Solvent Effect on Acidity: A Hybrid Approach Based on the RISM and the Hartree−Fock Equations

First Principles Calculations of Aqueous pKa Values for Organic and Inorganic Acids Using COSMO-RS Reveal an Inconsistency in the Slope of the pKa Scale

The COSMO-RS method, a combination of the quantum chemical dielectric continuum solvation model COSMO with a statistical thermodynamics treatment for more realistic solvation (RS) simulations, has been used for the direct prediction of pKa constants of a large variety of 64 organic and inorganic acids. A highly significant correlation of r(2) = 0.984 with a standard deviation of only 0.49 between the calculated values of the free energies of dissociation and the experimental pKa values was found, without any special adjustment of the method. Thus, we have a theoretical a priori prediction method for pKa, which has the regression constant and the slope as only adjusted parameters. Such a method can be of great value in many areas of physical chemistry, especially in pharmaceutical and agrochemical industry. To our surprise, the slope of pKa vs ΔGdiss is only 58% of the theoretically expected value of 1/RTln(10). A careful analysis with respect to different contributions as well as a comparison with the work of other authors excludes the possibility that the discrepancy is due to weaknesses of the calculation method. Hence, we must conclude that the experimental pKa scale depends differently on the free energy of dissociation than generally assumed.

Computation of pKaValues of Substituted Aniline Radical Cations in Dimethylsulfoxide Solution

A newly developed computation strategy was used to calculate the absolute pKa values of 18 substituted aniline radical cations in dimethylsulfoxide (DMSO) solution with the error origin elucidated and deviation minimized. The B3LYP/6-311++G(2df,2p) method was applied and was found to be capable of reproducing the gas-phase proton-transfer free energies of substituted anilines with a precision of 0.83 kcal/mol. The IEF-PCM solvation model with gas-phase optimized structures was adopted in calculating the pKa values of the substituted neutral anilines in DMSO, regenerating the experimental results within a standard deviation of 0.4 pKa unit. When the IEF-PCM solvation model was applied to calculate the standard redox potentials of anilide anions, it showed that the computed values agreed well with experiment, but the redox potentials of substituted anilines were systematically overestimated by 0.304 eV. The cause of this deviation was found to be related to the inaccuracy of the calculated solvation free energies of aniline radical cations. By adjusting the size of the cavity in the IEF-PCM method, we derived a reliable procedure that can reproduce the experimental pKa values of aniline radical cations within 1.2 pKa units to those from experiment.

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.

Theoretical Prediction of the Hydride Affinities of Various p- and o-Quinones in DMSO

The hydride affinities of 80 various p- and o-quinones in DMSO solution were predicted by using B3LYP/6-311++G (2df,p)//B3LYP/6-31+G* and MP2/6-311++G**//B3LYP/6-31+G* methods, combined with the PCM cluster continuum model for the first time. The results show that the hydride affinity scale of the 80 quinones in DMSO ranges from -47.4 kcal/mol for 9,10-anthraquinone to -124.5 kcal/mol for 3,4,5,6-tetracyano-1,2-quinone. Such a long scale of the hydride affinities (-47.4 to -124.5 kcal/mol) indicates that the 80 quinones can form a large and useful library of organic oxidants, which can provide various organic hydride acceptors that the hydride affinities are known for chemists to choose in organic syntheses. By examining the effect of substituent on the hydride affinities of quinones, it is found that the hydride affinities of quinones in DMSO are linearly dependent on the sum of the Hammett substituent parameters sigma: DeltaGH-(Q) approximately -16.0Sigmasigmai - 70.5 (kcal/mol) for p-quinones and DeltaGH-(Q) approximately -16.2Sigmasigmai - 81.5 (kcal/mol) for o-quinones only if the substituents have no large electrostatic inductive effect and large ortho-effect. Study of the effect of the aromatic properties of quinone on the hydride affinities showed that the larger the aromatic system of quinone is, the smaller the hydride affinity of the quinone is, and the decrease of the hydride affinities is linearly to take place with the increase of the number of benzene rings in the molecule of quinones, from which the hydride affinities of aromatic quinones with multiple benzene rings can be predicted. By comparing the hydride affinities of p-quinones and the corresponding o-quinones, it is found that the hydride affinities of o-quinones are generally larger than those of the corresponding p-quinones by ca. 11 kcal/mol. Analyzing the effect of solvent on the hydride affinities of quinones showed that the effects of solvent (DMSO) on the hydride affinities of quinones are mainly dependent on the electrostatic interaction of the charged hydroquinone anions (QH-) with solvent (DMSO). All the information disclosed in this work should provide some valuable clues to chemists to choose suitable quinones or hydroquinones as efficient hydride acceptors or donors in organic syntheses and to predict the thermodynamics of hydride exchange between quinones and hydroquinones in DMSO solution.

Computational Study on the Relative Acidity of Acetic Acid by the QM/MM Method Combined with the Theory of Energy Representation

We have applied the quantum mechanical/molecular mechanical (QM/MM) method combined with the theory of energy representation (ER) to study the acidity of acetic acid in aqueous solution. We have focused our attention on the relative acidity DeltapK(a) of the molecule with respect to water solvent to circumvent the ambiguity of the solvation free energies of the molecular species referred to as proton. The value of DeltapK(a) for the acetic acid has been computed as -11.5 when we adopt the free energy change in the gas phase obtained by the B3LYP functional, which is in excellent agreement with the experimental value of -11.0. It has been demonstrated that the QM/MM-ER approach recently developed gives an adequate description for the solvation free energies related to the acidity/basicity calculations of organic molecules.

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 new method to locate saddle points for reactions in solution by using the free-energy gradient method and the mean field approximation

A new method for calculating saddle points of reactions in solution is presented. The main characteristics of the method are: (1) the solute-solvent system is described by the averaged solvent electrostatic potential/molecular dynamics method (ASEP/MD). This is a quantum mechanics/molecular mechanics method (QM/MM) that makes use of the mean field approximation (MFA) and that permits one to simultaneously optimize the electronic structure and geometry of the solute molecule and the solvent structure around it. (2) The transition state is located by the joint use of the free-energy gradient method and the mean field approximation. An application to the study of the Menshutkin reaction between NH(3) and CH(3)Cl in aqueous solution is discussed. The accuracy and usefulness of the proposed method is checked through comparison with other methods.

First-Principle Predictions of Absolute pKa's of Organic Acids in Dimethyl Sulfoxide Solution

MP2/6-311++G(d,p) and B3LYP/6-311++G(2df,p) methods were found to be able to predict the gas-phase acidities of various organic acids with a precision of 2.2 and 2.3 kcal/mol. A PCM cluster-continuum solvation method was developed that could predict the solvation free energies of various neutral, cationic, and anionic organic species in DMSO with a precision of about 2.0 kcal/mol. Using these carefully tested methods, we successfully predicted the pKa's of 105 organic acids in DMSO with a precision of 1.7-1.8 pKa units. We also predicted the pKa's of a variety of organosilanes in DMSO for the first time using the newly developed methods. This study was one of the first that employed first-principle methods for calculating pKa's of unrelated compounds in organic solutions.