Electrostatic energy of interaction

In view of the assumed lack of individual lateral adsorbate-adsorbate interactions the only electrostatic energy to be accounted for in expressing the electrochemical potential, p j, of the adsorbate is the electrostatic energy of interaction of the adsorbate dipole with the effective double layer field. This is accounted for by ... 

Let J,o be the dipole moment of a solvent molecule and Tq its radius. The electrostatic energy of interaction between the ion and hj solvent molecules in the primary shell when computed per mole of ions can be written as... 

In a linear +/- chain with the charges separated by a distance, d picks a central charge. Then, the electrostatic energy of interaction of the central... 

More or less arbitrarily, the electrostatic energy of interaction AEcoxs is defined directly in the isolated molecules. The renormalization correction of the electrostatic energy (UooSoo) is included in the exchange term AE k-... 

Furthermore, in this scheme of partitioning the formula for AEqov becomes identical with the semiclassical electrostatic energy of interaction (4). As we shall see later a closely related quantity can be defined in the framework of intermolecular MO theory and thereby comparison of different approaches is largely facilitated. 

The intermolecular distance was calculated here relative to the center of mass (C. M.) of the water molecule. For this particular choice of the origin the quadruple term is rather small and the total electrostatic energy of interaction is reproduced fairly well by the first term of the expansion, the ion-dipole term alone. The difference between zIEcou and zIEcou of course is not exclusively... 

Whenever possible, we will attempt to identify the effects of interactions between relatively few frontier orbitals, which describe the distribution of relatively few electrons of a molecule. We effectively ignore the vast numbers of the rest of the electrons in the system as well as the nuclear charges. In some cases this neglect is not justified and may lead to misleading results. When a molecule or parts of it are charged, coulombic interactions may dominate. The electrostatic energy of interaction of each pair of centers, i and j, with net charges, qt and qj, respectively, separated by a distance Ry in a medium with dielectric constant em has the form... 

The electrostatic energy of interaction Ee between the nuclear charge density pn ijk) at point (ijk) and the surrounding electric charge is given by 28,49)... 

The total electrostatic energy of interaction is made up of four components ... 

Here qt and qj are point atomic charges and/GB is a distance-dependent function. The summation is over all pairs of atoms in the solute. The fGB function is chosen to satisfy certain boundary conditions for a distance ry = 0,/GB = Rh and for a long distance ry = oo, foB = ry- These conditions turn Eq. (31) into the Born formula when ry = 0 and would recover the Coulomb interactions for ry = oo. Indeed, the total electrostatic energy of interaction between charges at large distance is given by... 

Step 8 Calculation of the potential at the surface of the central j-ion due to the ionic atmosphere, and thence finding the electrostatic energy of interaction between an ion and its ionic atmosphere... 

DIPOLE-DIPOLE INTERACTION In order to find the attractive energy of two dipoles that point in the same sense along their own direction, add the electrostatic energies of interaction of all the charge pairs within the dipoles ... 

Based on the above simplifications, analytical formulae can be produced for the calculation of the electrostatic energy of interaction between two flat surfaces. Appropriate formulae for two different models, i.e. constant potential and constant charge, are given as follows Constant potential (4)... 

Because a crystalline solid is composed of a three-dimensional array or lattice of ions, the total electrostatic energy of interaction E i must account for all the resulting pairwise interactions ... 

Knowledge of the reaction field factors allows us to obtain the electrostatic energy of interaction of the molecule with the continuum... 

Suppose now that the charge r at the reaction center changes during the reaction by an amount 5 r. The electrostatic energy of interaction Ep in equation (4.131)] will then change by an amount dEp given by... 

In terms of the general theory of Kirkwood, the electrostatic energy of interaction of a solute molecule with the solvent, assumed to be an isotropic dielectric with the dielectric permittivity s will be ... 

The second term in Eq. (3.20) is a quantum mechanical analog of the classic electrostatic energy of interaction ... 

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