Electrostatic field Madelung

In ionic systems it is essential to chose clusters that are electrostatically neutral, otherwise electrostatic boundary effects tend to dominate computed results. In the application of embedded methods care has to be taken to correct properly for boundary effects between cluster and medium. Madelung electrostatic field simulations have to be done with proper choice of charges and dielectric constants. For these reasons periodic calculations, when feasible, are typically preferred for ionic systems. 

Solvent potential. The averaged solvent electrostatic field, , is important for inhomogeneous media, such as enzymes, membranes, miscelles and crystalline environments systems. Due to the existence of strong correlations, such a field does not cancel out. This factor becomes an important contribution to solvent effects at a microscopic level. In a study of non-rigid molecules in solution, Sese et al. [25] constructed a by using the solute-solvent atom-atom radial distribution function. Electrostatic interactions in three-dimensional solids were treated by Angyan and Silvi [26] in their self-consistent Madelung potential approach such a procedure can be traced back to a calculation of . An earlier application of the ISCRF theory to the study of proton mechanisms in crystals of hydronium perchlorate both [Pg.441]

MnO is approximately 0.1 eV. The results of Nesbet s calculations are given in Table XIII. Although the agreement between observed and calculated N6el temperatures is quite good, it is important to realize that Uaa has been estimated only for a three-atom cluster, and considerable modification of this term can be anticipated for a solid where the clusters are located in the electrostatic Madelung field of the crystal. 

In the atomic-sphere approximation the electrostatic interactions of (7.15), i.e. the Hartree term and (8.31,32), reduce to the interaction with the field -2Zt/r inside the sphere. In addition, the spheres interact via the Madelung term... 

In strongly ionic materials, four types of interactions are found to be important, namely, the electrostatic interaction that gives rise to the Madelung potential, the polarization of ions in the crystal field, the repulsion between ions at close range due to orbital overlap, and the dispersion force due to dynamic correlated electron fiuctuations. The first of these is dominant in ionic systems and accounts for most of the cohesive force. 

The second method extends these ideas and is able to calculate reversible potentials for reactions that occur within the double layer. The model can be used to simulate both oxidation and reduction within the double layer. The influence of counterions from the electrolyte on the reactions can also be included. This is accomplished by using point charges and a Madelung sum in order to calculate the longer range electrostatic interactions and the field that arises from these ions and their influence on the reaction center. 

The stabilisation of the peroxy qiecies results from a balance between electrostatic repulsion of the O ions, the covalent bonding of a character and the Madelung field. 

The anion-cation bond-breaking produced by the formation of a surface is responsible for several phenomena. Some have an electrostatic origin. This is the case for polarization which is induced by surface electric fields which are much larger than those in the bulk. This is also the case for shifts of the renormalized atomic energies of surface atoms and shifts of surface bands, which are induced by reduction of the Madelung potential at the surface. On the other hand, as far as covalent effects are concerned, a modification of the anion-cation hybridization takes place, due to the lower coordination of the surface atoms. This has important consequences on the gap width and on the electron distribution. 

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