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Title: Natural Indices for the Chemical Hardness/Softness of Metal Cations and Ligands

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 (r Mn+), Gibbs free energy of formation (ΔG° f,Mn+), and solvation energy (ΔG° s,Mn+)] by 2.303RT log K ML = (α* MLΔG° f,Mn+ – β* MLr Mn+ + 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 complexingmore » ligand. Proton (H +) with the softness index of zero is a unique acid that has strong interactions with both soft and hard bases. The stability energy resulting from the acid–base interactions is determined by the term α* MLΔG° f,Mn+; a positive product of α* ML and ΔG° f,Mn+ indicates that the acid–base interaction between the metal cation and the complexing ligand stabilizes the complex. The terms β* MLr Mn+ and γ* MLΔG° s,Mn+, which are related to ionic radii of metal cations, represent the steric and solvation effects of the cations. The new softness indices proposed here will help to understand the interactions of ligands (Lewis bases) with metal cations (Lewis acids) and provide guidelines for engineering materials with desired chemical reactivity and selectivity. As a result, the new correlation can also enhance our ability for predicting the speciation, mobility, and toxicity of heavy metals in the earth environments and biological systems.« less
ORCiD logo [1] ;  [1] ;  [2]
  1. Univ. of Wisconsin-Madison, Madison, WI (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 2470-1343; 658130
Grant/Contract Number:
Accepted Manuscript
Journal Name:
ACS Omega
Additional Journal Information:
Journal Volume: 2; Journal Issue: 10; Journal ID: ISSN 2470-1343
American Chemical Society (ACS)
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Coordination chemistry (Organomet.); Electronic structure; Equilibrium constant; Free energy; Inorganic chemistry; Molecular association; Thermodynamic simulation
OSTI Identifier: