Natural Indices for the Chemical Hardness/Softnessof Metal Cations and Ligands

摘要

Quantitative understanding of reactivity and stability for a chemical species is fundamental to chemistry. The concept has undergone many changes and additions throughout the history of chemistry, stemming from the ideas such as Lewis acids and bases. For a given complexing ligand (Lewis base) and a group of isovalent metal cations (Lewis acids), the stability constants of metal–ligand (ML) complexes can simply correlate to the known properties of metal ions [ionic radii (rMⁿ⁺), Gibbs free energy of formation (ΔG°f,Mⁿ⁺), and solvation energy (ΔG°s,Mⁿ⁺)] by 2.303RT log KML = (α*MLΔG°f,Mⁿ⁺ – β*MLrMⁿ⁺ + γ*MLΔG°s,Mⁿ⁺ – δ*ML), where the coefficients (α*ML, β*ML, γ*ML, and intercept δ*ML) are determined by fitting the equation to the existing experimental data. Coefficients β*ML and γ*_ML have the same sign and are in a linear relationship through the origin. Gibbs free energies of formation of cations (ΔG°_f,Mⁿ⁺) are found to be natural indices for the softness or hardness of metal cations, with positive values corresponding to soft acids and negative values to hard acids. The coefficient α*_ML is an index for the softness or hardness of a complexing ligand. Proton (H⁺) with the softness index of zero isa unique acid that has strong interactions with both soft and hardbases. The stability energy resulting from the acid–base interactionsis determined by the term α*_MLΔG°_f,Mⁿ⁺; a positive productof α*_ML and ΔG°_f,Mⁿ⁺ indicates that the acid–baseinteraction between the metal cation and the complexing ligand stabilizesthe complex. The terms β*_MLr_Mⁿ⁺ and γ*_MLΔG°_s,Mⁿ⁺, whichare related to ionic radii of metal cations, represent the stericand solvation effects of the cations. The new softness indices proposedhere will help to understand the interactions of ligands (Lewis bases)with metal cations (Lewis acids) and provide guidelines for engineeringmaterials with desired chemical reactivity and selectivity. The newcorrelation can also enhance our ability for predicting the speciation,mobility, and toxicity of heavy metals in the earth environments andbiological systems.