Cation-anion resonance integral

To summarize, within the assumptions of the alternating lattice model, the gap width has two contributions related to the anion-cation difference in electronegativity and to covalent effects. The covalent contribution is an increasing function of the resonance integrals, but it also depends upon the vectors at which the gap opens and closes in reciprocal space, i.e. upon the symmetry of the orbitals and of the lattice. In specific cases, the orbital crystal field splitting and second-neighbour delocalization effects may slightly modify this simple picture. 

The shape of the density of states reveals the peculiarities of the hybridization between anion and cation orbitals, which depend upon three parameters the values of the resonance integrals the coordination number of the surface atoms and the energy separation between the relevant atomic levels. In the absence of relaxation, rumpling or reconstructions, the resonance integrals have the same values as in the bulk. The surface atom coordination numbers and the level separation, on the other hand, are smaller than in the bulk and they decrease as the surface becomes more open. We will first discuss how these modifications are reflected in the gross features of the local densities of states at the surface and, more specifically, in their second moments. Then we will focus on the details of the band shapes and on the possible occurrence of localized states in the gap. 

Moments of the density of states Within the assumption that electron delocalization takes place only between first neighbours, the second moment of the local density of states on an anion is related to its coordination number Za, to the effective anion-cation resonance integral / , to the anion atomic energies e x and to the degeneracy of the outer levels (Equation (1.4.40) in Chapter 1) ... 

Surface charges Inward relaxation effects have two antagonistic effects on the ionic charges. They increase the resonance integrals and increase the energy difference between anion and cation effective levels. Since the charges depend upon the ratio Z s / ecs — As). in most cases no noticeable variation results. 

In order to get deeper insight into the strength and spatial extension of screening effects in an insulator, one can develop an analytical approach in which the electronic susceptibility is estimated in first-order perturbation with respect to the resonance integrals p, and in which a single orbital per site is considered to describe the electronic structure (Harrison, 1980). Under these approximations, the anion and cation electron numbers then read ... 

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