Electrostatic potential energy term

The final term in Eq. [11] is the Coulombic or electrostatic potential energy term and can be represented as the interaction of bond dipoles or atomic monopoles. With the latter,... 

The energy of an ion in a given medium depends not only on chemical forces but also on the electrostatic held hence the chemical potential of an ion j customarily is called its electrochemical potential and labeled fi. The electrostatic potential energy of an ion j when reckoned per mole is given by ZjF, where / is the electrostatic (inner) potential of the phase containing the ion a plus sign for cations and a minus sign for anions. Hence, the electrochemical potential can be written as the sum of two terms ... 

The work function of a uniform surface is defined in terms of the difference between the electrochemical potential of an electron inside the surface and its electrostatic potential energy — e4>outer at a point just outside the surface. This is a distance of about 10 cm. from the surface where the electron is regarded as being removed from the range of significant surface interactions (9). Thus,... 

The Hamiltonian of the Coulomb term involves electrostatic potential energy operator for the interaction of all electrons and nuclei of donors with those of acceptors. The electrostatic potential can be expanded into multipole terms of the type... 

First we take up the electrostatic forces. We shall consider only the sodium chloride structure, though other types are not essentially more difficult to work out. Let the charge on an ion be ze, where z = I for monovalent crystals, 2 for divalent, etc. We shall now find the electrostatic potential energy of the crystal, by summing the terms z2e2/d for all pairs of ions in the crystal, where d is the distance between the ions. We start by choosing a certain ion, say a positive one, and... 

Here, and p are the electric potentials in the metal, in the bulk solution and at the inner Helmholtz plane, x = / rw max is the surface concentration of the adsorbed water molecules in the absence of chemisorption and f(Fwmax - v/J) is their activity in the presence of chemisorption. In Eq. (24) the electrostatic contributions of the adsorbed molecules H2O and S to their electrochemical potentials also include the electrostatic potential energy of their dipoles in the interfacial electric field, -dftdx and are average values of the normal components of these dipoles, regarded as positive when their positive end is directed towards the solution. By substituting Eq. (24) into Eq. (23), rearranging terms, and differentiating jus with respect to [Pg.315]

It is of considerable importance to note that the density-potential relationship (3) of the TF theory follows from a variational principle for the total energy. To see this, we note first that the classical electrostatic potential energy U consists of the sum of two terms in an atomic ion, the electron-nuclear potential energy Ken and the electron-electron potential energy Kee. We can write... 

In this context, Hanumantharao et al. [ 129] have carried out a QSAR analysis of the agonist activity of the thiazole derivatives (e) with the molecular descriptors generated from the MOE programme [71]. This has resulted in QSAR models (Eq. 23 and 24) of these compounds in terms of hydropho-bicity of VdW surface areas with different polarities (SlogP, SlogPvsAo and SlogPvsAs). electrostatic potential energy (Eeie). and zero-order connectivity... 

Formation of the chemical bond is associated with a reduction of the electrostatic potential energy and a release of this energy in the form of heat. The actual shape of Veff must be determined by analyzing the Coulomb terms in Equation 3.13. Different classical models of bond formation achieve this goal in different ways. We see how this is done for the two main models for ionic and covalent bonding in Sections 3.6 and 3.7. 

Provided that there is no additional surface charge, fj, is a pure bulk term which is independent of any electrostatic potential. The term is the contribution of surface dipoles [1, 2] (Fig. 2.1). Such a dipole can be caused by an unsymmetrical distribution of charges at the surface because there is a certain probability for the electrons to be located outside the surface. In the case of compound semiconductors, dipoles based on the surface structure caused by a particular ionic charge distribution occur. These effects depend on the crystal plane and on the reconstruction of the surface atoms [3, 4]. These dipole effects also influence the electron affinity and ionization energy. In the case of metals, the work function is a directly measurable quantity, and for semiconductors it is calculable from ionization measurements. However, the relative contributions of fi and ex are not accessible experimentally and data given in the literature are based on theoretical calculations (see e.g. ref. [1]). 

The aim is to calculate the mean ionic activity coefficient from the non-ideal part of the free energy. This is done in terms of the electrostatic potential energy of the coulomhic interactions between the ion and its ionic atmosphere. These interactions give rise to non-ideality. 

This communication outlines formulas that can be used when the energy is described (for S states) entirely in terms of the interparticle coordinates r,- and extends earlier work [11, 12] that shows how the combinations of integrals that describe the kinetic energy can be related to the overlap and Coulomb interaction integrals that enter the evaluation of the electrostatic potential energy. 

In the absence of external potentials, the electrostatic potential energy of nuclei and electrons can be represented by the Coulombic interactions among the electrons and nuclei. There are three groups of electrostatic interactions interactions between nuclei, interactions between electrons and nuclei, and interactions between electrons. Following the Born-Oppenheimer approximation, we neglect nuclei interactions in our DG-based model. Using Coulomb s law, the repulsive interaction between electrons can be expressed as the Hartree term ... 

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