Michael Diedenhofen

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.

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 pKa 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 pKa values (r2 = 0.97) in acetonitrile, corresponding to a standard deviation of 1.38 pKa units. Thus, we have a prediction method for acetonitrile pKa with the intercept and the slope as the only adjusted parameters. Furthermore, the pKa values of CH acids yielding large anions with delocalized charge can be predicted with a rmse of 1.12 pKa units using the theoretical values of slope and intercept resulting in truly ab initio pKa prediction. In contrast to our previous findings on aqueous acidity predictions the slope of the experimental pKa versus theoretical ΔGdiss 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 pKa units.

Towards a first principles prediction of pK a: COSMO-RS and the cluster-continuum approach

The COSMO-RS method, a post-quantum chemistry extension of the quantum chemical dielectric continuum solvation model COSMO with a statistical thermodynamics treatment for realistic solvation simulation, has been applied to the prediction of the aqueous pK a of acids and bases. The combination of the COSMO-RS approach to pK a prediction with the cluster-continuum approach (explicit solvation of the solute compound with one or more solvent molecules) was used on three data sets consisting of 94 acids and 75 bases. Correlation of the calculated free energies of dissociation in water with the experimental aqueous pK a of the solute acids and bases in their bare state and explicitly solvated by one or two solvent molecules showed an increase of the regression slope with the number of explicit solvent molecules, thus showing a regression slope that is closer to the theoretical value than the slope found for bare solutes. It was found that the cluster-continuum approach is limited to a pK a range of strong to moderately weak acids and bases, because the optimisations of the solvent–solute complexes of the ionic species of very weak acids (such as the anion of tert-butanol) did not lead to the desired complexes, but yielded dissociation products.

Reliable Quantum Chemical Prediction of the Localized/Delocalized Character of Organic Mixed-Valence Radical Anions. From Continuum Solvent Models to Direct-COSMO-RS

A recently proposed quantum-chemical protocol for the description of the character of organic mixed-valence (MV) compounds, close from both sides to the localized/delocalized borderline, is evaluated and extended for a series of dinitroaryl radical anions 1-6. A combination of global hybrid functionals with exact-exchange admixtures of 35% (BLYP35) or 42% (BMK) with appropriate solvent modeling allows an essentially quantitative treatment of, for example, structural symmetry-breaking in Robin/Day class II systems, thermal electron transfer (ET) barriers, and intervalence charge-transfer (IV-CT) excitation energies, while covering also the delocalized class III cases. Global hybrid functionals with lower exact-exchange admixtures (e.g., B3LYP, M05, or M06) provide a too delocalized description, while functionals with higher exact-exchange admixtures (M05-2X, M06-2X) provide a too localized one. The B2PLYP double hybrid gives reasonable structures but far too small barriers in class II cases. The CAM-B3LYP range hybrid gives somewhat too high ET barriers and IV-CT energies, while the range hybrids ωB97X and LC-BLYP clearly exhibit too much exact exchange. Continuum solvent models describe the situation well in most aprotic solvents studied. The transition of 1,4-dinitrobenzene anion 1 from a class III behavior in aprotic solvents to a class II behavior in alcohols is not recovered by continuum solvent models. In contrast, it is treated faithfully by the novel direct conductor-like screening model for real solvents (D-COSMO-RS). The D-COSMO-RS approach, the TURBOMOLE implementation of which is reported, also describes accurately the increased ET barriers of class II systems 2 and 3 in alcohols as compared to aprotic solvents and can distinguish at least qualitatively between different aprotic solvents with identical or similar dielectric constants. The dominant role of the solvent environment for the ET character of these MV radical anions is emphasized, as in contrast to some previous computational suggestions essentially all of the present systems have delocalized class III character in the gas phase. The present approach allows accurate estimates from the gas phase to aprotic and protic solvent environments, without the need for explicit ab initio molecular dynamics simulations, and without artificial constraints.

Prediction of the free energy of hydration of a challenging set of pesticide-like compounds.

In a blind validation test 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 transfer free energies of 55 demanding pesticide-like compounds. Comparison with experimental data yields an rms deviation of approximately 2 kcal/mol, which is in the order of the estimated inaccuracy of the experimental data. A detailed comparison reveals experimental and calculation pitfalls on conformational flexible, multifunctional, polar compounds.

Prediction of Blood-Βrain Partitioning and Human Serum Albumin Binding Based on COSMO-RS σ-Moments

Models for the prediction of blood-brain partitioning (logBB) and human serum albumin binding (logK(HSA)) of neutral molecules were developed using the set of 5 COSMO-RS σ-moments as descriptors. These σ-moments have already been introduced earlier as a general descriptor set for partition coefficients. They are obtained from quantum chemical calculations using the continuum solvation model COSMO and a subsequent statistical decomposition of the resulting polarization charge densities. The model for blood-brain partitioning was built on a data set of 103 compounds and yielded a correlation coefficient of r2 = 0.71 and an rms error of 0.40 log units. The human serum albumin binding model was built on a data set of 92 compounds and achieved an r2 of 0.67 and an rms error of 0.33 log units. Both models were validated by leave-one-out cross-validation tests, which resulted in q2 = 0.68 and a qms error of 0.42 for the logBB model and in q2 = 0.63 and a qms error of 0.35 for the logK(HSA) model. Together with t...

thermocalc — A poor man's approach to computational thermochemistry

We present thermocalc, a Perl module to perform the automated calculation of atomization energies and heats of formation for lists of molecules. The methods used are based on density functional theory and second‐order perturbation theory to ensure that data sets of medium sized to large molecules can be run at reasonable throughput rates. The quantum chemical calculations are performed using the program package TURBOMOLE in a three‐step protocol. In a first step, a pre‐optimization of the structure and a zero‐point energy calculation are performed. As second step, a geometry optimization is being carried out, and the last step is a single point energy calculation. The level of theory used in the different steps can be modified by the user to allow for customized protocols. The performance of example protocols is investigated on different test sets of molecules. In the course of this work, a simple, but efficient one‐parameter correction term based on the shared electron numbers has been developed, which reduces the error of calculated heats of formation significantly.