Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using complete basis set and gaussian-n models combined with CPCM continuum solvation methods

Complete basis set and Gaussian-n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pK(a) values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of -264.61 kcal/mol for the free energy of solvation of H+, DeltaG(s)(H+), was combined with a value for G(gas)(H+) of -6.28 kcal/mol, to calculate pK(a) values with cycle 1. The complete basis set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle I and the complete basis set models combined with the CPCM solvation methods yielded pK(a) values accurate to less than half a pK(a) unit. (C) 2001 John Wiley & Sons, Inc.