Anchor Points for the Unified Brønsted Acidity Scale: The rCCC Model for the Calculation of Standard Gibbs Energies of Proton Solvation in Eleven Representative Liquid Media

Abstract

The COSMO cluster-continuum (CCC) solvation model is introduced for the calculation of standard Gibbs solvation energies of protons. The solvation sphere of the proton is divided into an inner proton-solvent cluster with covalent interactions and an outer solvation sphere that interacts electrostatically with the cluster. Thus, the solvation of the proton is divided into two steps that are calculated separately: 1) The interaction of the proton with one or more solvent molecules is calculated in the gas phase with high-level quantum-chemical methods (modified G3 method). 2) The Gibbs solvation energy of the proton-solvent cluster is calculated by using the conductor-like screening model (COSMO). For every solvent, the solvation of the proton in at least two (and up to 11) proton-solvent clusters was calculated. The resulting Gibbs solvation energies of the proton were weighted by using Boltzmann statistics. The model was evaluated for the calculation of Gibbs solvation energies by using experimental data of water, MeCN, and DMSO as a reference. Allowing structural relaxation of the proton-solvent clusters and the use of structurally relaxed Gibbs solvation energies improved the accordance with experimental data especially for larger clusters. This variation is denoted as the relaxed COSMO cluster-continuum (rCCC) model, for which we estimate a 1σ error bar of 10 kJ mol(-1) . Gibbs solvation energies of protons in the following representative solvents were calculated: Water, acetonitrile, sulfur dioxide, dimethyl sulfoxide, benzene, diethyl ether, methylene chloride, 1,2-dichloroethane, sulfuric acid, fluorosulfonic acid, and hydrogen fluoride. The obtained values are absolute chemical standard potentials of the proton (pH=0 in this solvent). They are used to anchor the individual solvent specific acidity (pH) scales to our recently introduced absolute acidity scale.

Absolute Brønsted Acidities and pH Scales in Ionic Liquids

“…Due to our theoretical [20,21,28] and experimental [26,[29][30][31] work on (super)acidity and our in-house use of bromoaluminate ILs Cat + [Al n Br 3n + 1 ] À (Cat + = typical IL cation such as imidazolium, pyrrolidinium; n = 0-3) as highly acidic IL media, we were interested in the extension of the absolute pH abs value concept to IL media. Thus, in this article we first develop the general principles to extend the pH concept to all ILs and turn next to how these examples can be used to reach the Cat + [Al n Br 3n + 1 ]…”

“…Recently, we constructed [20][21][22] an absolute acidity scale by defining the absolute chemical potential m abs (H + ) of the proton as the lowering of its chemical potential relative to that in the gaseous standard state, that is, by Equation (1) …”

“…[20] In this case, the thermodynamic information about the solvated proton is hidden in the concentrations of both HBr (solv) ). [21] The above constructed pH scales have the disadvantage that they are restricted to certain IL bulk-phase definitions. À .…”

The Al(ORF)3/H2O/Phosphane [RF = C(CF3)3] System – Protonation of Phosphanes and Absolute Brønsted Acidity

“…[57,58] In this medium-independent acidity scale, the absolute chemical potential of the proton μ abs (H + ), with the gaseous proton as a reference, is used as a universal measure of Brønsted acidity. In a solvent S, μ abs (H + ) depends on the standard Gibbs solvation energy of the proton Δ solv G°(H + ,S) and the pH of the solution through Equation (4).…”

“…For fluorobenzene, the standard solvent for this chemistry, the anchor point was hitherto neither experimentally nor computationally investigated. Using our recently established rCCC model, [58] we calculated Δ solv G°(H + ,PhF), as -887 kJ mol -1 (details in the Supporting Information). This is in line with expectations.…”