Energy Madelung

P.A.Korzhavhi, A.V.Ruban, I.A.Abrikosov and H.L.Skriver, Madelung energy for random metallic alloys in the coherent potential approximation , Phys. Rev. B51 5773 (1995) ... 

Table I. The electrostatic energies of the central silicon site and one nearest-neighbor oxygen site for a 977 point-ion cluster, and the Madelung energies for silicon and oxygen in alpha-quartz...

For simple monovalent metals, the pseudopotential interaction between ion cores and electrons is weak, leading to a uniform density for the conduction electrons in the interior, as would obtain if there were no point ions, but rather a uniform positive background. The arrangement of ions is determined by the ion-electron and interionic forces, but the former have no effect if the electrons are uniformly distributed. As the interionic forces are mainly coulombic, it is not surprising that the alkali metals crystallize in a body-centered cubic lattice, which is the lattice with the smallest Madelung energy for a given density.46 Diffraction measurements... 

The detachment of the Fe(II) into solution. This detachment is facilitated by the increase in surface protonation that is accompanied by the ligand binding. The fact that iron(II) is more readily detached than an iron(III) site from the mineral surface is due to the lower Madelung energy of the Fe(II)-oxygen bond than the Fe(III)-oxygen bond... 

Fig. 3.3 shows a similar ionic-model construction of the electronic energies for the isostructural transition-metal oxide MnO. In this case, the Madelung energy lifts the Mn 3d level above the top of the... 

A metallic band structure is realized when the CT solids have a partial CT state and molecules form uniform segregated columns or layers. Figure 1 shows electrical conductivity data for 1 1 low-dimensional TTF TCNQ system, as a function of redox potentials [82]. The two lines a and b are related to the equation expressing the relationship between 7d, Ea, and the Madelung energy M 5) (5 = degree of CT) between partially charged component molecules (eq. 2) [83], where and Ea are... 

The experimental trends in bonding and structure which we have discussed in the previous chapter cannot be understood within a classical framework. None of the elements and only very few of the thousand or more binary AB compounds are ionic in the sense that the electrostatic Madelung energy controls their bonding. And even for ionic systems, it is a quantum mechanical concept that stops the lattice from collapsing under the resultant attractive electrostatic forces the strong repulsion that arises as the ion cores start to overlap is direct evidence that Pauli s exclusion principle is alive and well and hard at work ... 

The Madelung energy, eqn (6.61), can also be expressed as a pairwise sum over coulomb interactions between the point ions, plus a q - 0 contribution arising from the electron-ion and electron-electron interactions. Grouping this together with the band-structure contribution we have... 

Fig. 8.15 The Madelung energy in ionic compounds as a function of the radius ratio for CsCl, NaCl and cubic ZnS lattices (assuming the anion radius, / , is held constant).

The Madelung energy, m. arising from the coulombic attraction of the partial... 

Two points of view are applicable to these species, as they also are to the isoelectronic noble gas fluorides (1) a valence bond approach with promotion of electrons to d orbitals and (2) three-center, four-electron bonds. The same arguments, pro and con. apply as given previously, so they will not be repeated here. Independent of die alternative approaches via VB or MO theory, all are agreed that Madelung energy ( ionic character ) is very important in stabilizing both the polyhalide tons and the polyhalogens.27... 

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