COSMO-RS theory

In order to be able to treat such partition phenomena with COSMO-RS, we have developed a slightly more empirical extension to the COSMO-RS theory, which is called the V-moment approach , [see C14,C16,C21 for more details]. The basic idea of this approach results from the finding that the er-potential /is(a) for almost all solvents can be well represented as a linear combination of about six er-functions. These are the simple polynomials with exponent i = 0,1,2, and 3,... 

NEW DEVELOPMENTS IN PREDICTION OF SOLID-STATE SOLUBILITY AND COCRYSTALLIZATION USING COSMO-RS THEORY... 

Those criteria are met by a cocrystal screening based on COSMO-RS theory, using the mixing enthalpy (or equivalently the excess enthalpy of a supercooled cocrystal mixture [18]. The main reason for the predictive capability of this theory concerning cocrystal formation is its accurate description of intermolecular interactions. The idea behind a COSMO-RS-based screening can be best understood by having a look at the thermodynamic cycle shown in Scheme 9.1. 

One has to conclude, that a large part of the decisive intermolecular interactions that make up the cocrystal are probably already dominating in solution and are well described by the term as calculated by COSMO-RS theory. Of course Equation... 

The PSP approach [39-43] is a novel predictive thermodynamic framework, which combines elements from the solubility parameter approach [112,114,116,126] detailed earlier, the solvatochromic/ LSER approach [127-133], and the COSMO-RS theory of solutions [134-136]. It retains the simplicity of the solubility parameter approach, it uses molecular descriptors that can be mapped one to one to the Abraham/LSER descriptors, and these descriptors are derived from the moments of the a-profiles of the quantum mechanics-based COSMO-RS model. Because of this combination, the PSP approach has a broader range of applications compared to each of the earlier three... 

Briefly, the PSP approach heavily resides on the quantum mechanics-based COSMO-RS theory of solutions [17-22], The COSMO model belongs to the class of continuum solvation models (CSM) of quantum mechanics. For the solvation picture, it considers the molecule embedded in a conductor of infinite permittivity that screens perfectly the molecular charges on the surface of its molecular cavity. This molecular cavity is characterized by a volume, Fcogni, and a molecular surface area, The crucial information is contained in the so-called COSMO tile of each compound obtained from quantum chemical calculations at various levels of theory. COSMO tiles give the detailed surface charge distribution or the o-protile of each molecule. The o-protile may be analyzed into its moments of various orders, known as COSMOments, out of which a large number of properties may be calculated, among them the molecular descriptors of Abraham s QSPR/LSER model [23,24]. 

Section 3 concerns the COSMO-RS approach. This is a theory that goes beyond the usual dielectric approximation, in contrast to all other CSMs, it treats solute and solvent on the same footing and it finally allows for the calculation of chemical potentials of molecules in almost arbitrary solvents. First, in Section 3.1 the principal inapplicability of the dielectric theory to electrostatic screening on a molecular scale is expounded. Section 3.2 gives the central COSMO-RS theory, i.e., an alternative ansatz for the interpretation of electrostatic screening of solutes in solvents and its combination with statistical thermodynamics. Section 3.3 illustrates the novel COSMO-RS view of solvation for some typical solvents, while Section 3.4 shows the potential of the approach using the results of a broad para-metrization and validation study. In Section 3.5 the range of applicability is outlined. 

Finally, in Section 4 a summarizing overview of the novel understanding of the role and value of continuum solvation models as achieved by the COSMO-RS theory is given. 

While the above examples concern partition properties and hence free energies, it should be noted that the COSMO-RS theory provides access to other properties such as heats of transfer between different media and surface tensions, as well. 

Finally it is worthwhile to mention that obviously the COSMO-RS theory can be applied to all the questions traditionally handled by CSMs, i.e., tautomeric equilibria, reaction barriers, spectra, and others, with the advantage of the more general and more realistic description of the solvent compared to dielectric CSMs. 

As explained in Section 3, the state of ideal solvation, i.e., the North Pole of our globe, is an excellent starting point for accessing the latitudes of solvation, i.e., the different islands denoting most different solvents, much better than the South Pole, i.e., the state of isolated molecules. From here we have a novel view on the problem and this view led to the development of an efficient vehicle, i.e., the COSMO-RS theory, to access any solvent starting from the state of ideal solvation. 

At this point, the reader who is mainly interested in the fluid-phase thermodynamics aspects should have sufficient information about COSMO to understand the theory of COSMO-RS. Thus, one may skip the following two or three sections, which present more details on COSMO and other continuum solvation models. 

Having recognized the theoretical inadequacy of the dielectric theory for polar solvents, I started to reconsider the entire problem of solvation models. Because the good performance of dielectric continuum solvation models for water cannot be a result of pure chance, in some way there must be an internal relationship between these models and the physical reality. Therefore I decided to reconsider the problem from the north pole of the globe, i.e., from the state of molecules swimming in a virtual perfect conductor. I was probably the first to enjoy this really novel perspective, and this led me to a perfectly novel, efficient, and accurate solvation model based upon, but going far beyond, the dielectric continuum solvation models such as COSMO. This COSMO for realistic solvation (COSMO-RS) model will be described in the remainder of this book. 

As mentioned earlier, I was not aware of the details of the chemical engineering models and Guggenheim s QUAC approximation, when I developed the COSMO-RS model. From a brief glance at that part of the literature I had got the impression that all these models are basically lattice theories, while I wanted to... 

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... 

On the other hand, there are several clear perspectives for future improvements and extensions of COSMO-RS. One of the most obvious perspectives is the improvement of the underlying quantum chemical methods. While density functional theory appears to have reached its limit regarding the quality of the electrostatics, and hence of the COSMO polarization charge densities, there will be an increase in the availability of higher correlated ab initio methods like coupled cluster calculations at affordable computational cost. Quantum chemical calculation of local polarizability and eventually of suitable descriptors for dispersion forces should provide additional information about the strength of local surface interactions and can be used to improve the various surface interaction functionals. At the other end, the quantum chemical COSMO calculations for larger biomolecules and enzymes, which have just become available at reasonable... 

Having reached the end of the book I thank the readers for their time and interest in my thoughts and developments. I also invite those who have become interested in the method, to use it on all occasions where they consider it applicable to their problems and in their projects. I especially invite those who feel the challenge to extend this novel theory toward new frontiers, or those who may already have developed ideas to improve the method while reading this book, to collaborate in the further development of COSMO and COSMO-RS. 

An alternative approach [24, 55, 56] of H-bonding ranking is based on COSMO-RS fluid thermodynamics theory [57], Abramov [24, 58] performed a study of the correlation of two independent schemes of atomic charge calculations (polarization a H-bonding charges and electrostatic potential (ESP) fitted charges, with Abraham s experimental H-bonding scales and available... 

If not stated otherwise the following results have been generated with recent COSMOt/ierm [6] and COSMOquick [21] releases and their respective COSMO-RS parameterizations, BP TZVP C30 1301.ctd (TZVP level of theory) and BP SVP AMl C30 1301.ctd (SVP level of theory). QSPR calculations have been done using the R statistics package [22],... 

TABLE 9.1 Summary of COSMO-RS Solubility Predictions of Some Drugs, Computed at the TZVP Level of Theory... 

COSMOlogic software product COSMO-RS, http //www.cosmologic.de/ theory/cosmo-rs.html (accessed 22/06/2015). 

CSM = continuum solvation model COSMO = conductorlike screening model COSMO-RS = generalization of COSMO to real solvents QC = quantum chemical PCM = polarizable continuum model SAS = solvent accessible surface SES = solvent excluding surface NPPA = average number of segments per full atom vdW = van der Waals, VWN = Vosko-Wilk-Nusair functional (see Density Functional Theory Applications to Transition Metal Problems). 

Because COSMO-RS is a quite general theory for pure or mixed fluid systems, which treats the solvent etnd the solutes on the same footing, it is applicable to a great variety of questions in chemistry. A special advantage of the COSMO-RS formalism is its computational efficiency, since the time-demanding COSMO calculations have only to be performed once per molecule, or once per relevant, electrostatically different conformation, while all variations of solvents, compositions, and temperature only require a recalculation of the a-potential. 

AMI COSMO and COSMO-RS Hydrogen Bonding 1 Hydrogen Bonding 2 Intermolecular Interactions by Perturbation Theory MNDO PM3 Self-consistent Reaction Field Methods Solvation Modeling Water Clusters,... 

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