COSMO accuracy

The conductor-like screening model (COSMO) is a continuum method designed to be fast and robust. This method uses a simpler, more approximate equation for the electrostatic interaction between the solvent and solute. Line the SMx methods, it is based on a solvent accessible surface. Because of this, COSMO calculations require less CPU time than PCM calculations and are less likely to fail to converge. COSMO can be used with a variety of semiempirical, ah initio, and DFT methods. There is also some loss of accuracy as a result of this approximation. 

An improved version, called COSMO for realistic solvents (COSMO-RS), has also been created. This method has an improved scheme for modeling nonelectrostatic effects. It can be adapted for modeling the behavior of molecules in any solvent and, gives increased accuracy of results as compared to COSMO. 

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. 

An alternative to the GB, COSMO, and Poisson electrostatic calculations is to model the solution to the Poisson equation in terms of pair potentials between solute atoms this procedure is based on the physical picture that the solvent screens the intra-solute Coulombic interactions of the solute, except for the critical descreening of one part of the solute from the solvent by another part of this solute. This descreening can be modeled in an average way to a certain level of accuracy by pairwise functions of atomic positions.18, M 65 One can obtain quite accurate solvation energies in this way, and it has recently been shown that this algorithm provides a satisfactory alternative to more expensive explicit-solvent simulations even for the demanding cases of 10-base-pair duplexes of DNA and RNA in water.66... 

Here, r denotes the position vector of the charges qt with respect to the center of the sphere, and r, the distance from the center. By applying the dielectric scaling function for dipoles (Eq. (2.3)), which—as we have seen in Fig. 2.1—is also a good approximation for most other multipole orders, it was immediately clear that the idea of using a scaled conductor instead of the EDBC leads to a considerable simplification of the mathematics of dielectric continuum solvation models, with very small loss of accuracy. It may also help the finding of closed analytic solutions where at present only multipole expansions are available, as in the case of the spherical cavity. Thus the Conductor-like Screening Model (COSMO) was bom. 

Summarizing, the reliable electrostatics of gradient-corrected DFT methods provides a good basis for CSMs. Nevertheless, advanced CSMs such as C-PCM or COSMO have achieved an accuracy that is mainly limited by the electrostatic accuracy of DFT, but the next better quantum chemical levels are presently much too expensive for most practical applications. Therefore, we will have to live with the acceptable DFT accuracy for the next years, and no big improvements of the CSMs beyond the present accuracy should be expected, until more accurate quantum levels as CC become practically useful. 

In section 6.1, we introduced the COSMO-RS polarization charge density, a, as a local average of the COSMO polarization charges over a region of ca. 0.5 A radius. In this section, we will introduce a list of other local surface descriptors. Some of them have already proved to be useful for improving the accuracy of COSMO-RS, while others are candidates for future improvements. Obviously the list given here only reflects the present state of our ideas, and it is open for good additional ideas. 

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. 

Although COSMO-RS generally provides good predictions of chemical potentials and activity coefficients of molecules in liquids, its accuracy in many cases is not sufficient for the simulation of chemical processes and plants, because even small deviations can have large effects on the behavior of a complex process. Therefore, the chemical engineer typically prefers to use empirical thermodynamic models, such as the UNIQUAC and NRTL, for the description of liquid-phase activity coefficients with... 

The general reliability and the accuracy limitations of COSMO-RS for a wide range of industrially relevant binary systems have been evaluated systematically in several studies [C18, C23-C25,99,106,107]. 

The rather fundamental and almost unparameterized COSMO-RS approach also allows for the calculation of pKa in aqueous mixtures and other solvents. As an example we applied it to DMSO (see Fig. 10.6), achieving about the same accuracy as in water, but a slightly higher slope. It is not clear whether the difference in slope is of physical significance. Thus, COSMO-RS may be used for pKa prediction in different solvents, but unfortunately a parameterization is required for each solvent. 

Owing to the individual fragmentation based on the described concept of maximum similar substructure the accuracy loss of COSMO/rag is only about 0.05-0.1 log-units compared to direct DFT/COSMO calculations (Fig. 11.9) for typical life science data sets. Water solubility appears to be especially insensitive to the approximations of COSMO/rag. As shown in Fig. 11.10, the rms error only increased from 0.66 to 0.71 log-units for the dataset used in the development of the drug solubility method. 

Computational quantum mechanics continues to be a rapidly developing field, and its range of application, and especially the size of the molecules that can be studied, progresses with improvements in computer hardware. At present, ideal gas properties can be computed quite well, even for moderately sized molecules. Complete two-body force fields can also be developed from quantum mechanics, although generally only for small molecules, and this requires the study of pairs of molecules in a large number of separations and orientations. Once developed, such a force field can be used to compute the second virial coefficient, which can be used as a test of its accuracy, and in simulation to compute phase behavior, perhaps with corrections for multibody effects. However, this requires major computational effort and expert advice. At present, a much easier, more approximate method of obtaining condensed phase thermodynamic properties from quantum mechanics is by the use of polarizable continuum models based on COSMO calculations. 

The previous considered methods usually depend on linear methods (MLR, PLS) to establish structure-solubility correlations for prediction of solubility of molecules. The work of Goller et al. [51] used a neural network ensemble to predict the apparent solubility of Bayer in-house organic compounds. The solubility was measured in buffer at pH 6.5, which mimics the medium in the human gastrointestinal tract. The authors used the calculated distribution coefficient log/1 (at several pH values), a number of 3D COSMO-derived parameters and some 2D descriptors. The final model was developed using 4806 compounds (RMSE = 0.72) and provided a similar accuracy (RMSE = 0.73) for the prediction of 7222 compounds that were not used to develop the model. The method, however, is quite slow, and it takes about 15 seconds to screen one molecule on an Intel Xeon 2.8 GHz CPU. 

For brevity s sake we do not report the demonstration of the formal equivalence between lEF and either PCM or COSMO, when the dielectric constant is put equal to a constant value e or to e = oo, respectively [38] in both cases this formal equivalence does not mean that calculations run in parallel using e.g. standard PCM or lEF-PCM for the isotropic model there are differences which ultimately lead to consider the use of lEF-PCM more effective (as measured by the computational costs) when an higher accuracy in the results is required. These topics will be treated later under the headings of Cavity errors , and Calculation of molecular response functions (sections 5 and 7, respectively). 

Depending on the structural information produced in the Step 1) static and dynamic analysis of the most representative bridges will be performed under the estimated service load distribution from train traffic and other heavy time-dependent loads. For this purpose, a three-dimensinal finite-element model of each most representative bridge, which is capable to reflect the actual structural properties with reasonable accuracy, will be used along with the COSMOS Structural Analysis Code (Cosmos 1990). In this way it will be possible to... 

At a somewhat reduced accuracy it is also possible to circumvent the sometimes costly quantum chemical calculations and to generate o-profiles on-the-fly from fragments of precomputed COSMO files stored in a database. This approach is implemented in the software COSMOquick and is particularly useful for solubility prediction using one or several reference solvents (see also Section 9.4). 

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