By Hansjörg Donnerberg

This ebook experiences the entire cutting-edge simulation tools used to enquire the atomistic-scale homes of technologically very important oxide fabrics. prior and plenty of fresh effects are conscientiously mentioned.

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**Example text**

As the latter has been fixed to be a pure Born-Mayer exponential function [12], it is reasonable to employ the HartreeFock approximation without configuration interaction (CI) in all subsequent cluster calculations and to fit the results with a Born-Mayer potential as well. Short-range potential energies may be calculated for various cluster geometries according to the following formula: NbS+ 0 2VSR .... 1 -- - - nNbO [ LEHF-- ~ 02- - - . 80) nNbO denotes the number of Nb-O bonds in the cluster, E HF the quantum mechanical cluster energy, ~-':Eself HF the sum of ionic self-energies, Ecb the rigid ion Coulomb contribution according to the formal charge model, ~ V~ ~ the occurring oxygen-oxygen short-range interactions and Epol, finally, an ionic polarization term.

Most of the available ab initio molecular codes can be used for this task. However, the programs must be modified as to include the required shortrange cluster-lattice interactions. The second cycle in Fig. 2 is devoted to the equilibration of the embedding shell model lattice. For corresponding computational details the reeler is referred to Sect. 2. Generally the lattice configuration/~ bears a pronounced relation to the cluster wavefunction $. This dependence requires us to employ during the optimization of the lattice configuration Re the accurate electrostatic potential produced by the quantum cluster.

Whereas this condition is fulfilled for delocalized eigenstates of large systems like crystals, it is not guaranteed for small clusters of atoms. As an example we consider the present (MnO6) -8 cluster. First, the 4A2g electronic state of this cluster has been calculated self-consistently. Then, without allowing any further orbital relaxations, the total energies of the two ionized states with one electron removed from either the top of the oxygen 2p levels or from the d(t2g) manganese orbitais have been determined.