Coulombic effects repulsion

The ionization properties of the side-chain of mepacrine are also relevant to its activity. The pK of the nitrogen atom at the free end of the chain is 10.48, but only 7.92 at the fixed end (at 20°C, cf. 10. i and 7.0 for ethyl-enediamine). Both ends of this side-chain are ionized at pH 7 (see Table 10.3), but the lower pK is greatly decreased by any shortening of the side-chain, with the result that both the ionization and the antimalarial action fall steeply away (Albert, 1966). This drop is caused by the coulombic effect (repulsion between like charges varies inversely with the square of the distance). 

Instead of MV2+ (in the photo-oxidation of leuco crystal violet (LCV)), a neutral species is sensitized by pyrene containing polymers and the Coulombic effect is not as drastic as in the case of MV2+. As shown in Figure 8, the cationic polymer is more effective than the neutral or anionic polymer. This is attributed to the Coulombic repulsion between LCV- and Py assisted by the cationic environment of the polycation. However, the Coulombic effect occurs only after forward electron transfer. 

Moreover the effective repulsive Coulomb pseudopotential in the Migdal-Eliashberg theory is expected to decrease (so the effective coupling strength increases) where the interband pairing is dominant. 

Recently, Forsman developed a correlation-corrected PB model by introducing an effective potential between like-charge ions (Forsman, 2007). The effective potential at large ion-ion separation approaches the classical Coulomb potential and becomes a reduced effective repulsive Coulomb potential for small ion-ion separation. Such an effective potential represents liquid-like correlation behavior between the ions. For electric double layer with multivalent ions, the model makes improved predictions for the ion distribution and predicts an attractive force between two planes in the presence of multivalent ions (Forsman, 2007). However, for realistic nucleic acid structures, the model is computationally expensive. In addition, the ad hoc effective potential lacks validation for realistic nucleic acid structures. 

To describe the electronic structure of carbon nanotubes the Hubbard model has been chosen as it can describe the electrical and magnetic properties and high temperature superconductivity effects also [11]. The model includes the terms of the electron jump energy in vicinity approach and the energy of Coulomb s repulsion of two electrons localized on the same point of unit cell. Hubbard Hamiltonian for the described system is following [11] ... 

If an approximate radial equation is constructed for a many-electron system, it must involve a non-Coulombic effective potential, because of the effects of electron-electron repulsion. Since the radial Schrodinger equation depends explicitly on , it is no surprise that the binding energy then depends on both n and , and so both must be specified for each electron when the configuration of the atom is written down. 

A striking example of this theory is the large a effect (ca. 103) of pyridine N-oxides in contrast to the normal behavior of trimethylamine N-oxide and phenoxide (47). According to my explanation, P -P repulsion in the phe-noxide and the inductive (Coulombic) effect in the aliphatic amine oxide alone do not produce an a effect. However, the combined action of the inductive effect and P -P repulsion in the aromatic N-oxide produces the observed a effect. 

In nonrelativistic quantum mechanics, the angular momentum barrier prevents the collaps to the center. The angular momentum barrier is an effective potential of the form + l)/r that appears if one writes the kinetic energy in polar coordinates. For the Dirac equation the role of the angular momentum barrier is obviously played by the term /c/r in the radial Dirac operator. This term is effectively repulsive for both signs of k, because it appears only off-diagonal. The point is, that the repulsive angular momentum barrier k jr cannot balance the attractive Coulomb potential 7/r for r —> 0, as soon as I7I > k. ... 

We now summarize the conclusions of this Section. On the one hand, the effective repulsion between carriers within the same plane is weakened, as compared to the usual Coulomb value. On the other hand. 

It is obvious that both intra-molecular and inter-polymer phenomena in polyelectrolyte solutions are dominated by coulomb forces. Repulsive interactions would be expected to diminish aggregation. At the same time, extended chain dimensions and the long-range character of electrostatic effects can promote forms of ordering unique to polyelectrolytes. Hydrodynamic, spectroscopic and thermodynamic methods have all been brought to bear on the coupled problems of conformation, counterion distribution and inter-polymer ordering in polyion solutions. These approaches are well represented in Part III by the works on Paoletti, Berry and Jamieson. 

Both coulombic and hydrophobic interactions of reactants with adsorbed surfactant on electrodes are important in determining electron transfer kinetics. Reactants in micellar solutions and microemulsions can be preconcentrated into adsorbed surfactant films on electrodes [30], yielding mixed layers of reactants and nonelectroactive surfactants. Coulombic effects in micellar solutions may result in small kinetic enhancements when ionic reactants interact with oppositely charged surfactant adsorbed on electrodes. Partial inhibition of electron transfer can occur by coulombic repulsion if the charge sign on the reactant and adsorbed surfactant are the same. Hydrophobic molecules and ions may show a small amount of preconcentration on the electrode. 

Thus, we argue that the fact that SeF is distorted C2y coupled with the realization that the fluorines are too far apart for any appreciable nonbonded interaction, means that the stereochemistry of AF (A = S, Se) "hypervalent" molecules is controlled by an interplay of "nonclassical" bonding effects, which allow ready distortions only in the geometry, and "classical" coulomb nonbonded repulsions which can be minimized without adversely affecting core-ligand bonding in the same geometry. In addition, we conclude that SH is not at all a model of SF at... 

Monte Carlo studies show that the Wigner lattice melts when the parameter r is about 155 10 (corresponding to /l 0.08). Thus, whatever the form of the effective repulsive interaction, from very soft (unscreened Coulomb) to hard (say r ), the empirical Lindemann rule provides melting curves that are, at worst, qualitatively correct. 

The first three terms in Eq. (10-26), the election kinetic energy, the nucleus-election Coulombic attraction, and the repulsion term between charge distributions at points Ti and V2, are classical terms. All of the quantum effects are included in the exchange-correlation potential... 

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