The CBS-QB3 method was used to calculate the gas-phase free energy difference between 20 phenols and their respective anions, and the CPCM continuum solvation method was applied to calculate the free energy differences of solvation for the phenols and their anions. The CPCM solvation calculations were performed on both gas-phase and solvent-phase optimized structures. Absolute pK(a) calculations with solvated phase optimized structures for the CPCM calculations yielded standard deviations and root-mean-square errors of less than 0.4 pK(a) unit. This study is the most accurate absolute determination of the pK(a) values of phenols, and is among the most accurate of any such calculations for any group of compounds. The ability to make accurate predictions of pK(a) values using a coherent, well-defined approach, without external approximations or fitting to experimental data, is of general importance to the chemical community. The solvated phase optimized structures of the anions are absolutely critical to obtain this level of accuracy, and yield a more realistic charge separation between the negatively charged oxygen and the ring system of the phenoxide anions.

ABSTRACT:A number of different methods have been proposed for assigning partial charges to the atoms of a molecule, including both quantum chemical and empirical schemes. A reasonable expectation for any successful calculational scheme is that the atomic charges it produces should vary in a manner consistent with chemical intuition and, more specifically, that these variations should be correlated in a sensible way with experimental observations. Seven of the most popular atomic charge schemes (Bader's AIM charges Q AIM , electrostatic potential charges Q ESP , GAPT charges Q GAPT , Gasteiger π charges Q Gast , Löwdin charges Q Löw , Mulliken charges Q Mul , and charges derived from natural population analysis Q NPA ) were tested for their ability to represent variations in the pK a 's of 19 monosubstituted anilines and 19 monosubstituted phenols. In most cases the calculations were performed at the B3LYP/6-311G * * level of theory. For the substituted anilines, the amino nitrogen, anilinium proton, and total amino group charges were taken as representative regression parameters, and for the phenols, the phenolic hydrogen, phenoxide oxygen, and hydroxyl group charges were employed. Overall, Q AIM , Q Löw , and Q NPA yielded the most successful correlations with the pK a 's of these compounds, although for the phenol series, Q GAPT and Q Mul also yielded good results. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 90: 445-458, 2002

Substituent effects on the physical properties and pK a of phenol were studied using density functional theory [B3LYP/6-311G(d,p)] calculations. Substituents alter the physical properties of phenol such as the hydroxyl-group C-O and O-H bond lengths, the C-O-H bond angle, and the energy barrier to rotation about the C-O bond, and also influence the hydroxyl-group pK a . Except for the rotational barrier, Hammett σ constants showed strong correlation with these property changes. Several quantum chemical parameters, including the natural charge on the phenolic hydrogen Q n (H) and the natural charge on the phenoxide oxygen Q n (O − ), the HF/6-311G(d,p) HOMO energy E homo , and the proton-transfer energy E prot , outperformed the empirical Hammett constants in modeling changes in the pK a . All of these latter parameters yielded correlation coefficients |r| > 0.94 for the pK a .

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