Single point charge

This field is not the physical electrostatic field observed in the crystal because the ionic model takes no account of the distribution of electrons within the atom. The distributed charge of the atom is replaced by a single point charge at its centre. 

It has been pointed out that the possibility of an atom in a molecule having both positive and negative regions on its surface should be taken into account in designing force fields, e.g., for molecular dynamics [7, 56], These often describe electrostatic interactions in terms of a single point charge associated with each atom. 

When the particle is represented by a single point charge (Fig. 13.1), the lines of force are radial and equal in all directions. The orthogonal surfaces of equal field strength are spherical surfaces with a common center at the center of the particle, with the flux through any of these spheres of radius r being... 

Here we consider fixed charges so that we treat the Poisson equation (not the Poisson-Boltzmann equation). If a single point charge Cj is located at position r, then... 

An array of positive point charges on a n-type semiconductor creates potential pockets whose depth and spatial extension depend on certain conditions defined in [91]. With a single point charge the same effect is expected. 

The Dewar-Golden-Harris approach (DGH), also called FMMF method (i.e. Field, Mesomeric and Mesomeric-Field method) [Dewar et al, 1971a] is a modification of the Dewar-Grisdale approach, where the substituent X is approximated by a finite dipole (represented by two point charges along the /-X bond) and the reaction site at position i as a single point charge. This approach is based on the equation ... 

If, for instance, a single point charge e is situated outside the conductor, electric field at any point inside the conductor is ... 

The problems associated with charging are illustrated by consideration of the implications of single point charging on the axis of the kiln. This produces a conical surface to the stone bed (Fig. 16.5). 

Figure 16. Cross-section of a single point charging system...

If our system consists of a single point charge located at (x, y, Za), then 4>i = QAl ohA) where r-iA is the distance between point A and point 1 with coordinates (xi, yi, zi). If our system consists of several point charges, then each contributes to and... 

The width parameters are chosen so as to approximate a uniform surface charge in the case of a single point charge centered in a spherical cavity [87], and are fixed parameters once the number of Lebedev discretization points per sphere is specified. The matrix... 

The Born ion is the simplest model of solvation It considers the solvation energy of a spherical, nonpolarizable (sp = 1) solute of radius R with a single point charge of magnitude z at its center. In this case, an analytical expression is available for the solvation energy ... 

If the two charges of the dipole featuring in the layer model are replaced with a single point charge, then the one-layer continuous model relating to electrolyte solutions is obtained. According to this model, the part of the free energy of solvation due to electrostatic interactions is [Ab 78 ]... 

While the Boltzmann distribution is relatively easy to evaluate for a single point charge, the situation can become quite complex in the case of a surface having many charges. For a detailed discussion of the finer points of doublelayer theory, the reader is referred to the works of Adamson, Kruyt, or Hiemenez dted in the Bibliography. From a practical (and very simplistic) point of view, it is normally assumed that the electrical potential in the solution surrounding the surface in question falls off exponentially with distance from the surface (Fig. 5.3) according to the Debye-Htickel approximation... 

To investigate the effect of an external electric field on the photodynamics, a single point charge of magnitude -1-0.25 qe was placed 3 A from one of the carbon atoms (Fig. 4). Both the ethylene molecule s center of mass and the position of the point charge were held fixed using the RATTLE algorithm [62] to constrain their positions relative to one another. 

Water-water potential functions have been reported from different laboratories. The procedure leads either to analytic functions fitted to empirical data, e.g. SPC (single point charge) [19] and TIPS (transferable intermolecular potential functions)... 

Multicomponent systems that present polyamorphism have also been reported in computer simulation studies. For example, in Ref. [35], it is found that silica has a LLCP at very low temperature. Silica is also a tetrahedral liquid and it shares many of the thermodynamic properties observed in water. In Ref. [35], two silica models were considered. In both models, the interactions among O and Si atoms are isotropic, due to single point charges and short-range interacting sites located on each atom. Both models considered in Ref. [35] are characterized by a LLCP at very low temperature and coexistence between two liquids is observed in out of equilibrium simulations close to one of the spinodal lines (see Fig. 2b). The location of the LLCP was estimated to be below the glass transition in real silica and hence, unaccessible in experiments. We note that polyamorphism in the glass state is indeed observed in compression experiments on amorphous silica [14], and is qualitatively reproduced in computer simulations [89]. Other examples of multicomponent systems that show LLPT in simulations are presented in Refs [65,90]. In these cases, a substance that already shows polymorphism is mixed with a second component. 

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