Toward the accurate calculation of pKa values in water and acetonitrile

Abstract

We present a simple approach for the calculation of accurate pKa values in water and acetonitrile based on the straightforward calculation of the gas-phase absolute free energies of the acid and conjugate base with use of only a continuum solvation model to obtain the corresponding solution-phase free energies. Most of the error in such an approach arises from inaccurate differential solvation free energies of the acid and conjugate base which is removed in our approach using a correction based on the realization that the gas-phase acidities have only a small systematic error relative to the dominant systematic error in the differential solvation. The methodology is outlined in the context of the calculation of a set of neutral acids with water as the solvent for a reasonably accurate electronic structure level of theory (DFT), basis set, and implicit solvation model. It is then applied to the comparison of results for three different hybrid density functionals to illustrate the insensitivity to the functional. Finally, the approach is applied to the comparison of results for sets of neutral acids and protonated amine cationic acids in both aqueous (water) and nonaqueous (acetonitrile) solvents. The methodology is shown to generally predict the pKa values for all the cases investigated to within 1 pH unit so long as the differential solvation error is larger than the systematic error in the gas-phase acidity calculations. Such an approach is rather general and does not have additional complications that would arise in a cluster-continuum method, thus giving it strength as a simple high-throughput means to calculate absolute pKa values. This article is part of a Special Issue entitled: Metals in Bioenergetics and Biomimetics Systems.

SAMPL6: calculation of macroscopic pKa values from ab initio quantum mechanical free energies

“…Predicted p K a values were computed for all compounds from the training data set using the protocol described by Muckerman et al [24] (see the Methods section for details). The correlation of these computed values with the experimental p K a s is shown in (Fig.…”

“…As described in detail in Section 2.2, the directly calculated p K a values have fairly poor accuracy and thus we derive a simple linear estimator to correct for shortcomings in the solvation model [24]. The linear model is based on our own training data set (described in the next section) and the resulting estimator ℒ is applied to the p K a from Eq.…”

“…Here we report on p K a calculations of the 24 compounds in the SAMPL6 challenge (Fig. 1) with a quantum-chemical approach originally developed by Muckerman et al [24]. The SAMPL6 compounds are, however, chemically more complex and 23 contain multiple titratable protons and, in some cases, tautomers so that macroscopic p K a have to be calculated.…”

“…However, it is well-known [15, 23] that direct calculations lead to large errors in the calculated p K a s, mainly due to the poor continuum solvation models that have to be employed in order to obtain free energies in solution. One approach to correct for these systematic errors is to generate a model to correct the raw quantum chemical free energies [24]. We generated linear models from a training set with 38 simple compounds with experimentally known p K a (Fig.…”

Electrospray Ionization Mass Spectrometry of Non-Covalent Complexes Formed between N-Alkylimidazolium-Containing Zwitterionic Sulfonates and Protonated Bases

“…The less acidic group should form protonated species, which will be preferentially transferred into the gas phase without any binding to 5-MCH. A rough comparison of the acidity of the sulfonate and carboxylate groups can be made on the basis of the experimental pK a values of methanesulfonic and acetic acids in acetonitrile (9.97 and 23.51, respectively 36 ). Taking into account this difference, it is expected that the unprotonated SO 3 -group of the zwitterion preferentially forms ion pairs with 5-MCH in acetonitrile.…”