Short range Coulombic interactions

One of the most obvious perturbations of the surface excitons by the bulk crystal is the short-range coulombic interactions causing surface-exciton transfer to the bulk. We discard these perturbations on the grounds both of theoretical calculations27 and of the experimental observations, which show the presence of a surface exciton (the second subsurface exciton S3 see Fig. 3.2) resolved at about 2cm-1 above the bulk-exciton resonance. 

The near-infrared reflectance provides the response to plasmon oscillations of the electron gas (which are uniform excitations). This region of the spectrum is, however, not sensitive to the strength of the short-range coulombic interactions, which prevent conductivity in a Mott-Hubbard insulating state. This is illustrated by the frequency-dependent conductivity cx((o) measured in various salts exhibiting very different values of the conductivity at room temperature (Fig. 27). The peak of the conductivity at the frequency w0 correlates with the metallic character namely, a low frequency of the peak position corresponds to a high dc conductivity and vice versa. The structures below 0)o are attributed to the coupling with intramolecular modes. 

Bjerrum argued that it is only short-range Coulombic interactions that lead to ion-pair formation and, further, when a pair of oppositely charged ions are situated at a distance apart ofr> q, it is more appropriate to consider them free ions. 

We have developed a model to study the basic structural properties of solid C<,q. The model consists of two distinct types of intermolecular interactions. The dominant one is the van der Waals-type interactions between carbon atoms on different Cm molecules. A secondary short-range Coulomb interaction is modeled by a small charge transfer between the two types of bonds in the C60 molecule. In contrast to early calculations [6] which include the van der Waals interactions only, our model predicts correctly the observed cubic ground-state structure Pa3. Many structural properties calculated, such as the compressibility, cohesive energy, and specific heat, are in good agreement with experiments l7l. 

The contribution of the short-range Coulomb interaction was later taken into account by Fano in (10) for the same classical model. A generalization for the case of liquids has been given in (11). 

If the two values are similar, then it is likely that ion pairing is involved since Bjerrum s theory deals explicitly with short-range coulombic interactions which are predominantly dependent on the charges on the ions. 

As mentioned above, the model has to be extended to take account of the short range coulombic interactions of ion pairs over and above the long range coulombic interactions of the ionic atmosphere dealt with in the theory. 

Given the substantial differences between the systems being simulated, the force-fields traditionally used by researchers in computational electronics and in chemistry are necessarily different. In particular, short-range coulombic interactions are either neglected in electron device simulations, or they are treated with a stochastic approach rather than deterministically. The same considerations apply for finite size effects. 

So, the potential of an electron at rest in a macroscopic distance away from the surface v(oo) is larger than the average potential deep in the crystal v(- co). This potential step serves, in part, to keep the electrons within the crystal. v(oo) often is called the vacuum level . The second part of the surface barrier keeping the electrons within the solid matter (at low temperature) is due to short range Coulomb interactions - exchange and correlation - which is a pure bulk effect. 

If the backbone as well as the side chains consist of flexible units, the molecular conformation arises out of the competition of the entropic elasticity of the confined side chains and the backbone [ 153 -155]. In this case, coiling of the side chains can occur only at the expense of the stretching of the backbone. In addition to the excluded volume effects, short range enthalpic interactions may become important. This is particularly the case for densely substituted monoden-dron jacketed polymers, where the molecular conformation can be controlled by the optimum assembly of the dendrons [22-26,156]. If the brush contains io-nizable groups, the conformation and flexibility may be additionally affected by Coulomb forces depending on the ionic strength of the solvent [79,80]. 

Real proteins are built up both from hydrophobic and polar amino acid residues, some of the latter can be charged. Many of the conformational and collective properties of proteins are due to a complex interplay between short-range (hydrophobic) effects and long-range (Coulomb) interactions. Electrostatic effects can also determine some of the unique solution properties of globular proteins. We have already discussed the results of simulations... 

For species with strong polar bonds (e.g., metal oxides or halides) the interaction between ions can be described as the sum of Coulomb and short-range pair interactions. The latter is usually written in the Born-Mayer form... 

In the intermediate domain of values for the parameters, an exact solution requires the specific inspection of each configuration of the system. It is obvious that such an exact theoretical analysis is impossible, and that it is necessary to dispose of credible procedures for numerical simulation as probes to test the validity of the various inevitable approximations. We summarize, in Section IV.B.l below, the mean-field theories currently used for random binary alloys, and we establish the formalism for them in order to discuss better approximations to the experimental observations. In Section IV.B.2, we apply these theories to the physical systems of our interest 2D excitons in layered crystals, with examples of triplet excitons in the well-known binary system of an isotopically mixed crystal of naphthalene, currently denoted as Nds-Nha. After discussing the drawbacks of treating short-range coulombic excitons in the mean-field scheme at all concentrations (in contrast with the retarded interactions discussed in Section IV.A, which are perfectly adapted to the mean-field treatment), we propose a theory for treating all concentrations, in the scheme of the molecular CPA (MCPA) method using a cell... 

The metal to nonmetal transition, a basic electronic change, has proven surprisingly difficult to understand in detail. The underlying reason is the diametrically opposite modes of description natural for the metal (extended electronic states) and for the insulator (localized states, often with local constraints on electron number). The observed diversity of systems and phenomena indicates that a number of causes may be at work, e.g., disorder, short-range electron correlation, long-range Coulomb interaction, and election lattice coupling. The effects... 

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