Polarization charge density

As mentioned above, the PCM is based on representing the electric polarization of the dielectric medium surrounding the solute by a polarization charge density at the solute/solvent boundary. This solvent polarization charge polarizes the solute, and the solute and solvent polarizations are obtained self-consistently by numerical solution of the Poisson equation with boundary conditions on the solute-solvent interface. The free energy of solvation is obtained from the interaction between the polarized solute charge distribution and the self-... 

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. 

Given a cavity segmentation by m segments i, of sizes s, and centered at positions fj, the dielectric surface polarization charge densities, at, and the corresponding apparent surface charges, qt = Sjffj, can be calculated from the exact dielectric boundary... 

Fig. 4.1. COSMO surfaces of water and CO2 color coded by the polarization charge density a. Red areas denote strongly negative parts of the molecular surface and hence strongly positive values of a. Deep blue marks denote strongly positive surface regions (strongly negative a) and green denotes nonpolar surface.

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... 

We could continue this discussion of er-surfaces and (7-profiles with many other interesting and colorful examples, but this would exceed the limits of this book. From the representative examples discussed so far, the basic principles of the surface polarities of organic compounds expressed by the polarization charge densities, (7, should have become clear. We leave it to the reader to study additional examples in the supplementary material. 

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. 

Fig. 10.2. Predictions of the logarithmic relative rate constants of the Menschutkin reaction in various solvents [C32]. The COSMO polarization charge densities a of the transition state are visualized in the inset.

Fig. 10.9. Collection of ionic surfactants (without counterions). It can clearly be seen that the polarization charge densities of the charges are localized on the head groups, while the tails already look like normal alkane or fluoroalkane chains after two carbon units from the head...

Having resolved the molecular perception problem and achieved a unique representation of all atoms, bonds, and rings in the molecule, the second major step is the definition of the most useful measure for local similarity of atoms and atomic environment. For the purpose of COSMO/rag, we need to achieve the state that atoms are considered as most similar, if their partial molecular surfaces and surface polarities, i.e., polarization charge densities, are most similar. But since the latter is not known, at least for the new molecule under consideration, we have to ensure that the local geometries and the electronic effects of the surrounding atoms are most similar. Obviously, two similar atoms should at legist be identical with respect to their element and their hybridization. Turning this information into a unique real number, a similarity index of the lowest order (zeroth order) can be defined for each atom from the atom element numbers and... 

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... 

The functional (1.76) still depends on the total electrostatic potential, but it can be turned into a functional of the polarization charge density, see ref. [24],... 

Since the same voltage is applied in both situation (a) and situation (b), E remains the same. However, in (b) the polarization charge density np appearing on the surfaces of the dielectric compensates part of the total charge density nT... 

The surrogate Hamiltonian is expressed in terms of renormalized solute-solvent interactions, a feature that leads to a simple and natural linear response description of the solvent dynamics in the vicinity of the solute. In addition to the measurable solvation time correlation function (tcf), we can also calculate observables needed to elucidate the detailed mechanism of solvation response, such as the evolution of the solvent polarization charge density around the solute. 

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