Prediction of acidity in acetonitrile 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 pK(a) values in acetonitrile. For a variety of 93 organic acids, the directly calculated values of the free energies of dissociation in acetonitrile showed a very good correlation with the pK(a) values (r(2) = 0.97) in acetonitrile, corresponding to a standard deviation of 1.38 pK(a) units. Thus, we have a prediction method for acetonitrile pK(a) with the intercept and the slope as the only adjusted parameters. Furthermore, the pK(a) values of CH acids yielding large anions with delocalized charge can be predicted with a rmse of 1.12 pK(a) units using the theoretical values of slope and intercept resulting in truly ab initio pK(a) prediction. In contrast to our previous findings on aqueous acidity predictions the slope of the experimental pK(a) versus theoretical DeltaG(diss) was found to match the theoretical value 1/RT ln (10) very well. The predictivity of the presented method is general and is not restricted to certain compound classes. However, a systematic correction of -7.5 kcal mol(-1) is required for compounds that do not allow electron-delocalization in the dissociated anion. The prediction model was tested on a diverse test set of 129 complex multifunctional compounds from various sources, reaching a root mean square deviation of 2.10 pK(a) units.     

Acidity of anilines: calculations vs experiment

The gas-phase acidities of ca. 60 monosubstituted anilines (with acidity span of almost 50 kcal mol(-1)) have been calculated using density functional theory (DFT) at the B3LYP/6-311+G** level. At this relatively simple level of theory the calculated (ΔG(calc)) and available experimental (ΔG(exp)) acidities are in reasonable quantitative correlation according to the following equation: ΔG(obs) = a + bΔG(calc), where a=20.79, b=0.942, n=27, R(2)=0.990, and s=0.78 kcal·mol(-1). The slope is not far from its ideal value. Substituent effects on the acidities were dissected separately into those operating in the neutral acid molecule and in its conjugated anion using the isodesmic homodesmotic reactions. All in all, both forms, neutral and anionic, are contributing in combination to make up the gross acidity of anilines. However, the contributions of the anions into the gross substituent effects are much larger than the substituent effects in the neutral anilines. Some of the systems were used in testing a relatively new theoretical model, COSMO-RS (conductor-like screening model for real solvents), using it for the prediction of pK(a) values in DMSO. The method proved to be rather accurate for showing pK(a) trends (R(2)=0.980 in DMSO). However, the predicted absolute pK(a) values were all somewhat lower (rmsd=2.49 kcal·mol(-1)) than the respective experimental values.     

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.     

Supramolecular binding thermodynamics by dispersion-corrected density functional theory

The equilibrium association free enthalpies ΔG(a) for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG(a) values in the range 0 to -21?kcal?mol(-1) (on average -6?kcal?mol(-1) ) are investigated. The theoretical approach employs a (nondynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to determine structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low-lying vibrational modes are treated by a free-rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60?kcal?mol(-1) (up to 200?% of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG(a) values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG(a) values with errors of only 2?kcal?mol(-1) on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300-400 atoms. The various contributions to binding and enthalpy-entropy compensations are discussed.     

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.     

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.     

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.     

Specific adsorption of simple organic acids on metal(hydr)oxides: a radiotracer approach

The pH dependence of adsorption of (14)C-labeled benzoic and oxalic acids on gamma-Al(2)O(3) and hematite was studied in acid medium in the presence of 0.5 mol dm(-3) NaClO(4) supporting electrolyte. It was found that the adsorption of the organic species starts at pH values where the protonation of the oxide surface takes place. In the case of benzoic acid the extent of adsorption with decreasing pH goes through a sharp maximum at a pH value not far from the pK (4.2) of the acid, while in the case of oxalic acid only a small decrease can be observed at very low pH values (pH<1). In indirect radiotracer studies using (35)S-labeled sulfate ions it was shown that the competitive adsorption of formic, malonic, maleic, and oxalic acids with sulfate ions depends on pH and the effect of the organic acid on the anion adsorption becomes pronounced at pH values about and above the pK of the acid. On the basis of these observations and considerations concerning the dissociation of the organic acids studied it is assumed that the specific adsorption of the anionic form of the acids takes place. It is, however, emphasized that the negative charge of the anions, consequently the electrostatic forces, do not play significant role in the adsorption.     

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).     

Theoretical prediction of pKa values of seleninic, selenenic, sulfinic, and carboxylic acids by quantum-chemical methods

Aqueous acid dissociation constants of substituted areneseleninic, areneselenenic, arenesulfinic, and benzoic acids are calculated by ab initio (MP2) and DFT (B3LYP) methods in combination with bulk solvation models (IEFPCM, CRSrad) from appropriate thermodynamic cycles. Mean absolute deviations (MAD) between experimental and calculated pK(a) values are quite large for basis sets without diffuse functions; however, trends are reasonably well described. Best agreement with experiment as described by MAD as well as correlation coefficient and slope of the correlation equation pK(a) = a*ΔG(calc)/RT ln(10) + b is obtained with the CPCM solvation model using the defaults optimized within COSMO-RS (CRSrad; MAD = 1.54, R(2) = 0.94, a = 0.83). Sulfenic (selenenic) acid tautomers are significantly more stable than the corresponding sulfoxide (selenoxide) forms.     

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.     

Adding explicit solvent molecules to continuum solvent calculations for the calculation of aqueous acid dissociation constants

Aqueous acid dissociation free energies for a diverse set of 57 monoprotic acids have been calculated using a combination of experimental and calculated gas and liquid-phase free energies. For ionic species, aqueous solvation free energies were calculated using the recently developed SM6 continuum solvation model. This model combines a dielectric continuum with atomic surface tensions to account for bulk solvent effects. For some of the acids studied, a combined approach that involves attaching a single explicit water molecule to the conjugate base (anion), and then surrounding the resulting anion-water cluster by a dielectric continuum, significantly improves the agreement between the calculated pK(a) value and experiment. This suggests that for some anions, particularly those concentrating charge on a single exposed heteroatom, augmenting implicit solvent calculations with a single explicit water molecule is required, and adequate, to account for strong short-range hydrogen bonding interactions between the anion and the solvent. We also demonstrate the effect of adding several explicit waters by calculating the pK(a) of bicarbonate (HCO(3)(-)) using as the conjugate base carbonate (CO(3)(2-)) bound by up to three explicit water molecules.     

Modeling acid and cationic catalysis on the reactivity of duocarmycins

Several catalyzed alkylation reactions of 9-methyladenine by a model [CPI, cyclopropa[c]pyrrolo[3,2-e]indol-4(5H)-one (1)] of duocarmycin anticancer drugs have been compared to the uncatalyzed reaction in gas phase and in water solvent bulk, using density functional theory at the B3LYP level with the 6-31+G(d,p) basis set and C-PCM solvation model. The effect on the CPI reactivity induced by water, formic and phosphoric acids (general acid catalysis), H3O+ (specific acid catalysis), sodium, and ammonium cation complexation (cationic catalysis) has been investigated. The calculations indicate that the specific acid catalysis and the catalysis induced by sodium cation complexation are strong in the gas phase, but solvation reduces them dramatically by electrostatic effects. The specific acid catalysis is still operative, but strongly reduced in water solution, where the reaction barrier is reduced by 8.6 kcal mol(-1) in comparison to the uncatalyzed reaction. The general acid catalysis induced by phosphoric acid (-7.3 kcal mol(-1)) and the catalysis induced by Na+ and NH4+ complexation become competitive, with a catalytic effect of -3.6 and -4.1 kcal mol(-1) in water, respectively. With the specific acid catalysis, the high acidity (low pK(a) value) of the conjugated acid of CPI (CPIH+), computed in water solution using both C-PCM (pK(a) = +2.6) and PCM-B3LYP/6-31+G(d,p) (pK(a) = +2.4) solvation models, suggests that the catalytic effects induced by NH4+ complexation could become more important than the specific acid catalysis and the general catalysis by H3PO4 under physiological conditions, due to concentration effects of the catalysts.     

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.     

Equilibrium acidities and homolytic bond dissociation energies of acidic C-H bonds in alpha-arylacetophenones and related compounds

The equilibrium acidities (pK(AH)s) and the oxidation potentials of the congugate anions [E(ox)(A(-))s] were determined in dimethyl sulfoxide (DMSO) for eight ketones of the structure GCOCH(3) and 20 of the structure RCOCH(2)G, (where R = alkyl, phenyl and G = alkyl, aryl). The homolytic bond dissociation energies (BDEs) for the acidic C-H bonds of the ketones were estimated using the equation BDE(AH) = 1.37pK(AH) + 23.1E(ox)(A(-)) + 73.3. While the equilibrium acidities of GCOCH(3) were found to be dependent on the remote substituent G, the BDE values for the C-H bonds remained essentially invariant (93.5 +/- 0.5 kcal/mol). A linear correlation between pK(AH) values and [E(ox)(A(-))s] was found for the ketones. For RCOCH(2)G ketones, both pK(AH) and BDE values for the adjacent C-H bonds are sensitive to the nature of the substituent G. However, the steric bulk of the aryl group tends to exert a leveling effect on BDEs. The BDE of alpha-9-anthracenylacetophenone is higher than that of alpha-2-anthracenylacetophenone by 3 kcal/mol, reflecting significant steric inhibition of resonance in the 9-substituted system. A range of 80.7-84.4 kcal/mol is observed for RCOCH(2)G ketones. The results are discussed in terms of solvation, steric, and resonance effects. Ab initio density functional theory (DFT) calculations are employed to illustrate the effect of steric interactions on radical and anion geometries. The DFT results parallel the trends in the experimental BDEs of alpha-arylacetophenones.     

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.     

Influence of Water Content on Basicities in Acetonitrile

The influence of water content at impurity level (5–10,000 ppm) in acetonitrile, on the changes in relative basicity differences (ΔpK _a values) of 13 pairs of bases, was studied both experimentally and computationally (COSMO-RS). The ΔpK _a values involving smaller bases with localized charge in the cationic form were found to be more affected. A computational parameter, weighted average negative sigma (WANS), was proposed to quantify the charge delocalization in cations and succeeded in describing the observed changes of ΔpK _a. The results validate the previously published basicity scale in acetonitrile with respect to solvent dryness and give guidelines for better experimental planning.     

Proton solvation in protic and aprotic solvents

Protonation pattern strongly affects the properties of molecular systems. To determine protonation equilibria, proton solvation free energy, which is a central quantity in solution chemistry, needs to be known. In this study, proton affinities (PAs), electrostatic energies of solvation, and pK_A values were computed in protic and aprotic solvents. The proton solvation energy in acetonitrile (MeCN), methanol (MeOH), water, and dimethyl sulfoxide (DMSO) was determined from computed and measured pK_A values for a specially selected set of organic compounds. pK_A values were computed with high accuracy using a combination of quantum chemical and electrostatic approaches. Quantum chemical density functional theory computations were performed evaluating PA in the gas‐phase. The electrostatic contributions of solvation were computed solving the Poisson equation. The computations yield proton solvation free energies with high accuracy, which are in MeCN, MeOH, water, and DMSO ?255.1, ?265.9, ?266.3, and ?266.4 kcal/mol, respectively, where the value for water is close to the consensus value of ?265.9 kcal/mol. The pK_A values of MeCN, MeOH, and DMSO in water correlates well with the corresponding proton solvation energies in these liquids, indicating that the solvated proton was attached to a single solvent molecule. © 2016 Wiley Periodicals, Inc.     

pKa of acetate in water: a computational study

Several computational methods including the conductor-like polarizable continuum model, CPCM with both UAKS and UAHF cavities, Cramer and Truhlar's generalized Born solvation model, SM5.4(AM1), SM5.4(PM3), and SM5.43R(mPW1PW91/6-31+G(d)), and mixed QM/MM-Ewald simulations were used to calculate the pK(a) values of acetate and bicarbonate anions in aqueous solution. This work provided a critical and comprehensive assessment of the quality of these theoretical models in the calculation of aqueous solvation free energies for the singly charged acetate and bicarbonate ions, as well as the doubly charged acetate dianion and carbonate dianion. It was shown that QM/MM-Ewald simulations could give an accurate and consistent evaluation of the pK(a) values of acetate and bicarbonate based on both the relative and absolute pK(a) formulas, while other methods could yield satisfactory results only for certain calculations. However, this does not mean that the current QM/MM-Ewald protocol is superior to other methods. The useful information obtained in this investigation is that both the absolute and relative pK(a) formulas should better be tested in accurate calculations of pK(a) values based on any methods.     

Do Keggin anions repulse each other in solution? The effect of solvent,counterions and ion representation investigated by free energy (PMF) simulations

To investigate whether polyoxometallate α-PW₁₂O₄₀^3? Keggin anions (noted PW^3?) repulse each other in water, we calculated the changes in free energy ΔG(d) as a function of the P…P distance d (potential of mean force “PMF” calculations). As the anions approach each other, the free energy profiles are found to be quite flat, with a tiny minimum at ca. 11 Å, showing that the anions can form “contact ion pairs” in the presence of either H₃O⁺, UO₂²⁺ or Eu³⁺ counterions. The results obtained with different methodological variants (water models, PW^3? charge models, sampling procedures) support our previous finding that PW^3? ions can form dimers or oligomers in water (A. Chaumont and G. Wipff (2008) [13]). The importance of stabilizing bridging water molecules and solute granularity is demonstrated by comparing PW^3? to S^3? spherical analogues and to PW³⁺ cations (with all atomic charges of PW^3? inverted). With these analogues, a somewhat repulsive behavior (ca +2 to 3 kcal/mol) is observed at short distances. The role of water is further demonstrated by comparing PMFs in water and in methanol solution where there is no contact ion pair, but a free energy minimum at ca. 17 Å, corresponding to an ion separated pair PW^3?…Eu(MeOH)₉³⁺…PW^3?. These findings are important for understanding processes like condensation and assembling of POMs and macro-ions in water or at aqueous interfaces.