Dipole self-energy

Lastly, as shown in eqn (7.17), the energies contributed from atomic polarizability are the dipole self-energy, the dipole-charge interaction, and the dipole-dipole interaction, respectively. 

The subscripts i which have been added refer to the different species of ion-dipoles, and the symbols ax(D),... indicate that the respective coefficients have to be calculated with the value of D and n2. From the way our work function A has been derived, it is evident that it contains the contributions which are caused by the presence of the solutes and by the change in dielectric constant of the solvent. The contributions which result from the first term in Equation 19 and which represent the work which is required to build up the ion-dipole in a standard environment (e.g., a vacuum) have disappeared from Equation 24 (being identical in A and A o). This self-energy of the particles is without interest for the present investigation and depends, of course, in a decisive way on the underlying model. 

We now have the tools for constructing the spectral function A4p(E). We begin by studying the energy dependence of the self-energy and the solution to the Dyson equation, keeping the static monopole and the dynamic dipole terms and neglecting Fermi sea correlations... 

Fig. 52. (aMd) Self-energy for an inner valence 2gg hole, describing the excitation of triplet and singlet mi satellites, (e) and (1) suggest that the singlet mi excitation is associated with distortions and dipole moments along the molecular axis (e), and the triplet mi excitation with distortions and dipole moments perpendicular to the axis (f)... 

The self-energy, self, due to the classical induced dipole moments [52] is given by... 

Other ions in the solution. The self-energy of a dipole embedded in a dielectric sphere is the key to Onsager s theory of the dielectric constant of dipolar fluids. Equally, in any theory for, say, the surface energy of water, or adsorption of molecule, the self-energy of a molecule as a function of its distance from an interface is involved. In adsorption proper, the same selfenergy for a molecule appears in the partition function of statistical mechaiucs from which the adsorption isotherm is derived. 

The total potential energy of the Drude polarizable model contains the terms representative of the interaction with the static electric field, interaction with other dipoles and the self-energy associated with the Drude oscillators, in addition to the standard contributions representing bonding terms (bonds, angles, dihedrals, etc.) and intermolecular interactions represented by Lennard-Jones (Lj) "6-12" term ... 

The evaluation of the lattice sum (16) is cumbersome and details of this calculation are given in the Appendix. The final expression for the electrostatic energy of the cell interacting with all its periodic images (16) can be represented as a sum of four terms sums in the direct Udtr ( ij ) and reciprocal C/ c ( ij ) space, self-energy term, and shape term that depends on the net dipole moment of the cell... 

Because many effective pairwise additive potentials do not include the self-energy of the dipoles in their original parameterizations, their reported enthalpy values require corrections to make a proper comparison with experi-... 

Electrostatic self energy is associated with the work in producing an external electric field due to dipole surface charges. 

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