Embedded cluster model energy levels

Another pertinent question is related to the accuracy of the common approximation to describe relativistic effects at the pseudopotential level. Our AE scalar relativistic DKH scheme allows to evaluate the precision of the latter scheme. A relativistic pseudopotential [196] was utilized to treat the heavy element Pd in the Pd-0 complexes employing extended EPE-embedded cluster models of the quality comparable to that for the AE cluster model. This resulted in the adsorption energy value 123 kJ/mol and the Pd-0 bond length 213 pm. For the Pd-0 complexes under scrutiny the deviations from the corresponding scalar relativistic values, by 3 kJ/mol and 2 pm respectively, are rather small. Clearly, relativistic pseudopotentials for heavier atoms have to be constructed with due care [8]. The AE scalar relativistic DKH approach certainly provides an attractive alternative. 

An important question when one addresses the stability of charged defects in insulators is that of the relative position of the corresponding energy levels with respect to the vacuum level. This problem has been considered for the MgO(lOO) surface [61]. Using cluster models embedded in polarizable ions and PCs, the ionization energies and electron affinities of oxygen vacancies located at the terraces and corners of the MgO surface have been determined. 

In [710] a 65-atom molecular cluster is used that was treated semiempiricaUy at the INDO level and embedded in the electrostatic field generated by multipoles. To model the F and F+ centers in corundum additional 2s and 2p Slater-type atomic orbitals were placed in the vacancy after removing one O atom. The relaxation of the four aluminum atoms nearest to the vacancy resulted in an outward displacement by 2-3% and 5-6% for the F and F+ center, respectively. Prom the 12 next-nearest oxygen atoms only two were allowed to relax. In contrast to the results of [709] the two oxygen atoms moved toward the vacancy by about -2.2% and -4.6% for the F and F+ center, respectively. Defect-formation energies were not calculated. 

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