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

Abstract

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

Authors:
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:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1406372
Report Number(s):
SAND-2017-11533J
Journal ID: ISSN 2470-1343; 658130
Grant/Contract Number:
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
ACS Omega
Additional Journal Information:
Journal Volume: 2; Journal Issue: 10; Journal ID: ISSN 2470-1343
Publisher:
American Chemical Society (ACS)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Coordination chemistry (Organomet.); Electronic structure; Equilibrium constant; Free energy; Inorganic chemistry; Molecular association; Thermodynamic simulation

Citation Formats

Xu, Huifang, Xu, David C., and Wang, Yifeng. Natural Indices for the Chemical Hardness/Softness of Metal Cations and Ligands. United States: N. p., 2017. Web. doi:10.1021/acsomega.7b01039.
Xu, Huifang, Xu, David C., & Wang, Yifeng. Natural Indices for the Chemical Hardness/Softness of Metal Cations and Ligands. United States. doi:10.1021/acsomega.7b01039.
Xu, Huifang, Xu, David C., and Wang, Yifeng. 2017. "Natural Indices for the Chemical Hardness/Softness of Metal Cations and Ligands". United States. doi:10.1021/acsomega.7b01039. https://www.osti.gov/servlets/purl/1406372.
@article{osti_1406372,
title = {Natural Indices for the Chemical Hardness/Softness of Metal Cations and Ligands},
author = {Xu, Huifang and Xu, David C. and Wang, Yifeng},
abstractNote = {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 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*MLrMn+ 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.},
doi = {10.1021/acsomega.7b01039},
journal = {ACS Omega},
number = 10,
volume = 2,
place = {United States},
year = 2017,
month =
}

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  • We extend the definition of the electronic chemical potential (μ{sub e}) and chemical hardness (η{sub e}) to finite temperatures by considering a reactive chemical species as a true open system to the exchange of electrons, working exclusively within the framework of the grand canonical ensemble. As in the zero temperature derivation of these descriptors, the response of a chemical reagent to electron-transfer is determined by the response of the (average) electronic energy of the system, and not by intrinsic thermodynamic properties like the chemical potential of the electron-reservoir which is, in general, different from the electronic chemical potential, μ{sub e}.more » Although the dependence of the electronic energy on electron number qualitatively resembles the piecewise-continuous straight-line profile for low electronic temperatures (up to ca. 5000 K), the introduction of the temperature as a free variable smoothens this profile, so that derivatives (of all orders) of the average electronic energy with respect to the average electron number exist and can be evaluated analytically. Assuming a three-state ensemble, well-known results for the electronic chemical potential at negative (−I), positive (−A), and zero values of the fractional charge (−(I + A)/2) are recovered. Similarly, in the zero temperature limit, the chemical hardness is formally expressed as a Dirac delta function in the particle number and satisfies the well-known reciprocity relation with the global softness.« less
  • The chemical reactivity indices as the equilibrium state-function derivatives are revisited. They are obtained in terms of the central moments (fluctuation formulas). To analyze the role of the chemical hardness introduced by Pearson [J. Am. Chem. Soc. 105, 7512 (1983)], the relations between the derivatives up to the third-order and the central moments are obtained. As shown, the chemical hardness and the chemical potential are really the principal indices of the chemical reactivity theory. It is clear from the results presented here that the chemical hardness is not the derivative of the Mulliken chemical potential (this means also not themore » second derivative of the energy at zero-temperature limit). The conventional quadratic dependence of energy, observed at finite temperature, reduces to linear dependence on the electron number at zero-temperature limit. The chemical hardness plays a double role in the admixture of ionic states to the reference neutral state energy: it determines the amplitude of the admixture and regulates the damping of its thermal factor.« less
  • Correlations reported by Jones and Vaughn between chemical softness parameters and LD50s for metal compounds in rodents have been confirmed and extended. In the present study 14-day LD50s for mice were determined under uniform experimental conditions for 24 metal salts injected ip. For certain ions the correlation between the LD50 and the Pearson and Mawby softness parameter, sigma/sup p/, is better than that obtained by Jones and Vaughn using data from diverse sources. Notably, however, we found no correlation for the alkaline-earth metals either with sigma/sub p/ or with other softness parameters. In parallel experiments with the same metal compounds,more » we also found correlations between sigma/sub p/ and 4-day LC50s for Drosophila exposed to the salts in their food. For both the mouse and Drosophila, soft ions were generally found to be more toxic than hard ions such that their rankings are significantly correlated. Several differences in relative toxicities of the metal ions were found to occur between mice and Drosophila, and some interpretations of these findings are given. Correlations between toxicity and physicochemical parameters of toxic materials can offer insights into biochemical mechanisms of toxicity and may be useful in predicting toxicity.« less
  • Regression of standard state equilibrium constants with the revised Helgeson-Kirkham-Flowers (HKF) equation of state allows evaluation of standard partial molal entropies ({bar S}{degrees}) of aqueous metal-organic complexes involving monovalent organic acid ligands. These values of {bar S}{degrees} provide the basis for correlations that can be used, together with correlation algorithms among standard partial molal properties of aqueous complexes and equation-of-state parameters, to estimate thermodynamic properties including equilibrium constants for complexes between aqueous metals and several monovalent organic acid ligands at the elevated pressures and temperatures of many geochemical processes which involve aqueous solutions. Data, parameters, and estimates are given formore » 270 formate, propanoate, n-butanoate, n-pentanoate, glycolate, lactate, glycinate, and alanate complexes, and a consistent algorithm is provided for making other estimates. Standard partial molal entropies of association ({delta}{bar S}{sub r}{degrees}) for metal-monovalent organic acid ligand complexes fall into at least two groups dependent upon the type of functional groups present in the ligand. It is shown that isothermal correlations among equilibrium constants for complex formation are consistent with one another and with similar correlations for inorganic metal-ligand complexes. Additional correlations allow estimates of standard partial molal Gibbs free energies of association at 25{degrees}C and 1 bar which can be used in cases where no experimentally derived values are available.« less
  • The complexes formed by the Na/sup +/, K/sup +/, Rb/sup +/, Ca/sup 2 +/, UO/sub 2//sup 2 +/, and Ag/sup +/ cations with the macrocyclic polyethers 18-crown-6, benzo-15-crown-5, and dicyclohexyl-18-crown-6 are investigated. The stability constants of these complexes have been determined potentiometrically in (90% vol.) ethanol-water solutions at 25/sup 0/C and an ionic strength ..mu.. = 0.1 (achieved with tetrabutylammonium perchlorate). The stability of the investigated complexes was interpreted in terms of caging the metal cation into the cavity of the macrocyclic ligand, an effect which depends on the ratio of the diameter of the complexed cation over the diametermore » of the cavity of the complexing ligand.« less