Interactions, collective Coulomb

In the simplest model, the interactions with the solvent were completely neglected and the collective Coulomb interactions between the ions were imitated by a screened Coulomb potential the result is (see Eq. (321))... 

Collective Coulomb interactions. We should consider the whole class of ring diagrams generated by the simple diagrams of Fig. 23, as is illustrated in Fig. 25a. 

In the presence of the large fields present in the space-charge region, the collective coulombic interaction is overcome and there is a net separation of charge. In fact, the field magnitude is well in excess of the ambipolar fields and the carriers experience a large acceleration in the field region. 

In the SAPT method, the total Hamiltonian H of the dimer is partitioned dsH = Ha + Hb + V, where Hx, X = A or B, is the total Hamiltonian for monomer X, and V is the intermolecular interaction operator. The operator V collects Coulomb interactions of all the particles of monomer A with those of monomer B. This partition means that the unperturbed operator is chosen as Ha = Ha + Hb and V is the perturbation. The interaction energy is then obtained directly in the form of a perturbation series in V,... 

Bohm, D., and Pines, D., Phys. Rev. 92, 609, Collective description of electron interactions. III. Coulomb interactions in a degenerate electron gas."... 

As already mentioned, the existence of a C3/a term in Eq. (312) is related to the long-range character of the Coulombic interactions between any pair of ions. We then have to take into account the collective interactions between many ions in the system this in turn introduces a natural cut-off of the Coulomb force at a distance of the order ic-1, where ... 

Present-day diffraction facilities provide easy access to very low-temperature data collection and hence to an accurate determination of electron densities in crystals. Application of standard theorems of classical physics then provides an evaluation of the Coulombic interaction energies in crystal lattices [27]. These calculations are parameter-less and hence are as accurate as the electron density is. Moreover, for highly polar compounds, typically aminoacid zwitterions and the like, a fortunate coincidence cancels out all other attractive and repulsive contributions, and the Coulombic term almost coincides with the total interaction energy. 

Nevertheless, certain collective excitations can occur in the condensed phase. These may be brought about by longitudinal coulombic interaction (plasmons in thin films) or by transverse interaction, as in the 7-eV excitation in condensed benzene, which is believed to be an exciton [12]. Special conditions must be satisfied by the real and imaginary parts of the dielectric function of the condensed phase for collective excitations to occur. After analyzing these factors, it has been concluded that in most ordinary liquids such as water, collective excitations would not result by interaction of fast charged particles [13,14]. 

The collective excitations may decay in a number of ways. In an electron gas they decay owing to the interaction between electrons. In this case the Coulomb interaction of electrons is strongly screened by the electron cloud and is noticeable only at short distance. Owing to this short-range interaction, the oscillational energy of a plasmon transforms into kinetic energy of individual electrons, that is it is distributed all over the electron gas.1... 

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... 

Motion in ionic liquids is predominantly collective. The strength of interion Coulomb interactions makes independent motion of ions impossible, and transport modes are collective. Further, solvation dynamics involve... 

From the four-component Dirac-Coulomb-Breit equation, the terms [99]—[102] can be deduced without assuming external fields. A Foldy-Wouthuysen transformation23 of the electron-nuclear Coulomb attraction and collecting terms to order v1 /c1 yields the one-electron part [99], Similarly, the two-electron part [100] of the spin-same-orbit operator stems from the transformation of the two-electron Coulomb interaction. The spin-other-orbit terms [101] and [102] have a different origin. They result, among other terms, from the reduction of the Gaunt interaction. 

Having obtained the zero frequency limit of the dynamic polarizability i.e., a = Iin, o7 (—wja ), we use a simplified approach to evaluate the screened dynamic response. This is necessary, since the expression given above, Eq. (40), for the polarizability neglects the induced collective effects essentially due to direct and exchange terms of the Coulomb interaction. To treat this screening approximately, we have used the simplified approach of Bertsch et al. [96] to include the induced electron interaction in the Ceo molecule, by a simple RPA type correction [92,95]... 

Molecules are traditionally considered as being composed of atoms or, in a more general sense, as a collection of charged particles, positive nuclei and negative electrons. The only important physical force for chemical phenomena is the Coulombic interaction between these charged particles. Molecules differ because they contain different nuclei and number of electrons, or the nuclear centres may be in different geometrical... 

Today, collectively those interactions are called van der Waals interactions. Electrostatic (coulomb) and hydrogen-bonding forces, however, are excluded from this group basically due to the nature of the force. 

In this contribution we have reviewed the recent results concerning the collective dynamics of charged liquids. In order to establish the role of long-range Coulombic interactions we have concentrated our attention on the comparison of the results obtained for binary mixtures of neutral and charged particles. Such a comparison has been performed on two levels of consideration - on the level of analytical theories and numerical simulations. The main conclusions from our studies are as follows. 

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