Accurate prediction of basicity in aqueous solution with COSMO-RS

The COSMO-RS method, a combination of the quantum chemical dielectric continuum solvation model COSMO with a statistical thermodynamics treatment for realistic solvation simulations, has been used for the prediction of base pK(a) constants. For a variety of 43 organic bases the directly calculated values of the free energies of dissociation in water showed a very good correlation with experimental base pK(a) values (r2 = 0.98), corresponding to a standard deviation of 0.56 pK(a) units. Thus, we have an a priori prediction method for base pK(a) with the regression constant and the slope as only adjusted parameters. In accord with recent findings for pK(a) acidity predictions, the slope of pK(a) vs. DeltaG(diss) was significantly smaller than the theoretically expected value of 1/RTln(10). The predictivity of the presented method is general and not restricted to certain compound classes, but systematic corrections of 1 and 2 pKa units for secondary and tertiary aliphatic amines are required, respectively. The pK(a) prediction method was validated on a set of 58 complex multifunctional drug-like compounds, yielding an RMS accuracy of 0.66 pK(a) units.     

A reliable and efficient first principles-based method for predicting pKa values. III. Adding explicit water molecules: Can the theoretical slope be reproduced and pKa values predicted more accurately?

A popular method for predicting pK(a) values for organic molecules in aqueous solution is to establish empirical linear least-squares fits between calculated deprotonation energies and known experimental pK(a) values. In virtually all such calculations, the empirically observed slope of the pK(a) vs. ΔE fit is significantly less than the theoretical value, 1/(2.303RT) (which is 0.73 mol/kcal at room temperature). In our own continuum solvation calculations (Zhang et al., J Phys Chem A 2010, 114, 432), the empirical slope for carboxylic acids was only 0.23 mol/kcal, despite the excellent fit to the experimental pK(a) values. There has been much speculation about the reason for this phenomenon. Although the ΔE - pK(a) relation neglects entropic effects, these are expected to largely cancel. The most likely cause for the strange behavior of the fitted slope is explicit solute-solvent (water) interactions, especially involving the ions, which cannot be described accurately by continuum solvation models. We used our previously developed pK(a) protocol (OLYP/6-311+G(d,p)//3-21G(d) with the COSMO solvation model) to investigate the effect of adding one or two explicit water molecules to the system. The slopes for organic acids (especially carboxylic acids) are much closer to the theoretical value when explicit water molecules are added to both the neutral molecule and the anion. However, explicit water molecules have almost no effect on the slopes for organic bases. Adding explicit water molecules to the ions only produces intermediate results. Unfortunately, linear fits involving explicit water molecules have much larger errors than with continuum solvation models alone and are also much more expensive. Consequently, they are not suitable for large-scale pK(a) calculations. The results compared with literature values showed that our predicted pK(a) s are more accurate.     

Extension of the self-consistent spectrophotometric basicity scale in acetonitrile to a full span of 28 pKa units: unification of different basicity scales

The earlier compiled self-consistent spectrophotometric basicity scale in acetonitrile (AN) was expanded to range from 3.8 to 32.0 pK(a) units, that is 28 orders of magnitude. Altogether 54 new relative basicity measurements (DeltapK(a) measurements) were carried out and 37 new compounds were introduced to the scale (it now includes altogether 89 bases). The relative basicity of any two bases in the scale can be obtained by combining at least two independent sets of measurements. Multiple overlapping measurements make the results more reliable. The overall consistency (as defined earlier) of the measurements is s = 0.03 pK(a) units. Thorough analysis of all of our experimental data (DeltapK(a) values of this and earlier works) and experimental pK(a) data in AN available in the literature (works from the groups of Coetzee and Padmanabhan, Kolthoff and Chantooni, Jr., the Schwesinger group, Bren' et al. and some others, altogether 19 papers) was carried out. On the basis of this analysis the anchor point of the scale-pyridine-was shifted upward by 0.20 pK(a) units thereby also revising the absolute pK(a) values of all the bases on the scale. This way very good agreement between our relative data and the absolute pK(a) values of the abovementioned authors was obtained. The revised basicity scale was interconnected with the earlier published self-consistent acidity scale by DeltapK(a) measurements between acids and bases. The rms deviation between the directly measured DeltapK(a) values and the absolute pK(a) values of the compounds was 0.10 pK(a) units.     

Accurate pK(a) calculations for 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 CPCM continuum solvation methods to calculate pK(a) values for six carboxylic acids. An experimental value of -264.61 kcal/mol for the free energy of solvation of H(+), DeltaG(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. 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.     

Influence of water content on the acidities in acetonitrile. Quantifying charge delocalization in anions

The effect of traces of water on the relative strengths of acids (ΔpK(a) values) in acetonitrile was quantitatively evaluated experimentally and computationally (COSMO-RS). Water affects first of all the anions by selective solvation. Expectedly, the more localized is the charge in acid anions the higher is the effect of water. The energetic effect of increasing water content from 0 to ca. 10,000 ppm on solvation enthalpies of anions ranged from 0.2-0.4 kcal mol?1 (anions with delocalized charges) to 15 kcal mol?1 in the case of the highly charge-localized acetate ion. In the case of ΔpK(a) values the change ranges from 0.01 to ca. 1.7 pK(a) units (acid pair involving acetic acid). The COSMO-RS method was found to satisfactorily describe the trends in ΔpK(a) values. To quantify the extent of charge localization/delocalization in anions a parameter, weighted average positive σ (WAPS), was introduced, which can be conveniently computed using the COSMO approach. WAPS characterizes the distribution of charge density across the molecular surface and was found to correlate well with the extent of water influence on the dissociation of the respective acid.     

Prediction of the dissociation constant pKa of organic acids from local molecular parameters of their electronic ground state

A quantum chemical method has been developed to estimate the dissociation constant pK(a) of organic acids from their neutral molecular structures by employing electronic structure properties. The data set covers 219 phenols (including 29 phenols with intramolecular H-bonding), 150 aromatic carboxylic acids, 190 aliphatic carboxylic acids, and 138 alcohols, with pK(a) varying by 16 units (0.38-16.80). Optimized ground-state geometries employing the semiempirical AM1 Hamiltonian have been used to quantify the site-specific molecular readiness to donate or accept electron charge in terms of both charge-associated energies and energy-associated charges, augmented by an ortho substitution indicator for aromatic compounds. The resultant regression models yield squared correlation coefficients (r(2)) from 0.82 to 0.90 and root-mean-square errors (rms) from 0.39 to 0.70 pK(a) units, corresponding to an overall (subset-weighted) r(2) of 0.86. Simulated external validation, leave-10%-out cross-validation and target value scrambling demonstrate the statistical robustness and prediction power of the derived model suite. The low intercorrelation with prediction errors from the commercial ACD package provides opportunity for a consensus model approach, offering a pragmatic way for further increasing the confidence in prediction significantly. Interestingly, inclusion of calculated free energies of aqueous solvation does not improve the prediction performance, probably because of the limited precision provided by available continuum-solvation models.     

Critical validation of a new simpler approach to estimate aqueous pKa of drugs sparingly soluble in water

A simple linear approach to estimate the aqueous pK_a of compounds sparingly soluble in water, mainly drugs, from solely one pK_a value determined in any methanol/water mixture is evaluated. The parameters (slope and intercept) of the linear relationships are related to the solvent composition and can be easily calculated according to the acidic or basic functional group of the compound. The method has been tested using the available literature data for phenols, aliphatic carboxylic acids, benzoic acid derivatives, both ortho and non-ortho substituted, amines and imidazole derivatives. The study involves the whole range of solvent composition and about one hundred compounds which show a wide variety of aqueous pK_a, from 1.3 to 12.4. The differences between calculated and previously published aqueous pK_a values are less of 0.2 pK units. Consistent values are obtained whatever the composition of methanol/water mixture employed in the experimental measurements. The results support the usefulness of the tested method as a very simple approach to get reliable aqueous pK_a values for sparingly soluble drugs.     

Calculations of pKa of superacids in 1,2-dichloroethane

Acidity calculations for some CH and NH superacids in 1,2-dichloroethane (DCE) were carried out using SMD and COSMO-RS continuum solvation models. After comparing the results of calculations with respective experimental pK(a) values it was found that the performance of SMD/M05-2X/6-31G* method is characterized by the mean unsigned error (MUE) of 0.5 pK(a) units and the slope of regression line of 0.915. The similar SMD/B3LYP/6-31G* approach was slightly less successful. The strong correlation over entire data set is confirmed by R(2) values of 0.990 and 0.984 for M05-2X and B3LYP functionals, respectively. The COSMO-RS method, while providing the value of the linear regression line slope similar to the corresponding values from SMD approach, characterized by rather loose correlation (R(2) = 0.823, MUE = 1.7 pK(a) units) between calculated and experimental pK(a) values in DCE solution.     

Quantum-chemical predictions of absolute standard redox potentials of diverse organic molecules and free radicals in acetonitrile

A calibrated B3LYP/6-311++G(2df,2p)//B3LYP/6-31+G(d) method was found to be able to predict the gas-phase adiabatic ionization potentials of 160 structurally unrelated organic molecules with a precision of 0.14 eV. A PCM solvation model was benchmarked that could predict the pK(a)'s of 15 organic acids in acetonitrile with a precision of 1.0 pK(a) unit. Combining the above two methods, we developed a generally applicable protocol that could successfully predict the standard redox potentials of 270 structurally unrelated organic molecules in acetonitrile. The standard deviation of the predictions was 0.17 V. The study demonstrated that computational electrochemistry could become a powerful tool for the organic chemical community. It also confirmed that the continuum solvation theory could correctly predict the solvation energies of organic radicals. Finally, with the help of the newly developed protocol we were able to establish a scale of standard redox potentials for diverse types of organic free radicals for the first time. Knowledge about these redox potentials should be of great value for understanding the numerous electron-transfer reactions in organic and bioorganic chemistry.     

pKa prediction from an ab initio bond length: part 3--benzoic acids and anilines

The prediction of pK(a) from a single ab initio bond length has been extended to provide equations for benzoic acids and anilines. The HF/6-31G(d) level of theory is used for all geometry optimisations. Similarly to phenols (Part 2 of this series of publications), the meta-/para-substituted benzoic acids can be predicted from a single model constructed from one bond length. This model had an impressive RMSEP of 0.13 pK(a) units. The prediction of ortho-substituted benzoic acids required the identification of high-correlation subsets, where the compounds in the same subset have at least one of the same (e.g. halogens, hydroxy) ortho substituent. Two pK(a) equations are provided for o-halogen benzoic acids and o-hydroxybenzoic acids, where the RMSEP values are 0.19 and 0.15 pK(a) units, respectively. Interestingly, the bond length that provided the best model differed between these two high-correlation subsets. This demonstrates the importance of investigating the most predictive bond length, which is not necessarily the bond involving the acid hydrogen. Three high-correlation subsets were identified for the ortho-substituted anilines. These were o-halogen, o-nitro and o-alkyl-substituted aniline high-correlation subsets, where the RMSEP ranged from 0.23 to 0.44 pK(a) units. The RMSEP for the meta-/para-substituted aniline model was 0.54 pK(a) units. This value exceeded our threshold of 0.50 pK(a) units and was higher than both the m-/p-benzoic acids in this work and the m-/p-phenols (RMSEP = 0.43) of Part 2. Constructing two separate models for the meta- and para- substituted anilines, where RMSEP values of 0.63 and 0.33 pK(a) units were obtained respectively, revealed it was the meta-substituted anilines that caused the large RMSEP value. For unknown reasons the RMSEP value increased with the addition of a further twenty meta-substituted anilines to this model. The C-N bond always produced the best correlations with pK(a) for all the high-correlation subsets. A higher level of theory and an ammonia probe improved the statistics only marginally for the hydroxybenzoic acid high-correlation subsets.     

Accurate pKa determination for a heterogeneous group of organic molecules.

Single-molecule studies that allow to compute pKa values, proton affinities (gas-phase acidity/basicity) and the electrostatic energy of solvation have been performed for a heterogeneous set of 26 organic compounds. Quantum mechanical density functional theory (DFT) using the Becke-half&half and B3LYP functionals on optimized molecular geometries have been carried out to investigate the energetics of gas-phase protonation. The electrostatic contribution to the solvation energies of protonated and deprotonated compounds were calculated by solving the Poisson equation using atomic charges generated by fitting the electrostatic potential derived from the molecular wave functions in vacuum. The combination of gas-phase and electrostatic solvation energies by means of the thermodynamic cycle enabled us to compute pKa values for the 26 compounds, which cover six distinct chemical groups (carboxylic acids, benzoic acids, phenols, imides, pyridines and imidazoles). The computational procedure for determining pKa values is accurate and transferable with a root-mean-square deviation of 0.53 and 0.57 pKa units and a maximum error of 1.0 pKa and 1.3 pKa units for Becke-half&half and B3LYP DFT functionals, respectively.     

A comprehensive self-consistent spectrophotometric acidity scale of neutral Brønsted acids in acetonitrile

For the first time, the self-consistent spectrophotometric acidity scale of neutral Br?nsted acids in acetonitrile (AN) spanning 24 orders of magnitude of acidities is reported. The scale ranges from pK(a) 3.7 to 28.1 in AN. The scale includes 93 acids that are interconnected by 203 relative acidity measurements (DeltapK(a) measurements) and contains compounds with gradually changing acidities, including representatives from all of the conventional families of OH (alcohols, phenols, carboxylic acids, sulfonic acids), NH (anilines, diphenylamines, disulfonimides), and CH acids (fluorenes, diphenylacetonitriles, phenylmalononitriles). The CH acids were particularly useful in constructing the scale because they do not undergo homo- or heteroconjugation processes and their acidities are rather insensitive to traces of water in the medium. The scale has been fully cross-validated: the relative acidity of any two acids on the scale can be found by combining at least two independent sets of DeltapK(a) measurements. The consistency standard deviation of the scale is 0.03 pK(a) units. Comparison of acidities in many different media has been carried out, and the structure-acidity relations are discussed. The large variety of the acids on the scale, its wide span, and the quality of the data make the scale a useful tool for further acidity studies in acetonitrile.     

Quantum-chemical predictions of redox potentials of organic anions in dimethyl sulfoxide and reevaluation of bond dissociation enthalpies measured by the electrochemical methods

A first-principle theoretical protocol was developed that could predict the absolute pK(a) values of over 250 structurally unrelated compounds in DMSO with a precision of 1.4 pK(a) units. On this basis we developed the first theoretical protocol that could predict the standard redox potentials of over 250 structurally unrelated organic anions in DMSO with a precision of 0.11 V. Using the two new protocols we systematically reevaluated the bond dissociation enthalpies (BDEs) measured previously by the electrochemical methods. It was confirmed that for most compounds the empirical equation (BDE = 1.37 pK(HA) + 23.1E(o) + constant) was valid. The constant in this equation was determined to be 74.0 kcal/mol, compared to 73.3 kcal/mol previously reported. Nevertheless, for a few compounds the empirical equation could not be used because the solvation energy changed dramatically during the bond cleavage, which resulted from the extraordinary change of dipole moment during the reaction. In addition, we found 40 compounds (mostly oximes and amides) for which the experimental values were questionable by over 5 kcal/mol. Further analyses revealed that all these questionable BDEs could be explained by one of the three following reasons: (1) the experimental pK(a) value is questionable; (2) the experimental redox potential is questionable; (3) the solvent effect cannot be neglected. Thus, by developing practical theoretical methods and utilizing them to solve realistic problems, we hope to demonstrate that ab initio theoretical methods can now be developed to make not only reliable, but also useful, predictions for solution-phase organic chemistry.     

Ab initio prediction of the gas- and solution-phase acidities of strong Brønsted acids: the calculation of pKa values less than -10

The intrinsic gas-phase acidities of a series of 21 Br?nsted acids have been predicted with G3(MP2) theory. The G3(MP2) results agree with high level CCSD(T)/CBS acidities for H(2)SO(4), FSO(3)H, CH(3)SO(3)H, and CF(3)SO(3)H to within 1 kcal/mol. The G3(MP2) results are in excellent agreement with experimental gas-phase acidities in the range 342-302 kcal/mol to within <1 kcal/mol for 14 out of 15 acids. Five of the six acids in the range of 302-289 kcal/mol had an average deviation of 5.5 kcal/mol and the strongest acid, (CF(3)SO(2))(3)CH, deviated by 15.0 kcal/mol. These high-level calculations strongly suggest that the experimental acidities in this very acidic part of the scale need to be remeasured. The CCSD(T)/CBS (mixed exponential Gaussian) additive approach for CH(3)CO(2)H, HNO(3), H(2)SO(4), CH(3)SO(3)H, FSO(3)H, and CF(3)SO(3)H gives excellent agreement (+/-1 kcal/mol) with experiment for the DeltaH(f)(0)'s of non-sulfur containing species, and supports the low end of the experimental values for H(2)SO(4) and FSO(3)H. Use of a larger basis set (aug-cc-pV5Z) in the CBS extrapolation improves the agreement with experiment for both H(2)SO(4) and FSO(3)H. The G3(MP2) heats of formation for RSO(3)H molecules tend to be underestimated as compared to the CCSD(T)/CBS approach by 2.5-7.0 kcal/mol. COSMO solvation calculations were used to predict solution free energies and pK(a) values with pK(a)'s up to -17.4. Including the solvation of the proton gives good agreement with experimental pK(a) values in the very acidic regime, whereas it is less reliable for weaker acids. The use of CH(3)CO(2)H and HNO(3) as reference acids in the less acidic and more acidic regions of the scale, respectively, provided improved results to within +/-2 pK(a) units in nearly all cases (+/-3 kcal/mol accuracy).     

Dependence of pKa on solute cavity for diprotic and triprotic acids

A systematic study of ΔG(aq)/pK(a) for monoprotic, diprotic, and triprotic acids has been carried out based on DFT/aug-cc-pVTZ combined with CPCM and SMD solvation modeling. All DFT/cavity set combinations considered showed similar accuracy for ΔG(aq)(1)/pK(a1) (70% within ±2.5 kcal mol(-1) of experiment) while only the M05-2X/Pauling cavity combination gave reasonable results for ΔG(aq)(2)/pK(a2) when both pK(a) values are separated by more than three units (70% within ±5.0 kcal mol(-1) of experiment). The choice of experimental data is critical to the interpretation of the calculated accuracy especially for several inorganic acids. For the calculation of ΔG(aq)(3)/pK(a3), the larger experimental uncertainty and an unrealistic orbital population of diffuse function for trianions in the gas phase hinders an evaluation of the predictive performance. We find the M05-2X functional with the Pauling cavity set is the best choice for ΔG(aq)(2)/pK(a2) prediction in aqueous media while all DFT/cavity sets considered were competitive for ΔG(aq)(1)/pK(a1).     

Protonation equilibria of quinolone antibacterials in acetonitrile-water mobile phases used in LC

Ionization constants of nine quinolone antibacterials in acetonitrile-water mixtures containing 0, 5.5, 10, 16.3, 25, 30, 40, 50 and 70% (w/w) acetonitrile were obtained and assignment of these pK values to the several potentially ionizable functional groups was made. The variation of the pK values obtained over the whole composition range studied can be explained by consideration of the preferential solvation of electrolytes in acetonitrile-water mixtures. In order to obtain pK values in any of the unlimited number of possible binary solvent acetonitrile-water mixtures, relationships between pK values and different bulk properties (such as dielectric constant) were examined. The linear solvation energy relationships method, LSER, was applied to study the correlation of pK values with the solvatochromic parameters of acetonitrile-water mixtures. The equations obtained allow calculation of the pK values of the quinolone antimicrobials in any acetonitrile-water mixtures up to 70% (w/w) and thus permit the knowledge of the acid-base behaviour of these important antimicrobials in the widely used acetonitrile-water media.     

Molecular Modeling for Mobile Phase Optimization in RP-HPLC

Abstract

The applicability of molecular parameters calculated on the bases of molecular mechanics have been investigated for the prediction of reversed-phase retention behavior of structurally unrelated series of drug molecules. Non-polar, non-polar unsaturated and polar surface areas, surface energies, dipole moments, van der Waals radii and hydrophobicity values expressed by the logarithm of the octanol/water partition coefficients have been calculated from the molecular structure. The reversed-phase retention behavior was described by the slope and the intercept of the straight lines obtained by plotting the log k¹ values against the acetonitrile concentration of the mobile phase. The acetonitrile concentration (OP%₀) which was needed for the log k¹ = 0 retention was also calculated from the slope and intercept values. Step-wise linear regression analyses have been applied for revealing the correlations between the investigated parameters. The slope values could be described by the difference of the non-polar and non-polar accessible surface areas or by the total surface energy values and the van der Waals radii. The intercept values could be described by the hydrophobicity parameter, the slope and the reciprocal values of dipole moment. The acetonitrile concentration for the log k'=O retention (OP%₀) could have been calculated from the hydrophobicity and the non-polar unsaturated surface area values of the investigated compounds.     

First-principle calculation of equilibrium cesium ion-pair acidities in tetrahydrofuran

The ion-pair acidities of organic acids in THF are fundamental to synthetic organic chemistry. Although the ion-pair acidities of a number of carbon acids have been experimentally measured by Streitwieser and co-workers, it is important to develop a theoretical method that can accurately predict these quantities because not all the organic acids (e.g., very weak acids or complex synthetic intermediates with multiple acidic positions) are amenable to experimental characterization. In the present study is reported the first theoretical protocol for predicting the cesium ion-pair acidities in THF whose reliability has been tested against almost all the available experimental data. It is found that the root-mean-square error of the current theoretical model equals 1.2 pK units. With the newly developed theoretical method in hand, the structures of cesium ion pairs of different types of carbon acids are then studied. The cesium ion-pair acidities in THF and absolute ionic acidities in DMSO are also systematically compared, which confirms Streitwieser's previous finding that the two scales of acidities have only minor difference. Significantly, from detailed energy analysis the mechanism for the "fortunate" match of the two scales of acidities is found. That is, the combined process of the Cs binding ("micro"-solvation) and the solvation of the ion pair resembles the one-step solvation of a carbanion in DMSO. Finally, it is found that the cesium ion-pair acidities of nitrogen acids in THF have only minor difference from the absolute ionic acidities in DMSO. Consequently, one can easily estimate the cesium ion-pair acidities of almost all types of organic nitrogen acids in THF on the basis of Bordwell's data.     

First-principles prediction of the pK(a)s of anti-inflammatory oxicams

The gas- and aqueous-phase acidities of a series of oxicams have been computed by combining M05-2X/6-311+G(3df,2p) gas-phase free energies with solvation free energies from the CPCM-UAKS, COSMO-RS, and SMD solvent models. To facilitate accurate gas-phase calculations, a benchmarking study was further carried out to assess the performance of various density functional theory methods against the high-level composite method G3MP2(+). Oxicams are typically diprotic acids, and several tautomers are possible in each protonation state. The direct thermodynamic cycle and the proton exchange scheme have been employed to compute the microscopic pK(a)s on both solution- and gas-phase equilibrium conformers, and these were combined to yield the macroscopic pK(a) values. Using the direct cycle of pK(a) calculation, the CPCM-UAKS model delivered reasonably accurate results with MAD ~ 1, whereas the SMD and COSMO-RS models' performance was less satisfactory with MAD ~ 3. Comparison with experiment also indicates that direct cycle calculations based on solution conformers generally deliver better accuracy. The proton exchange cycle affords further improvement for all solvent models through systematic error cancellation and therefore provides better reliability for the pK(a) prediction of compounds of these types. The latter approach has been applied to predict the pK(a)s of several recently synthesized oxicam derivatives.