Correlation of aqueous pK a values of carbon acids with theoretical descriptors: A DFT study I.E. Charif a , S.M. Mekelleche a, * , D. Villemin b , N. Mora-Diez c a De ´partement de Chimie, Faculte ´ des Sciences, Universite ´ A. Belkaı ¨d, B.P.119, Tlemcen 13000, Algeria b ENSICAEN, Universite ´ de Caen, LCMT, UMR 6507 CNRS, 6, Bd Mare ´chal Juin, Caen 14050, France c Department of Chemistry, Thompson Rivers University, Kamloops, BC, Canada V2C 5N3 Received 17 January 2007; received in revised form 15 April 2007; accepted 27 April 2007 Available online 10 May 2007 Abstract Theoretical calculations are carried out to predict gas- and aqueous-phase acidities of a series of 21 carbon acids with pK a values varying from 6.20 to 50. Acceptable linear correlations (R 2 > 0.93, SD < 4) are obtained between calculated deprotonation Gibbs free energy changes and experimental pK a values (measured in water). Solvent effects are taken into account by means of the polarizable con- tinuum model (PCM). Our calculations also show that the high acidity of a-proton carbonyl compounds and electron-withdrawing substituted methanes can be related to the strong increase in the vicinal charge interactions n c fi p * in anion species. Calculations are performed at the B3LYP/6-311++G(d,p) level of theory. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Carbon acidity; Aqueous pK a ; Deprotonation energy; DFT calculations; NBO analysis 1. Introduction The deprotonation energies of organic acids and the proton affinities of the corresponding conjugate bases are widely used for the prediction of gas-phase and aqueous- phase Bro ¨ nsted acidities [1–8]. Strong acids have small val- ues of deprotonotion energy (i.e., the release of the proton is easier) while strong bases have large values of proton affinity (i.e., the binding to the proton is stronger). Several works on the prediction of the acidity of organic and inor- ganic acids can be found in the literature. For instance, Smith and Radom [9,10] have shown that the G2 and G2(MP2) methods provide excellent results for both depro- tonation enthalpies and proton affinities of small mole- cules. Catalan and Palomar [11] have investigated gas- phase acidities of a number of species and have shown that calculations at the B3LYP method with 6-311+G(d) and 6- 311+G(3df,3pd) basis sets correlate well with the experi- mental data. Good correlations have been obtained between experimental pK a values of a wide range of organic Bro ¨ nsted acids and their calculated gas-phase deprotonation enthalpies [12]. Correlations between theo- retical descriptors and gas-phase acid-base equilibrium constants of organic compounds have been reported for amines, alcohols and thiols [13–15]. An excellent correla- tion was obtained between the aqueous-phase acidity cal- culated with the HF/3-21G(d) method and experimental pK a values for a series of nitrogen bases [16]. Recently, various theoretical descriptors were used to investigate their correlation with the carbon acidity of com- pounds having the CHR 1 R 2 R 3 structure. A reasonable cor- relation was obtained between the deprotonation energies of the compounds calculated at the HF/3-21G and B3LYP/6-31G(d) levels of theory and their aqueous pK a values [17,18]. The ability to predict acidity using a coher- ent, well-defined theoretical approach, without external approximation or fitting to experimental data, would be very useful to chemists. Thanks to the rapid development 0166-1280/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2007.04.037 * Corresponding author. E-mail address: sm_mekelleche@mail.univ-tlemcen.dz (S.M. Mekel- leche). www.elsevier.com/locate/theochem Journal of Molecular Structure: THEOCHEM 818 (2007) 1–6