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⁺, ΔG_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 1 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. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Avoiding gas-phase calculations in theoretical p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> predictions

CBS-QB3, two simplified and less computationally demanding versions of CBS-QB3, DFT-B3LYP, and HF quantum chemistry methods have been used in conjunction with the CPCM continuum solvent model to calculate the free energies of proton exchange reactions in water solution following an isodesmic reaction approach. According to our results, the precision of the predicted pK _a values when compared to experiment is equivalent to that of the thermodynamic cycles that combine gas-phase and solution-phase calculations. However, in the aqueous isodesmic reaction schema, the accuracy of the results is less sensitive to the presence of explicit water molecules and to the global charges of the involved species since the free energies of solvation are not required. In addition, this procedure makes easier the prediction of pK _a values for molecules that undergo large conformational changes in solvation process and makes possible the pK _a prediction of unstable species in gas-phase such as some zwitterionic tautomers. The successive pK _a values of few amino acids corresponding to the ionization of the α-carboxylic acid and α-amine groups, which is one of the problematic cases for thermodynamic cycles, were successfully calculated by employing the aqueous isodesmic reaction yielding mean absolute deviations of 0.22 and 0.19 pK _a units for the first and second ionization processes, respectively.     

SAMPL6: calculation of macroscopic p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values from ab initio quantum mechanical free energies

Macroscopic pK_a values were calculated for all compounds in the SAMPL6 blind prediction challenge, based on quantum chemical calculations with a continuum solvation model and a linear correction derived from a small training set. Microscopic pK_a values were derived from the gas-phase free energy difference between protonated and deprotonated forms together with the Conductor-like Polarizable Continuum Solvation Model and the experimental solvation free energy of the proton. pH-dependent microstate free energies were obtained from the microscopic pK_as with a maximum likelihood estimator and appropriately summed to yield macroscopic pK_a values or microstate populations as function of pH. We assessed the accuracy of three approaches to calculate the microscopic pK_as: direct use of the quantum mechanical free energy differences and correction of the direct values for short-comings in the QM solvation model with two different linear models that we independently derived from a small training set of 38 compounds with known pK_a. The predictions that were corrected with the linear models had much better accuracy [root-mean-square error (RMSE) 2.04 and 1.95 pK_a units] than the direct calculation (RMSE 3.74). Statistical measures indicate that some systematic errors remain, likely due to differences in the SAMPL6 data set and the small training set with respect to their interactions with water. Overall, the current approach provides a viable physics-based route to estimate macroscopic pK_a values for novel compounds with reasonable accuracy.     

Absolute and relative p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> predictions via a DFT approach applied to the SAMPL6 blind challenge

In this work, quantum mechanical methods were used to predict the microscopic and macroscopic pK_a values for a set of 24 molecules as a part of the SAMPL6 blind challenge. The SMD solvation model was employed with M06-2X and different basis sets to evaluate three pK_a calculation schemes (direct, vertical, and adiabatic). The adiabatic scheme is the most accurate approach (RMSE?=?1.40 pK_a units) and has high correlation (R²?=?0.93), with respect to experiment. This approach can be improved by applying a linear correction to yield an RMSE of 0.73 pK_a units. Additionally, we consider including explicit solvent representation and multiple lower-energy conformations to improve the predictions for outliers. Adding three water molecules explicitly can reduce the error by 2–4 pK_a units, with respect to experiment, whereas including multiple local minima conformations does not necessarily improve the pK_a prediction.     

Infrared spectrometric study of the interaction between 2-dimethylamino-3,3-dimethyl-1 azirine and some phenol derivatives

The H-bonded complexes between 2-dimethylamino-3,3-dimethyl-1-azirine (TMAAZ) and some phenol derivatives have been studied by IR spectrometry in carbon tetrachloride. The equilibrium constants at 300, 315 and 328 K and the ? ΔH°, ? Δν_OH and Δν_CN values have been determined. The comparison with previously studied OH … N complexes shows that TMAAZ forms stronger complexes than would be expected from the pK_a value. These facts are discussed in terms of steric, hybridization, solvation and charge transfer effects. From a pK_a of 8, the IR spectrum shows the appearance of ion pairs N⁺-H …^?O. A predominance of protonated species can be calculated for a pK_a of 6. This can explain why 1,2-ring cleavage whose first step is probably the formation of an azirinium cation, occurs for acids characterized by pK_a values lower than 5 but not for enolizable ketones having pK_a values higher than 9.     

Studies on the effect of ethanol on the solvation behaviour of thiamine hydrochloride in water

The specific conductance of Thiamine hydrochloride in water and water-ethanol mixtures was measured at different temperatures 283, 293, 303 and 313 K. Kraus-Bray and Shedlovsky models of conductivity were used for analyzing conductance data. The limiting molar conductance, association constant K _a, energy of activation of the rate process E _a, and related thermodynamic parameters have been determined. Based on viscosity of the solvent, Walden product and Stokes molecular radius were also been determined. Born model of ion solvation was proved. Standard thermodynamic parameters of association (G _a, H _a and S _a) were calculated and discussed. The results show the decrease in limiting molar conductance and increase in K _a with decrease in relative permittivity. Such computed values have been used to discuss the solvation behaviour of Thiamine hydrochloride in water-ethanol mixtures.     

Thermodynamic cycle for the calculation of ab initio pKa values for hydroxamic acids

A thermodynamic cycle to calculate pK_a values (Minus log of acid dissociation constants) of hydroxamic acids is presented. Hydroxamic acids exist mainly as amide isomers in the aqueous medium. The amide form of hydroxamic acids has two deprotonation sites and may yield either an N-ion or an O-ion upon deprotonation. The thermodynamic cycle proposed includes the gas-phase N–H deprotonation of the hydroxamic acid, the solvent phase transformation of the N-ion to the O-ion and the solvation of the hydroxamic acid molecule and the O-ion in water. The CBS-QB3 method was employed to obtain gas-phase free energy differences between 12 hydroxamic acids and their respective anions. The aqueous solvation Gibbs free energy changes were calculated at the HF/6-31G(d)/CPCM and HF/6-31+G(d)/CPCM levels of theory using HF/6-31+G(d)/CPCM geometries. For the proton, literature values of the gas-phase free energy of formation and the solvation free energy change were used. The free energy change for the transformation of the N-ion to O-ion in the aqueous medium was calculated by employing CBS-QB3/CPCM in the aqueous medium. For this, the hydroxamic acids were divided in two classes according to the substituent at the carbonyl carbon. A common transformation free energy difference for aliphatic substituted hydroxamic acids and a separate common transformation free energy difference for aromatic substituted hydroxamic acids were obtained. The pK_a calculation yielded a root mean square error of 0.32 pK_a units.     

Author index

Electromotive-force measurements on cells without liquid junction have been used to determine the pK_a values of 7 mono-, 6 di-, and 2 tricarboxylic acids in formamide at 9 temperatures from 5 to 45°C. From the pK_a values, the thermodynamic quantities ΔG⁰, ΔH⁰, and ΔS⁰ for the acids have been calculated in formamide at 25°C.     

A Correlation Between Solvatochromic Solvent Polarity Parameters and the Ionization Constants of Various Phenols in 1,4-Dioxane–Water Mixtures

Precise thermodynamic ionization constants K for 3-nitrophenol, 3,4-dichlorophenol, and 4-cyanophenol have been obtained in 1,4-dioxane-water mixtures (0–70% volume fraction in dioxane) at 25°C using a potentiometric method. The same information for another twelve cationic, neutral, and anionic phenols were taken from the literature. Three different methods were used to study the effects of the solvents on the ionization constants: one involves a single polarity parameter, E _T(30); the next involves the Kamlet–Taft multiparametric method; and the last involves the preferential solvation model. The pK values follow the preferential solvation model, but the parameters obtained are highly correlated. Using the data for the phenol molecule as reference, a linear correlation between ΔpK and E _T(30) has been used to develop a new method of obtaining pK values for any binary solvent composition, with only the pK in water known. The pK(s) values correlate with the molecular parameters for the dipolarity/polarizability of the solvent π* and its hydrogen-bond donor ability α. The preferential solvation parameter, f _12/1, correlates with the parameter for the hydrogen-bond donor ability of the solvent. All the phenols follow Hammett's equation and the reaction constants have been calculated for the different water–dioxane mixtures.     

The SAMPL5 challenge for embedded-cluster integral equation theory: solvation free energies,aqueous p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript>, and cyclohexane–water log <Emphasis Type="Italic">D</Emphasis>

We predict cyclohexane–water distribution coefficients (log D _7.4) for drug-like molecules taken from the SAMPL5 blind prediction challenge by the “embedded cluster reference interaction site model” (EC-RISM) integral equation theory. This task involves the coupled problem of predicting both partition coefficients (log P) of neutral species between the solvents and aqueous acidity constants (pK _a) in order to account for a change of protonation states. The first issue is addressed by calibrating an EC-RISM-based model for solvation free energies derived from the “Minnesota Solvation Database” (MNSOL) for both water and cyclohexane utilizing a correction based on the partial molar volume, yielding a root mean square error (RMSE) of 2.4 kcal mol^?1 for water and 0.8–0.9 kcal mol^?1 for cyclohexane depending on the parametrization. The second one is treated by employing on one hand an empirical pK _a model (MoKa) and, on the other hand, an EC-RISM-derived regression of published acidity constants (RMSE of 1.5 for a single model covering acids and bases). In total, at most 8 adjustable parameters are necessary (2–3 for each solvent and two for the pK _a) for training solvation and acidity models. Applying the final models to the log D _7.4 dataset corresponds to evaluating an independent test set comprising other, composite observables, yielding, for different cyclohexane parametrizations, 2.0–2.1 for the RMSE with the first and 2.2–2.8 with the combined first and second SAMPL5 data set batches. Notably, a pure log P model (assuming neutral species only) performs statistically similarly for these particular compounds. The nature of the approximations and possible perspectives for future developments are discussed.     

Calculations of pKa values of carboxylic acids in aqueous solution using density functional theory

With the specific aim of calculating the acidity equilibrium constant (K_a) of carboxylic acids in aqueous solution we investigated the solute-solvent interactions of these acids and their corresponding anions. The pK_a (−lg K_a) values have been calculated using density functional theory (DFT). The polarized continuum model (PCM) is used to describe the solvent. Using these methods, we successfully predicted the pK_as of 66 carboxylic acids in aqueous with the average error of 0.5 in pK_a units. Two different thermodynamic cycles have been studied. The theoretical values are in better agreement with the experimental results for those acids with moderate strength of acidity with the pK_a value higher than 3.     

The influence of hydrophobic amino acid side groups on the acidity of the aromatic imidazole ring of histidine: A theoretical study

In this study we have calculated the acidity constant (pKa) of imidazole ring in Histidine‐Hydrophobic amino acid dipeptides using the quantum chemistry and continuum solvation methods. Density functional theory calculations with the large basis sets are used to determine the Gibbs free energy of deprotonate in the gas and liquid phases. Based on our results ΔG_S values are located between ?69.38 and ?18.82 kcal mol^?1 which are related to His⁺–Gly and His forms, respectively. pKa of the dipeptides in the aqueous phase was obtained from the calculated gas‐phase and solvation free energies through a thermodynamic cycle and the solvation model chemistry of Martin Karplus et al. Solvation effects are treated using a self‐consistent reaction field formalism involving polarized continuum models. According to our calculations pKa values are between 5.50 and 8.19 that are belong to His⁺–ILe and His⁺–Ala forms, respectively. Natural bond orbital analysis of dipeptides reveals that the electron delocalization in imidazole ring is the most effective factor in determination of acidity order for these compounds. Structural analysis confirmed that the orientation of carbonyl group with respect to imidazole ring is an effective factor in imidazole ring stability. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Thermodynamic Estimate of pKa Values of the Carboxylic Acids in Aqueous Solution with the Density Functional Theory

The 96 pK_a values of 85 carboxylic acids in aqueous solution were calculated with the density functional theory method at the level of B3LYP/6‐31+G(d,p) and the polarizable continuum model (PCM) was used to describe the solvent. In the calculations of pK_a values, the dissociation Gibbs free energies were directly calculated using carboxylic acid dissociation reactions in aqueous solution, i. e., no thermodynamic cycle was employed, which is different from the previous literatures. A highly significant correlation of R²=0.95 with a standard deviation (SD) of 0.36 between the experimental pK_a values and the calculated dissociation Gibbs free energies [ΔG(calc.)] was found. The slope of pK_a vs. (G(calc.)/(20303RT) is only 47.6% of the theoretically expected value, which implies that the ΔG(calc.) value from the theoretical calculation is larger than the actual one for all 85 carboxylic acids studied. Thus, by adding the 0.476 scaling‐factor into the slope, we can derive a reliably procedure that can reproduce the experimental pK_a values of carboxylic acids. The pK_a values furnished by this procedure are in good agreement with the experimental results for carboxylic acids in aqueous solution.     

Determination of thermodynamic pKa values of pharmaceuticals from five different groups using capillary electrophoresis

A determination of the thermodynamic acid dissociation constants (pK_a) of 22 frequently used pharmaceuticals using capillary electrophoresis in aqueous media is presented in this work. The investigated pharmaceuticals belong to different pharmacological groups: macrolides, fluoroquinolones, sulfonamides, β‐lactams, tetracyclines, and other miscellaneous pharmaceuticals. The electrophoretic mobilities of the investigated analytes were monitored in a pH range from 2.00 to 10.82. The data were fitted with an appropriate mathematical model using a nonlinear regression analysis to obtain pK_a values. Experimentally obtained data were well described by the mathematical model chosen for each analyte that was confirmed by r² values higher than 0.99 for most of the investigated analytes. Extrapolations to zero ionic strength were used to determine the thermodynamic pK_a values. Experimentally obtained acid dissociation constants were interpreted using structural formulae of investigated analytes and the moieties corresponding to specific pK_a were identified.     

A universal approach for continuum solvent pK a calculations: are we there yet?

This paper reviews several pK _a calculation strategies that are commonly used in aqueous acidity predictions. Among those investigated were the direct or absolute method, the proton exchange scheme, and the hybrid cluster–continuum (Pliego and Riveros) and implicit–explicit (Kelly, Cramer and Truhlar) models. Additionally, these protocols are applied in the pK _a calculation of 55 neutral organic and inorganic acids in conjunction with various solvent models, including the CPCM-UAKS/UAHF, IPCM, SM6 and COSMO-RS, with a view to identifying a universal approach for accurate pK _a predictions. The results indicate that the direct method is unsuitable for general pK _a calculations, although moderately accurate results (MAD <3 units) are possible for certain classes of acids, depending on the choice of solvent model. The proton exchange scheme generally delivers good results (MAD <2 units), with CPCM-UAKS giving the best performance. Furthermore, the sensitivity of this approach to the choice of reference acid can be substantially lessened if the solvation energies for ionic species are calculated via the IPCM cluster–continuum approach. Reference-independent hybrid approaches that include explicit water molecules can potentially give reasonably accurate values (MAD generally ~2 units) depending on the solvent model and the number of explicit water molecules added.     

A pH Scale for the Protic Ionic Liquid Ethylammonium Nitrate

To quantify the properties of protic ionic liquids (PILs) as acid–base reaction media, potentiometric titrations were carried out in a neat PIL, ethylammonium nitrate (EAN). A linear relationship was found between the 14 pK_a values of 12 compounds in EAN and in water. In other words, the pK_a value in EAN was found to be roughly one unit greater than that in water regardless of the charge and hydrophobicity of the compounds. It is possible that this could be explained by the stronger acidity of HNO₃ in EAN than that of H₃O⁺ in water and not by the difference in the solvation state of the ions. The pH value in EAN ranges from ?1 to 9 on the pH scale based on the pH value in water.     

Relative pKa of some anilinium derivatives in methanol,acetonitrile, and tetrahydrofurane solvents

In this study, the relative pK_a values of nine anilinium derivatives in methanol (MeOH), acetonitrile (AN), and tetrahydrofurane (THF) solutions were successfully calculated with mean absolute deviations of 0.63, 0.68, and 0.75 pK_a units, respectively. To this aim, their gas‐phase basicities were computed using the CBS‐QB3 composite method. Also, conductor‐like polarizable continuum model (CPCM) with UAHF, UAKS and UA0 cavities and SM8 solvation models at HF/6‐31+G(d) level of theory were applied for the calculation of the solvation Gibbs free energies. The obtained results indicate that there is reliable correlation between the experimental and computed pK_a values in the studied solutions. Therefore, to extend the pK_a database for anilines, correlation equations were used to predict the pK_a values in the investigated solvents.     

Calculation of dissociation constants and chemical hardness of some biologically important molecules: A theoretical study

The gas‐phase geometries of neutral, protonated, and deprotonated forms of some biologically important molecules, alanine (Ala), glycine (Gly), phenylalanine (Phe), and tyrosine (Tyr), were optimized using density functional theory at B3LYP/6‐311++G(d) and the ab initio HF/6‐311++G(d) level of theories. The neutral and different stable ionic states of Ala, Gly, Phe, and Tyr have also been solvated in aqueous medium using polarizable continuum model for the determination of solvation free energies in the aqueous solution. The gas‐phase acidity constants of above four molecules have been also calculated at both levels of theories and found that the values calculated at HF/6‐311++G(d) method are in good agreement with experimental results. A thermodynamic cycle was used to determine the solvation free energies for the proton dissociation process in aqueous solution and the corresponding pK_a values of these molecules. The pK_a values calculated at B3LYP/6‐311++G(d) method are well supported by the experimental data with a mean absolute deviation 0.12 pK_a units. Additionally, the chemical hardness and the ionization potential (IP) for these molecules have been also explored at both the level of theories. The Tyr has less value of chemical hardness and IP at both levels of theories compared with other three molecules, Ala, Gly, and Phe. The calculated values of chemical hardness and IP are decreasing gradually with the substitution of the various functional groups in the side chain of the amino acids. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Determination of thermodynamic pKa values of benzimidazole and benzimidazole derivatives by capillary electrophoresis

Thermodynamic pK_a values for benzimidazole and several substituted benzimidazoles were determined by CE. Electrophoretic mobilities of benzimidazoles were determined by CE at different pH levels and ionic strengths. The dependence of electrophoretic mobilities on pH was used to obtain pK_a values at different ionic strengths. Extrapolations to zero ionic strength were used to determine the thermodynamic pK_a values. Using this method the thermodynamic pK_a values of 15 benzimidazoles were determined and found to range from 4.48 to 7.38. Results from the CE measurements were compared with spectrophotometric measurements which were evaluated at wavelengths where the highest absorbance difference for varying pH was recorded. The two analytical techniques were in good agreement.     

Potentiometric and spectrophotometric pKa determination of water-insoluble compounds: validation study in a new cosolvent system

In this paper the validation of pK_a determination in MDM-water mixtures is presented. The MDM-water mixture is a new multicomponent cosolvent mixture (consisting of equal volumes of methanol, dioxane and acetonitrile, as organic solvents) that dissolves a wide range of poorly water-soluble compounds. The cosolvent dissociation constants (p_sK_a) of 50 chemically diverse compounds (acids, bases and ampholytes) were measured in 15-56 wt% MDM-water mixtures by potentiometric or spectrophotometric titration and the aqueous pK_a values obtained by extrapolation. Three different extrapolation procedures were compared in order to choose the best extrapolation in MDM-water mixture using a sub-set of 30 water-soluble compounds. The extrapolated results are in good agreement with pK_a values measured in aqueous medium. No significant difference was found among these extrapolation procedures thus the widely used Yasuda-Shedlovsky plot was proposed for MDM cosolvent also. Further we also present that the single point estimation based on measurement in 20%/v MDM-mixture using a general calibration equation may be suitable for rapid pK_a determination in the early phase of drug research.