8(I - A) and ω₂ = I·A/(I - A), are discussed, using ionization energies, I, and electron affinities, A, obtained from either ground-state (GS) or valence-state (VS) energies. The performances of ω₁ and ω₂ are compared for a wide range of chemical species from diatomic molecules, through large clusters to liquid water and solid crystals. New analytical arguments in support of MEP are found. Two new theorems are proved, and three new rules rationalize the changes Δω₁ and Δω₂ in association reactions, X + Y → XY. They explain why MEP is much more successful as a guiding rule than the maximum hardness postulate in such reactions. On the other hand, they also identify the increased electron affinity of the product as the reason for the rare but highly significant failures of MEP, e.g., in B₂, C₂, Si₂, and CN. As a rule, electrophilicity is minimized in association reactions. However, both ω₁ and ω₂ are increased if the bond dissociation energy D(XY^-) is larger than D(XY), which is equivalent to an increased product electron affinity. The large positive changes Δω₁ and Δω₂ in 2C → C₂ exhibit a strong contrast to MEP. The changes in electrophilicity indices may help gain insights into the versatility of the chemistries of carbon and other elements. Solid-state double-exchange reactions are correctly assessed by Kaya's composite descriptor, somewhat less by ω₂, but not at all by ω₁. A wide class of failures of MEP is found as size-driven electrophilicity maximization, Δω > 0, e.g., in fullerenes, large metal clusters, and liquid water. Many electrophiles, especially superelectrophiles, show significantly larger electrophilicity indices than the largest index of their isolated atoms. The changes Δω₁ and Δω₂ provide important information on the reactivities of chemical systems; however, it appears that the minimum electrophilicity postulate cannot serve as a basis for a theory.