Frank Eckert

COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids

A novel and very efficient method for the a priori prediction of thermophysical data of liquids is presented. It is based on unimolecular quantum chemical calculations that provide the necessary information for the evaluation of molecular interactions in liquids. Combined with a very fast and accurate statistical thermodynamics, the new method is an alternative to structure-interpolating group contribution methods (GCMs). The most important advantages are the essentially general applicability, the sound physical basis, and the graphicness of the procedure, which easily allows for chemical interpretation and understanding of thermophysical behaviour. A methodological comparison with GCMs is given. Example applications are presented.

COSMO Implementation in TURBOMOLE: Extension of an efficient quantum chemical code towards liquid systems

The most recent algorithmic enhancements of the COSMO solvation model are presented and the implementation in the TURBOMOLE program package is described. Three demonstrative applications covering homogeneous catalysis, tautomeric equilibria, and binary phase diagrams show the efficiency and general applicability of the approach. Especially when combined with the COSMO-RS extension, the method very reliably predicts thermodynamic properties of liquid mixtures.

COSMO-RS: An Alternative to Simulation for Calculating Thermodynamic Properties of Liquid Mixtures

The conductor-like screening model for realistic solvation (COSMO-RS) method has been established as a novel way to predict thermophysical data for liquid systems and has become a frequently used alternative to force field-based molecular simulation methods on one side and group contribution methods on the other. Through its unique combination of a quantum chemical treatment of solutes and solvents with an efficient statistical thermodynamics procedure for the molecular surface interactions, it enables the efficient calculation of many properties that other methods can barely predict. This review presents a short delineation of the theory, the application potential and limitations of COSMO-RS, and its most important application areas.

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 aqueous solubility of drugs and pesticides with COSMO-RS.

The COSMO‐RS method, originally developed for the prediction of liquid–liquid and liquid–vapor equilibrium constants based on quantum chemical calculations, has been extended to solid compounds by addition of a heuristic expression for the Gibbs free energy of fusion. By this addition, COSMO‐RS is now capable of a priori prediction of aqueous solubilities of a wide range of typical neutral drug and pesticide compounds. Only three parameters in the heuristic expression have been fitted on a data set of 150 drug‐like compounds. On these data an rms deviation of 0.66 log‐units was achieved. Later, the model was tested on a set of 107 pesticides, which have been critically selected based on two experimental data sources and by a crosscheck with an independent HQSAR model. On this data set an rms of 0.61 log‐units was achieved, without any adjustments to the structurally extremely diverse pesticides. This result verifies the ability of this extended COSMO‐RS to predict aqueous solubilities of drugs and pesticides of almost arbitrary structural classes. The new method is COSMO‐RSol.

Ab initio geometry optimization for large molecules

Various geometry optimization techniques are systematically investigated. The rational function (RF) and direct inversion in the iterative subspace (DIIS) methods are compared and optimized for the purpose of geometry optimization. Various step restriction and line search procedures are tested. The model Hessian recently proposed by Lindh et al. has been used in conjunction with different Hessian update procedures. Optimization for over 30 molecules have been performed in Z‐matrix coordinates, local normal coordinates, and curvilinear natural internal coordinates, using the same approximations for the Hessian in all cases. The most effective and stable procedure for optimization of equilibrium structures was found to be the DIIS minimization in natural internal coordinates using the BFGS update of the model Hessian. Our method shows faster overall convergence than all previously published methods for the same test suite of molecules. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1473–1483, 1997

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.

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 pKa 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 pKa values (r2 = 0.98), corresponding to a standard deviation of 0.56 pKa units. Thus, we have an a priori prediction method for base pKa with the regression constant and the slope as only adjusted parameters. In accord with recent findings for pKa acidity predictions, the slope of pKa vs. ΔGdiss 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 pKa prediction method was validated on a set of 58 complex multifunctional drug‐like compounds, yielding an RMS accuracy of 0.66 pKa units.

A comparison between the two general sets of linear free energy descriptors of Abraham and Klamt.

Two sets of molecular descriptors, the five experimental Abraham, and the five COSMOments of Klamts COSMO-RS, have been compared for a data set of 470 compounds. Both sets are considered as almost complete sets of LFER. The two sets of descriptors are shown to exhibit a large overlap as far as their chemical content. The chemical information however is distributed differently in each set with the Abraham set incorporating extra information in the excess molar refraction descriptor E. Regression equations have been constructed to predict the experimental Abraham descriptors from theoretically calculated COSMOments. The chemical interpretation of these equations is however difficult because of the lack of clustering which characterizes the distribution of chemical information through the two sets of descriptors. The predictability of the regression equations is tested successfully using a reasonably large set of data, and the method is compared to recent attempts to calculate the Abraham descriptors from various theoretical bases.

COSMO-RS: a novel view to physiological solvation and partition questions.

Both, dielectric continuum solvation models as well as surface or group based methods using polarity and lipophilicity parameters have been proven to be useful tools for the analysis of solvation and partition questions. For the first time, COSMO-RS provides an integrated theory, which combines the aspects of continuum solvation and surface interactions, and which ends up with chemical potentials of molecules in almost arbitrary solvents and mixtures. Due to its sound theoretical basis, COSMO-RS does not only provide a new quantitative access to solvation and partition properties in well defined solvents, but it also opens a novel view and gives a better understanding of the general problem of solvation. Finally, this allows for a generalisation of COSMO-RS to sophisticatedphysiological partition problems involving as complex phases as blood, brain, or cell membranes. The use of COSMO-RS for drug discovery and design is demonstrated by applications to blood-brain partition coefficients, and water solubility.