Electrostatic interaction of point charges

Electrostatic Interaction of Point Charges in an Inhomogeneous Medium... 

Having estabUshed that the two principal components of the lattice energy, U, will be coub attractive (negative) term derived from the electrostatic interactions of point charges, and a short-range repulsive (positive) term, we can write Equation (8.8),... 

As in CNDO, in MNDO the penetration integrals are neglected (Section 6.2.3, CNDO/2). A consequence of this is that the core-core repulsions (Vcc in Eq. 6.2) cannot be realistically calculated simply as the sum of pairs of classical electrostatic interactions between point charges centered on the nuclei. Instead, Dewar and coworkers chose [38] the expression... 

In this discussion we limit ourselves to electrostatic interactions between point charges. The overall system is assumed to be neutral. The potential field of charge-charge interactions is in fact described by one of the classic differential equations, namely the Poisson equation with periodic boundary conditions. Because of the somewhat unusual boundary conditions it is important to realize that some care must be practiced when applying a solution strategy. 

In the case when all the ions are mononuclesir, as in NaCl, the electron distribution around each nucleus is isotropic, so that one can assume that the electrostatic energy results from the interaction of point charges centered on the nuclei. This is Madelung s classical calculation 38). 

Let us first make the extreme ionic assumption, namely, that the bonding between foe metal ion and foe ligands is a purely electrostatic interaction between point charges. This viewpoint was first explored by physicists in foe early 1930 s, in connection with foe spectra of ionic crystals, and foe ideas about bonding that are derived from it are called CRYSTAL-FIELD THEORY. 

Once the models for the charge distributions are in hand, the electrostatic interaction is computed as the interaction between the sets of point charges or distributed nuiltipoles, and added to an atom-atom, exp-6 fonn that represents the repulsion and dispersion interactions. Different exp-6 parameters, often from [140. 

Adsorption Forces. Coulomb s law allows calculations of the electrostatic potential resulting from a charge distribution, and of the potential energy of interaction between different charge distributions. Various elaborate computations are possible to calculate the potential energy of interaction between point charges, distributed charges, etc. See reference 2 for a detailed introduction. 

A number of intermolecular potentials have been developed over the years that treat molecules as collections of point charges. The intermolecular electrostatic potential is taken as a sum of the mutual electrostatic interaction of these point charges, summed over interacting pairs of molecules. Occasionally, extra van der Waals terms are added to the potential. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

From Table 2.5 it is clearly seen that becomes small (less than 0.001 kcal/ mol) beyond a distance of 10 A. The electrostatic interaction reaches the same level of importance at a distance of 30 A. The Table also shows that the interaction between point charges behaves much like a dipole-dipole interaction, i.e. an R dependence. However, the interaction between net charges is very long range even at 100 A separation, there is a 0.34kcal/mol energy contribution. The cut-off distance corresponding to a contribution of 0.001 kcal/mol is of the order of 3000 A ... 

More realistic treatment of the electrostatic interactions of the solvent can be made. The dipolar hard-sphere model is a simple representation of the polar nature of the solvent and has been adopted in studies of bulk electrolyte and electrolyte interfaces [35-39], Recently, it was found that this model gives rise to phase behavior that does not exist in experiments [40,41] and that the Stockmeyer potential [41,42] with soft cores should be better to avoid artifacts. Representation of higher-order multipoles are given in several popular models of water, namely, the simple point charge (SPC) model [43] and its extension (SPC/E) [44], the transferable interaction potential (T1PS)[45], and other central force models [46-48], Models have also been proposed to treat the polarizability of water [49],... 

It is generally unwise to think of ionic compounds as holding together with physical bonds it is better to think of an array of point charges, held together by the balance of their mutual electrostatic interactions. (By mutual here, we imply equal numbers of positive and negative ions, which therefore impart an overall charge of zero to the solid.)... 

These values for J R) and K R) may be rationalized in pirrely electrostatic terms involving charge distributions of various sizes and shapes. From the point of view of electrostatics, J R) is the interaction of points and spherical charge distributions. The well-known effect, where the interaction of a point and spherical charge at a distance R is due only to the portion of the charge inside a sphere of radius R, leads to an exponential fall-off J R), as R increases. 

The aqueous phase pH determines the ionization state of the surface-charged groups on the protein molecule. Solubilization of the protein in RMs is found to be dominated by electrostatic interactions between the charged protein and the inner layer of the surfactant head groups [112]. Solubilization of protein is favored at pH values above the isoelectric point (pi) of the protein in the case of... 

Concerning the electrostatic interaction of charged macromolecules with lipids and segregation in mixed films. I would like to point out that (to be published in Electrical Phenomena at Membrane Level, p. 273 Elsevier, Amsterdam, 1977) ... 

Compared to Eq. (13.1), there are three new terms, all involving the auxiliary region. However, two of these terms are entirely classical, T/aux and Haux/MM- The first is simply the electrostatic interaction of the frozen density and its nuclei with themselves, while the second is the interaction of the frozen density and its nuclei with the MM point charges and non-bonded L.1 terms between the two regions. 

In crystal field theory each ligand is approximated as a point charge or a point dipole and each metal-ligand interaction is taken to be purely electrostatic. So our problem is reduced to one of investigating the effect of point charges (or point dipoles) arranged tetrahedrally or octahedrally about an electron in a dai y or a dXI orbital. 

---