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.     

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     

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.     

Absolute calculations of acidity of C-substituted tetrazoles in solution

The CBS-QB3 method was used to calculate the gas-phase free energy difference between nine tetrazole derivatives and their anions, and the DPCM and CPCM continuum solvation methods were applied to calculate the free energy differences of solvation. The calculations were performed on both gas-phase and solvent-phase optimized structures. Absolute pKa calculations using the CPCM method and the gas-phase optimized structures yielded mean unsigned error of 0.4 pKa unit. The calculations were made with the routine settings implemented in Gaussian 98. The study is as accurate as the best reported so far for six carboxylic acids and phenols and, to our knowledge, the best reported for the acidities of heterocyclic compounds in solution.     

Determination of aqueous acid‐dissociation constants of aspartic acid using PCM/DFT method

Determination of acid‐dissociation constants, pK_a, of aspartic acid in aqueous solution, using density functional theory calculations combined with the conductor‐like polarizable continuum model (CPCM) and with integral‐equation‐formalism polarizable continuum model (IEFPCM) based on the UAKS and UAHF radii, was carried out. The computed pK_a values derived from the CPCM and IEFPCM with UAKS cavity model of bare structures of the B3LYP/6‐31+G(d,p)‐optimized tetrahydrated structures of aspartic acid species are mostly close to the experimental pK_a values. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Cavity shape effect on pKa prediction of small amines

Cavity shape affects the free energy of solvation by which pK_a changes. In this work, we have used different level of theories and basis sets combine with the PCM model of solvation to predict acidity constants of small ammonium ions during their protonation in aqueous solution. Three different kinds of models including UAHF, Bondi, and Pauling have been chosen to study that how a cavity shape changes acidity constant. Contrary to the previous results of literature for bulky ammonium ions, the difference between our results is not very much. Predictions show that in some levels and basis sets UAHF model is the best, while in some other cases it is the worst.     

Theoretical calculation of the pKa values of some drugs in aqueous solution

In this work, calculations of pK_a values have been performed on benzoic acid and its para‐substituted derivatives and some drugs by using Gaussian 98 software package. Gas‐phase energies were calculated with HF/6‐31 G** and B3LYP/6‐31 G** levels of theory. Free energies of solvation have been computed using the polarizable continuum model (PCM), conductor‐like PCM (CPCM), and the integral equation formalism‐PCM at the same levels which have been used for geometry determination in the gas‐phase. The results that show the calculated pK_a values using the B3LYP are better than those using the corresponding HF. In comparison to the other models, the results obtained indicate that the PCM model is a suitable solvation model for calculating pK_a values. For the investigated compounds, a good agreement between the experimental and the calculated pK_a values was also observed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Conformation dependence of pKa’s of the chromophores from the purple asFP595 and yellow zFP538 fluorescent proteins

Two members of the green fluorescent protein family, the purple asFP595 and yellow zFP538 proteins, are perspective fluorescent markers for use in multicolor imaging and resonance energy-transfer applications. We report the results of quantum based calculations of the solution pK_a values for selected protonation sites of the denatured asFP595 and zFP538 chromophores in the trans- and cis-conformations in order to add in the interpretation of photo-physical properties of these proteins. The pK_a values were determined from the theromodynamic cycle based on B3LYP/6-311++G(2df, 2p) calculations of the gas phase free energies of the molecules and the B3LYP/6-311++G(d, p) calculations of solvation energies. The results show that the pK_a’s of the protonation sites of the chromophore from asFP595 noticeably depend on the isomer conformation (cis- or trans-), while those of zFP538 are much less sensitive to isomerization.     

Computation of the influence of chemical substitution on the pK a of pyridine using semiempirical and ab initio methods

The physical properties of chemicals are strongly influenced by their protonation state, affecting, for example, solubility or hydrogen-bonding characteristics. The ability to accurately calculate protonation states in the form of pK _as is, therefore, desirable. Calculations of pK _a changes in a series of substituted pyridines are presented. Computations were performed using both ab initio and semiempirical approaches, including free energies of solvation via reaction-field models. The selected methods are readily accessible with respect to both software and computational feasibility. Comparison of calculated and experimental pK _as shows the experimental trends to be reasonably reproduced by the computations with root-mean-square differences ranging from 1.22 to 4.14 pK _a units. Of the theoretical methods applied the best agreement occurred using the second-order M?ller–Plesset/6-31G(d)/isodensity surface polarized continuum solvation model, while the more computationally accessible Austin model 1/Solvent model 2 (SM2) approach yielded results similar to the ab initio methods. Analysis of component contributions to the calculated pK _as indicates the largest source of error to be associated with the free energies of solvation of the protonated species followed by the gas-phase protonation energies; while the latter may be improved via the use of higher levels of theory, enhancements in the former require improvements in the solvation models. The inclusion of alternate minimum in the computation of pK _as is also indicated to contribute to differences between experimental and calculated pK _a values. Received: 27 April 1999 / Accepted: 27 July 1999 / Published online: 2 November 1999     

Accurate pKa Calculation of the Conjugate Acids of Alkanolamines,Alkaloids and Nucleotide Bases by Quantum Chemical Methods

The pK_a of the conjugate acids of alkanolamines, neurotransmitters, alkaloid drugs and nucleotide bases are calculated with density functional methods (B3LYP, M08‐HX and M11‐L) and ab initio methods (SCS‐MP2, G3). Implicit solvent effects are included with a conductor‐like polarizable continuum model (CPCM) and universal solvation models (SMD, SM8). G3, SCS‐MP2 and M11‐L methods coupled with SMD and SM8 solvation models perform well for alkanolamines with mean unsigned errors below 0.20 pK_a units, in all cases. Extending this method to the pK_a calculation of 35 nitrogen‐containing compounds spanning 12 pK_a units showed an excellent correlation between experimental and computational pK_a values of these 35 amines with the computationally low‐cost SM8/M11‐L density functional approach.     

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.     

Absolute pK(a) determinations for substituted phenols

The CBS-QB3 method was used to calculate the gas-phase free energy difference between 20 phenols and their respective anions, and the CPCM continuum solvation method was applied to calculate the free energy differences of solvation for the phenols and their anions. The CPCM solvation calculations were performed on both gas-phase and solvent-phase optimized structures. Absolute pK(a) calculations with solvated phase optimized structures for the CPCM calculations yielded standard deviations and root-mean-square errors of less than 0.4 pK(a) unit. This study is the most accurate absolute determination of the pK(a) values of phenols, and is among the most accurate of any such calculations for any group of compounds. The ability to make accurate predictions of pK(a) values using a coherent, well-defined approach, without external approximations or fitting to experimental data, is of general importance to the chemical community. The solvated phase optimized structures of the anions are absolutely critical to obtain this level of accuracy, and yield a more realistic charge separation between the negatively charged oxygen and the ring system of the phenoxide anions.     

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     

Hydrogen bond interactions at the TiO2 surface: Their contribution to the pH dependent photo-catalytic degradation of p-nitrophenol

We have obtained pK_a values of p-nitrophenol–TiO₂ by measuring the adsorption equilibrium constants of p-nitrophenol (PNP) on the TiO₂ surface at different pH values. These values have been obtained from Langmuir isotherms and from a plot of 1/rate vs. 1/[PNP]_o obtained during TiO₂ catalyzed solar light photo-degradation of PNP. Two limit equilibrium constants are readily obtained depending on the solution pH: at pH 5 at which the TiO₂ surface is mainly positively charged and at pH 8 when it is negatively charged. With these and other adsorption equilibrium constants and the PNP pK_a value in solution, thermodynamic cycles are established in order to obtain the PNP pK_a when it is adsorbed on positively charged, neutral and negatively charged TiO₂ surfaces. From these pK_a values useful information on the PNP–TiO₂ interaction is readily obtained. For instance, the PNP nitro group interacts with the TiO₂ surface via a hydrogen bond, arising from the complex of water molecules with the Ti⁴⁺ ions on its surface. The weaker the hydrogen bond donor, the stronger the oxygen nitro group basicity. Therefore, pK_a changes on the phenolic hydroxyl group result from these interactions. Linear free energy correlations, maximum PNP adsorption capacity values (Q_L) and FTIR ATR, spectrum support this proposal. A k_obs vs. pH degradation profile of p-nitrophenol is also provided.     

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.     

Thermodynamic quantities for the acid dissociation of alkylammonium ions in water over a wide temperature range

Enthalpies of protonation in aqueous solution have been determined from calorimetric measurements between 0 and 100°C for methylpentylamine, butyldimethylamine, and quinuclidine; between 0 and 125°C for di-iso-propylamine; and between 0 and 75°C for 1-azacycloheptane. Values ofpK_a at 25°C have been determined from pH measurements using a glass electrode for di-iso-propyl-, methylpentyl-, and butyldimethylamine. The calorimetric results are used together with values ofpK_a at 25°C to derive expressions which allow the calculation of accuratepK_a values over a large temperature range. The heat capacity and entropy changes for the protonation of aqueous alkylamines found in the present and in previous studies are discussed in terms of differences in hydrophobic solvation of the alkyl groups in the neutral amines and the ions.     

The role of isomerism and medium effects on stability of anions of formo- and thioformohydroxamic acid

The anionic forms of formo- and thioformohydroxamic acids have been analyzed for their relative stabilities and barriers for interconversion between the tautomeric forms employing ab initio and DFT methods. The deprotonation affinities and pK_a values are evaluated to differentiate the various deprotonation processes. The effect of medium on deprotonation behavior is analysed using Tomasi’s PCM model and examining free energy changes of deprotonation from isolated molecules, molecule–water aggregates and subsequently from anion–water aggregates in the gas phase and aqueous phase respectively. Variation of geometrical parameters, charges, electron delocalizations, intramolecular H-bonding and relative stabilities upon water aggregation of the anions all point towards NH deprotonation as the most favored process.     

Capillary zone electrophoresis of basic drugs in non-aqueous acetonitrile with buffers based on a conventional pH scale

Summary The pK _a ^* values of 10 nitrogen-containing basic drugs in non-aqueous acetonitrile were determined from the pH^* dependence of their electrophoretic mobilities. The pH^* scale in the organic solvent was established using background electrolytes with known conventional pK _a ^* values, making further calibration with reference pH electrodes unnecessary. In acetonitrile the pK _a ^* values of analytes (or their conjugated cation acids, BH⁺, respectively) were 5.2±8.9 pK units>those in water. The observed change in pK _a ^* values of cationic analytes was, however, much less than the known respective change for neutral acids type HA. From the pK _a ^* values and the actual mobilities, it is possible to predict pH^* conditions to enable separation of analytes, and this was demonstrated for two pairs of common drugs.     

Calculation of acidic dissociation constants in water: solvation free energy terms. Their accuracy and impact

Three polarizable continuum models, DPCM, CPCM, and IEFPCM, have been applied to calculate free energy differences for nine neutral compounds and their anions. On the basis of solvation free energies, the pK_a values were obtained for the compounds in question by using three thermodynamic cycles: one, involving the combined experimental and calculated data, as well as two other cycles solely with calculated data. This paper deals with the influence of factors such as the SCRF model applied, choice of a particular thermodynamic cycle, atomic radii used to build a cavity in the solvent (water), optimization of geometry in water, inclusion of electron correlation, and the dimension of the basis set on the solvation free energies and on the calculated pK_a values. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

Application of variable anti-connectivity index to active sites. Modelling pK a values of aliphatic monocarboxylic acids

A partial distance-weighted variable anti-connectivity topological index was introduced for modelling pK _a values of 31 aliphatic carboxylic acids and haloalkyl-carboxylic acids. The partial distance-weighted variable anti-connectivity index showed superior modelling capabilities compared with the index calculated from the complete graph, because it is capable of accounting correctly for the intramolecular interactions of unconnected vertices to specific bond strengths (active site), thereby improving the RMS_CV error by about 30% (0.221 pK _a units).