Combining ab initio quantum mechanics with a dipole-field model to describe acid dissociation reactions in water: First-principles free energy and entropy calculations

We introduce a novel approach to compute dissociation free energy and entropy values in simulations that employ a density functional theory description of the acidic moiety and of the solvent. The approach consists of utilizing an alchemical transformation of a weak acid A-COOH into the strong acid B-COOH, which makes it practical to employ alchemical free energy perturbation methods in the context of ab initio molecular dynamics simulations. The present alchemical transformation circumvents the need to tackle changes in the total number of electrons and atoms by replacing the chemical residue responsible for the change in acidity with an easily tunable external effective potential. Our investigation demonstrates that (1) a simple but effective class of external potentials that control acidity changes in the acetic/trifluoroacetic acid series can be achieved by replacing the methyl and trifluoromethyl substituents by screened dipoles. Using this dipole-field/quantum-mechanics (DF/QM) approach one can predict gas-phase geometries, proton dissociation energies, total dipole moments, and water binding energies in good agreement with full-QM values. (2) The resulting alchemical perturbation calculations are stable and well converged and allow one to compute absolute pKa values whose accuracy is limited primarily by the exchange-correlation functional employed: H–COOH=2.5±0.6 (full-QM calculation), 3.7 (exp); F3C–COOH=0.4±0.6 (DF/QM calculation), 0.5 (exp); H3C–COOH=3.1±0.7 (DF/QM calculation), 4.7 (exp); 3) Our DF/QM model predicts that the difference in acidity between H–COOH and H3C–COOH is dominated by solvent entropy effects, in excellent agreement with experimental observations. The calculated difference between the dissociation energies of these acids is ΔΔdU=0.0±0.26 kcal/mol while the experimental value is 0.0±0.1 kcal/mol.