A definitive physical model for chelation: ideal and non-ideal chelation, short and long chelates, and bridging

Abstract

For short chelating ligands of length l comparable with the contact distance a to the co-ordinating ion, ideal chelation is defined to occur when the ratio of the chelating constant K_chel to the cumulative formation constant β₂ of the equivalent bis(unidentate ligand) complex is closely approximated by K_chel/β₂=(4//₃πLa³)^–1exp(–Δu/kT) where Δu, the difference in interaction energies associated with K_chel and β₂, is equal to zero. For long chelates, ideality is correspondingly defined by K_chel/β₂=(4//₃πLl³)^–1exp(–Δu/kT) with Δu again zero. Specific molecular interactions can then be invoked to account for deviations. Contentions regarding the choice of concentration scale, as well as criteria for inferring chelation and the chelate effect, are resolved. The related associative process of bridging is shown to approximate to co-ordination, by one ion, of two equivalent unidentate ligands.