DOI: 10.1002/chem.201003164 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 Daniel Himmel, [a] Sascha K. Goll, [a] Ivo Leito, [b] and Ingo Krossing* [a] Dedicated to Professor Hansgeorg Schnçckel on the occasion of his 70th birthday Introduction According to Brønsteds definition, [1] acids are proton donors and bases are proton acceptors, a concept nowadays known as Brønsted acidity. It is used in all chemistry-related areas [2] including materials [3] and energy storage, [4] cataly- sis, [5, 6] environmental science [7] and molecular biology. [8] Brønsteds definition is in agreement with the newer and more universal acid concept [9] of Lewis, treating acids as electron-pair acceptors. In this way, the proton is a special case of an (extremely strong) Lewis acid. However, whilst a generally accepted quantitative measure for Brønsted acidi- ty inside one homogeneous medium exists, that is, the pH value, Lewis acidity cannot be quantified by one single pa- rameter, as the hard and soft acid and base (HSAB) princi- ple must be taken into account. For hard Lewis acids, the re- action thermodynamics with hard bases like H 2 O or fluoride serve as descriptors, while for soft acids, their affinities to soft bases like CO, cyanide, or methanide are more mean- ingful as a measure for acidity. An important limitation of all known Brønsted acidity concepts is that the absolute acidities in different media—for example, expressed as con- ventional pH values in different solvents—are not directly comparable. It is the goal of this manuscript to provide a basis for the quantitative comparison of Brønsted acidity over the bor- ders of different media (solvents, acids) and to establish anchor points for the direct comparison of Brønsted acidity in an absolute unified Brønsted acidity scale. A preliminary account on this idea and its extension to the gas and solid phase has already been reported. [ 10a] Abstract: The COSMO cluster-continu- um (CCC) solvation model is intro- duced 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 sepa- rately: 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 con- ductor-like screening model (COSMO). For every solvent, the sol- vation of the proton in at least two (and up to 11) proton–solvent clusters was calculated. The resulting Gibbs sol- vation energies of the proton were weighted by using Boltzmann statistics. The model was evaluated for the calcu- lation of Gibbs solvation energies by using experimental data of water, MeCN, and DMSO as a reference. Al- lowing structural relaxation of the proton–solvent clusters and the use of structurally relaxed Gibbs solvation en- ergies 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 1s error bar of 10 kJ mol 1 . Gibbs sol- vation energies of protons in the fol- lowing representative solvents were calculated : Water, acetonitrile, sulfur dioxide, dimethyl sulfoxide, benzene, diethyl ether, methylene chloride, 1,2- dichloroethane, sulfuric acid, fluorosul- fonic 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 specif- ic acidity (pH) scales to our recently introduced absolute acidity scale. Keywords: acidity · Brønsted acids · gas-phase acidity · solution acidity · thermodynamics [a] Dr. D. Himmel, Dipl.-Chem. S. K. Goll, Prof. Dr. I. 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 E-mail : krossing@uni-freiburg.de [b] Prof. Dr. I. Leito Institute of Chemistry, University of Tartu 14a Ravila Street, 50411 Tartu (Estonia) Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201003164.  2011 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim Chem. Eur. J. 2011, 17, 5808 – 5826 5808