Prediction of Liquid Solubility with COSMO-RS

In 1995, one of the authors (A.K.) introduced the state of a molecule embedded in a perfect conductor as an alternative reference state, which is almost as clean and simple as the vacuum state. In this state the conductor screens all long-range Coulomb interactions by polarization charges on the molecular interaction surface. Thus, we have a different reference state of noninteracting molecules. This state may be considered as the North Pole of our globe. Due to its computational accessibility by quantum chemical calculations combined with the conductor-like screening model (COSMO) [21] we will denote this as the COSMO state. 

Liquid solvents in this picture may be considered as islands in the northern hemisphere, because the state of molecules in a liquid solvent is quite definitely closer to the COSMO state than to the vacuum. The only exception may be alkane solvents, which are located somewhere close to the equator due to their fully nonpolar character. Solids may be considered as sunken islands and their depths below sea level may be considered as AG s. As discussed before, the methods to explore this depth are rather limited, but we can be quite sure that in general the depth below sea level will be much smaller than the distance of the islands from the North Pole or from each other. We now explore the methods to go from the sea level position of any island to the North Pole or vice versa. Given such a method we will be able to transfer a compound from any liquid or supercooled liquid state to any other such state. 

the statistical thermodynamics of the pairwise surface segment interactions can be performed exactly, i.e. without any additional approximations beyond the assumption of surface pair formation, using  

The segment chemical potential ps(o)is also called the o-potential of a solvent It is a specific function expressing the affinity of a solvent S for solute surface of polarity a. Typical o-profiles and o-potentials are shown in Fig. 11.4. From the a-potentials it can clearly be seen that hexane Ukes nonpolar surfaces and increasingly dislikes polar surfaces, that water does notUke nonpolar surfaces (hydrophobic effect), but that it likes both H-bond donor and acceptor surfaces, that methanol likes donor surfaces more than does water, but acceptors less, and many other features. 

Given the a-potenhal of a solvent S, the chemical potential of a molecule X in S can be essentially expressed as a surface integral of this o-potential ps(o) over the surface of the solute  

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