Embedded cluster model electronic states

Embedded Cluster Models for Electronic States of Silicate Glasses... 

Extensive DFT and PP calculations have permitted the establishment of important trends in chemical bonding, stabilities of oxidation states, crystal-field and SO effects, complexing ability and other properties of the heaviest elements, as well as the role and magnitude of relativistic effects. It was shown that relativistic effects play a dominant role in the electronic structures of the elements of the 7 row and heavier, so that relativistic calculations in the region of the heaviest elements are indispensable. Straight-forward extrapolations of properties from lighter congeners may result in erroneous predictions. The molecular DFT calculations in combination with some physico-chemical models were successful in the application to systems and processes studied experimentally such as adsorption and extraction. For theoretical studies of adsorption processes on the quantum-mechanical level, embedded cluster calculations are under way. RECP were mostly applied to open-shell compounds at the end of the 6d series and the 7p series. Very accurate fully relativistic DFB ab initio methods were used for calculations of the electronic structures of model systems to study relativistic and correlation effects. These methods still need further development, as well as powerful supercomputers to be applied to heavy element systems in a routine manner. Presently, the RECP and DFT methods and their combination are the best way to study the theoretical chemistry of the heaviest elements. 

The discrete variational (DV) Xa method is applied to the study of the electronic structure of silicate glasses in embedded model clusters. The effects of the cluster size, the size of embedded imits, and the Si-0-Si bond angles on the electronic states are discussed. Embeddii units drastically improve the description of the electronic state, when compared to the isolated Si044- cluster, which is the structural unit of silicate glasses e.g., the Fermi energy for the embedded cluster becomes smaller when compared to that of the... 

The need to model this distribution means that it is difficult to theoretically study the electronic states of oxide glasses. There are several ways to theoretically study the electronic state of oxide materials, these include band calculations and molecular orbital methods. (9-13) The randomness is a problem for the band approach because it requires translational symmetry of the unit cell a large super-cell may be chosen, but this is at the cost of increased computer time and possible spurious interactions between cells. On the other hand, the molecular orbital (MO) approach is usually applied to isolated molecules, (14-16) and can not handle infinite numbers of atoms as in the solid state. The embedded potential method is one of the improvements in moleculeir orbited methods which have been introduced in order to study solid state materials. (17) Basically, the cluster Hamilto-... 

Adsorption energies on metals calculated in a cluster approach often show considerable oscillations with size and shape of the cluster models because such (finite) clusters describe the surface electronic structure insufficiently [257-260]. These models may yield rather different results for the Pauli repulsion between adsorbate and substrate, depending on whether pertinent cluster orbitals localized at the adsorption site are occupied or empty. The discrete density of states is an inherent feature of clusters that may prevent a correct description of the polarizability of a metal surface and thus hinders cluster size convergence of adsorption energies [257]. Even embedding of metal clusters does not offer an easy way out of this dilemma [260,261]. Anyway, the form of conventional moderately large cluster models may be particularly crucial. Such models are inherently two-dimensional with substrate atoms from two or three crystal layers usually taken into accormt thus, a large fraction of atoms at the cluster boundaries lacks proper coordination. 

Relativistic Ab Initio Model Potential embedded cluster calculations on the structure and spectroscopy of local defects created by actinide impurity ions in solid hosts are the focus of attention here. They are molecular like calculations which include host embedding effects and electron correlation effects, but also scalar and spin-orbit coupling relativistic effects, all of them compulsory for a detailed understanding of the large manifolds of states of the 5f" the 5f" 6d configurations. The results are aimed at showing the potentiality of Relativistic Quantum Chemistry as a tool for prediction and interpretation in the field of solids doped with heavy element impurities. 

In the case of localized states related to the dopants—including transition-metal (TM) and rare-earth (RE) ions—the effect of hydrostatic pressure on the local energetic stmcture and electronic transitions is simulated by the reduction of the size of the cluster, which includes the dopant ion and the ligands. The influence of pressure on the energetic stmcture of the TM and RE ions can be simulated using crystal-field phenomenological model calculations [10-12]. However, a more advanced approach, i.e., ah initio model potential embedded-cluster method, also has been used [13]. 

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