Charged bodies, defined

To get the interaction potential we must first evaluate the free energy of formation of the electrical double layer between two charged bodies. This is defined as the work done in charging up the surfaces. The process by which uniformly charged surfaces are charged up from a neutral reference state has been discussed by Yerwey and Overbeek [4], who have shown that the electrostatic work of charging a surface is given by the simple formula... 

However, real molecules are quantum mechanical objects and they do not have a finite body defined in precise geometrical terms and a finite boundary surface that contains all the electron density of the molecule. The peripheral regions of a molecule can be better represented by a continuous, 3D electronic charge density function that approaches zero value at large distances from the nuclei of the molecule. This density function changes rapidly with distance within a certain range, but the change is continuous. The fuzzy, cloud-like electronic distribution of a molecule is very different from a macroscopic body [251], and no precise, finite distance can be specified that could indicate where the molecule ends. No true molecular surface exists in the classical, macroscopic sense. 

The electrical units require some special discussion. The force of attraction or repulsion between charged bodies was first used by the French engineer Charles Coulomb 1736-1806 as the basis for the definition of the unit of charge. He defined the electrostatic unit (esu) of charge as... 

A dipole is created when oppositely charged particles are held at a fixed distance from each other. It generates a directional charge distribution defined by its orientation, i.e. by a unit vector /i. Stockmayer [345] proposed a potential for the interaction of a pair of bodies at positions qi and q2, with associated dipoles, III, li2 (see Fig. 1.27). It can be shown that the potential energy of interaction... 

Dmg distribution into tissue reservoirs depends on the physicochemical properties of the dmg. Tissue reservoirs include fat, bone, and the principal body organs. Access of dmgs to these reservoirs depends on partition coefficient, charge or degree of ionization at physiological pH, and extent of protein binding. Thus, lipophilic molecules accumulate in fat reservoirs and this accumulation can alter considerably both the duration and the concentration—response curves of dmg action. Some dmgs may accumulate selectively in defined tissues, for example, the tetracycline antibiotics in bone (see Antibiotics,tetracyclines). 

A considerable body of scientific work has been accomplished in the past to define and characterize point defects. One major reason is that sometimes, the energy of a point defect can be calculated. In others, the charge-compensation within the solid becomes apparent. In many cases, if one deliberately adds an Impurity to a compound to modify its physical properties, the charge-compensation, intrinsic to the defect formed, can be predicted. We are now ready to describe these defects in terms of their energy and to present equations describing their equilibria. One way to do this is to use a "Plane-Net". This is simply a two-dimensional representation which uses symbols to replace the spherical images that we used above to represent the atoms (ions) in the structure. 

According to these considerations three subregions are defined as depicted in Fig. 1. The inner and outer parts of the QM region are termed the QM core and QM layer zone, respectively. As discussed solutes in the QM core do not require the application of non-Coulombic potentials—composite species with complex potential energy surfaces can be treated in a straightforward way, while complex potential functions are required in the case of classical and even conventional QM/MM simulation studies. Interactions at close solute-solvent distances are treated exclusively via quantum mechanics and account for polarization, charge transfer, as well as many-body effects. The solute-solvent... 

In sec. 1.4.3c we have already introduced the mean (average) electrostatic potential. The mean electrostatic potential yr x ) is related to the work necessary to bring an Infinitely small probe charge from Infinity to Xj without disturbing the environment. This potential can be defined In terms of the one- and two-body interactions, mentioned above, according to... 

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