Electrostatic interactions energy

The electrostatic potential at a point r, 0(r), is defined as the work done to bring unit positive charge from infinity to the point. The electrostatic interaction energy between a point charge q located at r and the molecule equals The electrostatic potential has contributions from both the nuclei and from the electrons, unlike the electron density, which only reflects the electronic distribution. The electrostatic potential due to the M nuclei is ... 

In a recent paper. Mo and Gao [5] used a sophisticated computational method [block-localized wave function energy decomposition (BLW-ED)] to decompose the total interaction energy between two prototypical ionic systems, acetate and meth-ylammonium ions, and water into permanent electrostatic (including Pauli exclusion), electronic polarization and charge-transfer contributions. Furthermore, the use of quantum mechanics also enabled them to account for the charge flow between the species involved in the interaction. Their calculations (Table 12.2) demonstrated that the permanent electrostatic interaction energy dominates solute-solvent interactions, as expected in the presence of ion species (76.1 and 84.6% for acetate and methylammonium ions, respectively) and showed the active involvement of solvent molecules in the interaction, even with a small but evident flow of electrons (Eig. 12.3). Evidently, by changing the solvent, different results could be obtained. 

Given a point charge Q located at the point r, then QV(r) is equal to the electrostatic interaction energy between the unpolarized molecule and the point charge. 

The electrostatic interaction energy between the solute (represented by the charge distribution Q) and the polarizable medium represented by the induced charge distribution QP° e) becomes ... 

All of these interactions involve a host and a guest as well as their surroundings like solvation, crystal lattice, and gas phase. Electrostatic interactions are the driving force behind the ion pairing (ion-ion, ion-dipole, dipole-dipole, etc.) interactions, which are undeniably important in natural and supramolecular systems. The electrostatic interaction energy E is given by... 

Proof The electrostatic interaction energy of Qt with the molecule would be Q,V(z,n)- By Equations 17.2 and 17.3, the force along the axis in either direction depends upon (dQtV(z)/dz)Zm, which is zero, since F(z) is a minimum at zm. 

FIGURE 27.5 Electrostatic interaction energy (A.Eeiec) between cytosine and the substituted benzenes Ph-X (kcal/mol) vs. the local hardness 17(f). (Reprinted from Mignon, P., Loverix, S., Steyaert, J., and Geerlings, P., Nucl. Acids Res., 33, 1779, 2005. With permission.)... 

The influence of the organocation structure on the exchange adsorption becomes evident from the data in table V. 4,4 Bipyridinium cations adsorb two times more energetically (AH s 2j2 kJ Eq ) than do 2,2 bipyridinium cations (AH° = 11 f5 Eq ). The former adapt a planar orientation (dnm = f 26 nm) in contrast to the inclined position of the latter ( qq = 1.4 nm), despite the fact that sufficient surface is available for adsorption in a flat configuration. Smaller enthalpy terms are consistent with smaller electrostatic interaction energies. The reason for the tilting is unknown however. 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

Equation 2.16 contains contributions from the translational entropy of the mobile species, the conformational entropy of polymer chains, the free energy associated with the different chemical equilibria in the system, the polymer-polymer and polymer-surface van der Waals (vdW) interaction energies, the electrostatic interaction energies and the repulsive interactions between all the different molecular species. The expressions for each of these terms are shown in Table 2.2, while the definition of the symbols is given in Appendix. Note that in Table 2.2, the densities. 

The electrostatic interaction energy between two spherical atoms or ions located at A and B is the sum of the internuclear repulsions, the nucleus-electron attractions, and the electron-electron repulsions (Su and Coppens 1995) ... 

Equation (2.20) can be used to model the behavior of a large collection of individual molecules efficiently because the electrostatic interaction energy is pairwise additive. That is, we may write... 

Inductive effects on dipole moments and the effects of intervening atoms on electrostatic interaction energies are represented by polarizability centers In conjunction with bond centered dipoles. Solvation energies are estimated by means of a continuum dlpole-quadrupole electrostatic model. Calculated energies of a number of conformations of meso and racemic 2,4-dichloropentane and the iso, syndio, and hetero forms of 2,4,6-triehloroheptane give satisfactory representations of isomer and conformer populations. Electrostatic effects are found to be quite important. 

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