Empirically Fitted Parameters for Calculating pK_a Values with Small Deviations from Experiments Using a Simple Computational Strategy

Abstract

Two empirically fitted parameters have been derived for 74 levels of theory. They allow fast and reliable pKa calculations using only the Gibbs energy difference between an acid and its conjugated base in aqueous solution (ΔGs(BA)). The parameters were obtained by least-squares fits of ΔGs(BA) vs experimental pKa values for phenols, carboxylic acids, and amines using training sets of 20 molecules for each chemical family. Test sets of 10 molecules per family-completely independent from the training set-were used to verify the reliability of the fitting parameters method. It was found that, except for MP2, deviations from experiments are lower than 0.5 pKa units. Moreover, mean unsigned errors lower than 0.35 pKa units were found for the 98.6%, 98.6%, and 94.6% of the tested levels of theory for phenols, carboxylic acids and amines, respectively. The parameters estimated here are expected to facilitate computationally based estimations of pKa values of species for which this magnitude is still unknown, with uncertainties similar to the experimental ones. However, the present study deals only with molecules of modest complexity, thus the reliability of the FP method for more complex systems remains to be tested.

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“…In this equation Δ G BA represents the difference in Gibbs energy between the conjugated base and the corresponding acid ( G calc(A–) – G calc(HA) ). The m and C 0 parameters are currently available, at several levels of theory for phenols, amines, carboxylic acids and thiols . In all cases the calculated p K a values result in deviations from experiments that are lower than 0.5 p K a units, in terms of mean unsigned errors.…”

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“…M05-2X is a global hybrid exchangecorrelation GGA functional designed for thermochemistry, kinetics and noncovalent interactions (96), it has also been recommended for calculating reaction energies involving free radicals (98). Furthermore, the M05-2X functional has been widely used for estimating the pKa values, the bonding dissociation energies and, in general, the free radical scavenging activity of several antioxidant molecules (99)(100)(101)(102)(103)(104)(105)(106)(107)(108)(109)(110)(111). SMD is considered a universal solvation model, due to its applicability to any charged or uncharged solute in any solvent or liquid medium for which a few key descriptors are known (97).…”

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“…The p K a for the deprotonation of N4 is trivially seen to be too high for consideration. Thus, the p K a values of MA were calculated based on the model reactions 1a , 1b and 2 ( 17 ) according to eq 2 . 3 , 18 where Δ G BA ° was obtained from reactions 1a , 1b , and 2 following eq 3 ; m and C 0 are fitted parameters directly obtained from ref ( 17 ).…”