Volume 17, Issue 21 p. 5808-5826
Full Paper

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

Dr. Daniel Himmel

Dr. Daniel Himmel

Institute for Inorganic and Analytical Chemistry, Freiburger Materialforschungszentrum FMF and Freiburg Institute for Advanced Studies (FRIAS), Albert–Ludwigs–Universität Freiburg, Albertstr. 21, 79104 Freiburg (Germany), Fax: (+49) 761-203-6001

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Dipl.-Chem. Sascha K. Goll

Dipl.-Chem. Sascha K. Goll

Institute for Inorganic and Analytical Chemistry, Freiburger Materialforschungszentrum FMF and Freiburg Institute for Advanced Studies (FRIAS), Albert–Ludwigs–Universität Freiburg, Albertstr. 21, 79104 Freiburg (Germany), Fax: (+49) 761-203-6001

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Prof. Dr. Ivo Leito

Prof. Dr. Ivo Leito

Institute of Chemistry, University of Tartu, 14a Ravila Street, 50411 Tartu (Estonia)

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Prof. Dr. Ingo Krossing

Corresponding Author

Prof. Dr. Ingo Krossing

Institute for Inorganic and Analytical Chemistry, Freiburger Materialforschungszentrum FMF and Freiburg Institute for Advanced Studies (FRIAS), Albert–Ludwigs–Universität Freiburg, Albertstr. 21, 79104 Freiburg (Germany), Fax: (+49) 761-203-6001

Institute for Inorganic and Analytical Chemistry, Freiburger Materialforschungszentrum FMF and Freiburg Institute for Advanced Studies (FRIAS), Albert–Ludwigs–Universität Freiburg, Albertstr. 21, 79104 Freiburg (Germany), Fax: (+49) 761-203-6001Search for more papers by this author
First published: 03 May 2011
Citations: 55

Graphical Abstract

Solvating protons in silico: A quantum chemical solvation model for the calculation of Gibbs solvation energies of protons with good accuracy is presented (see graphic). The values can be used to anchor individual pH scales in different solvents to our recently published universal scale.

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.