Electrostatic concepts, interaction forces

The purpose of the present chapter is to introduce some of the basic concepts essential for understanding electrostatic and electrical double-layer pheneomena that are important in problems such as the protein/ion-exchange surface pictured above. The scope of the chapter is of course considerably limited, and we restrict it to concepts such as the nature of surface charges in simple systems, the structure of the resulting electrical double layer, the derivation of the Poisson-Boltzmann equation for electrostatic potential distribution in the double layer and some of its approximate solutions, and the electrostatic interaction forces for simple geometric situations. Nonetheless, these concepts lay the foundation on which the edifice needed for more complicated problems is built. 

The chemical structure representation in Apex-3D is based on the concept of a descriptor center that represents a part of the hypothetical biophore. Descriptor centers can be atoms, sets of atoms, pseudo-atoms, or substructures that participate in ligand-receptor interactions. The interaction is derived from electrostatic, hydrophobic, dispersion force, and charge-transfer information that comes from quantum-chemical calculations or from atomic conkibutions to hydrophobicity or molar refractivity. 

TTHE MOST IMPORTANT FORCES ACTING BETWEEN MEMBRANE SURFACES are van der Waals, electrostatic, and hydration. The first two forces are explained by the Deijaguin-Landau-Verwey-Overbeek (DLVO) theory (I) the existence of the hydration force was anticipated before it was measured (2). The van der Waals force is always attractive and displays a power law distance dependence, whereas the electrostatic and hydration forces are repulsive and exponentially decay with distance. The electrostatic force describes the interaction between charged membrane surfaces when the separation between surfaces is above 10 molecular solvent diameters. The hydration force acts between charged and uncharged membrane surfaces and at distances below 10 molecular solvent diameters its value dominates the values of van der Waals and electrostatic forces (3). The term hydration reflects the belief that the force is due to the structure of water between the surfaces. Electrostatic and hydration forces are similar in some respects both are exponential and repulsive and their theoretical description involves coupling electrostatic concepts and ideas borrowed from statistical mechanics. Although the nature of the electrostatic force is solidly established, this is not the case for the hydration force. To illustrate the role the electrostatic... 

The formation of the former direction is closely associated with the works of J.N. Bronsted, E.A. Guggenheim and G. Scatchard (1976), who in the 1920 s and 1930 s came up with the specific ion interaction theory. Based on this theory the Bronsted-Guggenheim-Scatchard model or specific ion interaction theory - SIT model was formed. It merges interaction of electrostatic and Coulomb forces of components in the solution in consideration of their individual properties. Laid in its basis were concepts of... 

One area where the concept of atomic charges is deeply rooted is force field methods (Chapter 2). A significant part of the non-bonded interaction between polar molecules is described in terms of electrostatic interactions between fragments having an internal asymmetry in the electron distribution. The fundamental interaction is between the Electrostatic Potential (ESP) generated by one molecule (or fraction of) and the charged particles of another. The electrostatic potential at position r is given as a sum of contributions from the nuclei and the electronic wave function. 

The final part is devoted to a survey of molecular properties of special interest to the medicinal chemist. The Theory of Atoms in Molecules by R. F.W. Bader et al., presented in Chapter 7, enables the quantitative use of chemical concepts, for example those of the functional group in organic chemistry or molecular similarity in medicinal chemistry, for prediction and understanding of chemical processes. This contribution also discusses possible applications of the theory to QSAR. Another important property that can be derived by use of QC calculations is the molecular electrostatic potential. J.S. Murray and P. Politzer describe the use of this property for description of noncovalent interactions between ligand and receptor, and the design of new compounds with specific features (Chapter 8). In Chapter 9, H.D. and M. Holtje describe the use of QC methods to parameterize force-field parameters, and applications to a pharmacophore search of enzyme inhibitors. The authors also show the use of QC methods for investigation of charge-transfer complexes. 

It is important to note that the concept of osmotic pressure is more general than suggested by the above experiment. In particular, one does not have to invoke the presence of a membrane (or even a concentration difference) to define osmotic pressure. The osmotic pressure, being a property of a solution, always exists and serves to counteract the tendency of the chemical potentials to equalize. It is not important how the differences in the chemical potential come about. The differences may arise due to other factors such as an electric field or gravity. For example, we see in Chapter 11 (Section 11.7a) how osmotic pressure plays a major role in giving rise to repulsion between electrical double layers here, the variation of the concentration in the electrical double layers arises from the electrostatic interaction between a charged surface and the ions in the solution. In Chapter 13 (Section 13.6b.3), we provide another example of the role of differences in osmotic pressures of a polymer solution in giving rise to an effective attractive force between colloidal particles suspended in the solution. 

The concept of the vectorial coupling of quasispin momenta was first applied to the nucleus to study the short-range pairing nucleonic interaction [117]. For interactions of that type the quasispin of the system is a sufficiently good quantum number. In atoms there is no such interaction - the electrons are acted upon by electrostatic repulsion forces, for which the quasispin quantum number is not conserved. Therefore, in general, the Hamiltonian matrix defined in the basis of wave functions (17.56) is essentially non-diagonal. 

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