COSMO-RS Calculations

COSMO-RS is a surprisingly robust method suitable for predictive calculations in a broad range of application areas. For a comprehensive survey we refer to [14]. COSMO-RS has some limitations for instance, it is unable to treat dynamic properties such as viscosities and diffusion coefficients. Therefore COSMO-RS does not provide a complete description of liquid phases. In principle, the more rigorous molecular dynamics and Monte Carlo approaches offer a complete picture, but on the other hand they are several orders of magnitude more computationally demanding. 

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The advantage of the cr-moment approach compared with the direct COSMO-RS calculation of partition coefficients is its extremely broad applicability. However, it has the disadvantage that no temperature dependence is available and no extrapolation to finite concentrations can be made, because of the loss of the sound statistical thermodynamics. In his Ph.D. thesis [112], Mehler... 

Anyway, the first step toward any receptor-based COSMO-RS calculations is the calculation of qualitatively acceptable er-profiles of the receptor regions of enzymes. In a performance test of a highly parallel version of the TURBOMOLE program on the supercomputer at the Research Center Jiilich [141], we could show that TURBOMOLE presently can handle single point, i.e., fixed geometry, BP-SVP DFT-calculations of enzymes up to about 1,500 atoms. On the basis of preliminary data, an enzyme of 1,000 atoms requires about 6 CPU h on 32 CPUs of a supercomputer cluster with a minimum quadratic scaling of CPU-time with the number of atoms of the enzymes. Thus for medium-sized enzymes we would require a minimum of 600 h on such a supercomputer, which would be rather expensive, even if all the technical problems arising at these molecule sizes would be solved. Therefore, brute-force DFT calculations appear to be unfeasible at present, but they may be possible in the future. 

COSMO-RS calculations are performed for different ILs other than [HMIM][NTf2]. Figure 9.10 shows the experimental and the predicted activity coefficients of ethanol in various ILs at 333 K. The prediction is accurate for all [NTf2]-ILs. The chain length variation at the imidazolium cation is described correctly. Also the methylation of the C2 is predicted properly. 

Within COSMO-RS, the IL can be synthesized in three different ways [26]. The method suggested here is the individual treatment of ions, which would represent a dissociated state of the bulk IL. One alternative is the creation of the so-called meta files before the COSMO-RS calculation. In this case, the cation and anion are combined in one file, and the interactions between the two ions are not considered in the calculation. This procedure would... 

L, Smirnova, I., Maginn, E.J., and Arlt, W. (2009) COSMO-RS calculations of partition coefficients different tools for conformational search. Chem. Eng. Technol, 32 (6), 977-986. 

Several methods have been applied to calculate the void volume of RTILs (the fractional free volume, EFV), outstanding among these is the application of the COSMO-RS methodology by Palomar et al. and Shannon et al. [47, 298]. For 23 imidazolium RTILs (Cimim to Cgmim) with a variety of anions a negative bias of — 1.6 % was found [47] between the COSMO-RS-calculated densities and the experimental ones, and a standard deviation of 2.6 % also resulted. 

As a result of Eq. (11) we are able to calculate the chemical potential of any molecule X in any liquid system S, relative to the chemical potential in a conductor, i.e. at the North Pole. Hence, COSMO-RS provides us with a vehicle that allows us to bring any molecule from its Uquid state island to the North Pole and from there to any other liquid state, e.g. to aqueous solution. Thus, given a liquid, or a reasonable estimate of AGjis of a soUd, COSMO-RS is able to predict the solubility of the compound in any solvent, not only in water. The accuracy of the predicted AG of transfer of molecules between different Uquid states is roughly 0.3 log units (RMSE) [19, 22] with the exception of amine systems, for which larger errors occur [16, 19]. Quantitative comparisons with other methods will be presented later in this article. 

QuantlogP, developed by Quantum Pharmaceuticals, uses another quantum-chemical model to calculate the solvation energy. As in COSMO-RS, the authors do not explicitly consider water molecules but use a continuum solvation model. However, while the COSMO-RS model simpUfies solvation to interaction of molecular surfaces, the new vector-field model of polar Uquids accounts for short-range (H-bond formation) and long-range dipole-dipole interactions of target and solute molecules [40]. The application of QuantlogP to calculate log P for over 900 molecules resulted in an RMSE of 0.7 and a correlation coefficient r of 0.94 [41]. 

Klamt A, Eckert F, Diedenhofen M, Beck ME (2003) First Principles Calculations of Aqueous p Values for Organic and Inorganic Acids Using COSMO-RS Reveal an Inconsistency in the Slope of the pKa Scale. J Phys Chem A 107 9380-9386. 

Solubility modelling with activity coefficient methods is an under-utilized tool in the pharmaceutical sector. Within the last few years there have been several new developments that have increased the capabilities of these techniques. The NRTL-SAC model is a flexible new addition to the predictive armory and new software that facilitates local fitting of UNIFAC groups for Pharmaceutical molecules offers an interesting alternative. Quantum chemistry approaches like COSMO-RS [25] and COSMO-SAC [26] may allow realistic ab-initio calculations to be performed, although computational requirements are still restrictive in many corporate environments. Solubility modelling has an important role to play in the efficient development and fundamental understanding of pharmaceutical crystallization processes. The application of these methods to industrially relevant problems, and the development of new... 

Recently, Wichmann et al. [47] applied several COSMO-RS cr-moments as descriptors to model BBB permeability. The performance of the log BB model was reasonable given only four descriptors were applied n — 103, r2 = 0.71, RMSE = 0.4, LOO q2 — 0.68, RMSEtest = 0.42. The COSMO-RS cr-moments were obtained from quantum chemical calculations using the continuum solvation model COSMO and a subsequent statistical decomposition of the resulting polarization charge densities. 

The second direction for the numerical calculation of the interaction of a solute with a dielectric continuum is most important for the understanding of COSMO and COSMO-RS and hence it is treated in a separate chapter. 

When I discussed this idea with computational chemistry colleagues, I experienced strong resistance because molecular 3D geometry is usually considered as most important for all kinds of property calculations in computational chemistry. People could not believe that the approximation could make any sense, and, later, one reviewer of the first COSMO-RS paper called the idea... 

We have now collected almost all the pieces required for a first version of COSMO-RS, which starts from the QM/COSMO calculations for the components and ends with thermodynamic properties in the fluid phase. Although some refinements and generalizations to the theory will be added later, it is worthwhile to consider such a basic version of COSMO-RS because it is simpler to describe and to understand than the more elaborate complete version covered in chapter 7. In this model we make an assumption that all relevant interactions of the perfectly screened COSMO molecules can be expressed as local contact energies, and quantified by the local COSMO polarization charge densities a and a of the contacting surfaces. These have electrostatic misfit and hydrogen bond contributions as described in Eqs. (4.31) and (4.32) by a function for the surface-interaction energy density... 

Unfortunately, the rigorous evaluation of a reasonable measure of local polarizability would take an extreme amount of additional computation time in the DFT/COSMO calculations. An approximate, but very fast quantum chemical calculation method for the local polarizability has recently been suggested by Politzer, Jin, and Murray [95]. The variations of the local polarizability on the surface of acetic acid are visualized in Fig. 7.1 according to this method. Its use for the improvement of COSMO-RS is just being tested. 

It is very satisfying and useful that the COSMO-RS model—in contrast to empirical group contribution models—is able to access the gas phase in addition to the liquid state. This allows for the prediction of vapor pressures and solvation free energies. Also, the large amount of accurate, temperature-dependent vapor pressure data can be used for the parameterization of COSMO-RS. On the other hand, the fundamental difference between the liquid state and gas phase limits the accuracy of vapor pressure prediction, while accurate, pure compound vapor pressure data are available for most chemical compounds. Therefore, it is preferable to use experimental vapor pressures in combination with calculated activity coefficients for vapor-liquid equilibria predictions in most practical applications. 

With the previous refinements of the basic COSMO-RS, a first quantitative parameterization of COSMO-RS has been published, which is based on DFT/COSMO calculations with the DMol program [46,47]. The details are given in [CIO]. We shall now focus on a few important topics. 

Such tautomeric equilibria, which may be crucial for the understanding and appropriate description of phase equilibria, can technically be treated in the same way as conformational equilibria in COSMO-RS. Unfortunately, we must be aware that the total energy differences between the tautomers may be in error by 8 kJ/mol or even more, if we calculate them on our default DFT/COSMO level. To gain an accurate description of such phenomena, it is therefore necessary to correct the COSMO energy differences either by comparison with higher level QM calculations, or by treating them as adjustable parameters. 

Fig. 8.1. Original diagrams of the first COSMO-RS phase-diagram calculations by Iven Clausen [96] for four alcohol-water mixtures (methanol at 60 C, ethanol at 55 °C, 1-propanol at 60 °C and 1-butanol...

A few years ago, we decided to try whether COSMO-RS would be able to predict thermodynamic equilibrium data in ionic liquids. We calculated a series of typical anions and cations used for ionic liquids. Their selection is visualized in Fig. 8.3, and er-profiles of ionic liquids are shown in Fig. 8.4. 

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