First principles pKa calculations on carboxylic acids using the SMD solvation model: effect of thermodynamic cycle, model chemistry, and explicit solvent molecules

Aqueous pK(a) values are calculated from first principles for a set of carboxylic acids using the SMD solvation model with various model chemistries, thermodynamic cycles, and treatments of explicit solvation. In all, 108 unique theoretical protocols are examined. The direct (D) and water proton exchange (PX) cycles are trialled along with a new approach, termed the semidirect (SD) cycle. The SD thermodynamic cycle offers some improvements over the D and PX schemes, as it bypasses the gas-phase heterolytic bond dissociation calculation required in the conventional D approach while also avoiding an aqueous OH(-) calculation required by the PX method when using water as the reference acid. With all three cycles, the recommended model chemistry employs M05-2X/cc-pVTZ Gibbs energies of solvation with a single discrete water molecule and a high-level composite method for the gas-phase reaction energies. With the SD cycle, these calculations result in a mean unsigned error of less than 1 pK(a) units, with respective mean signed error and maximum unsigned error of less than 0.5 and 2 pK(a) units. Similar results are obtained with the D and PX cycles, and further improvement is required in both the gas and aqueous phase ab initio energy calculations before we can truly discriminate between the thermodynamic cycles investigated here.