Clusters embedding

One of the first cluster embedding schemes was put forth by Ellis and co-workers [172]. They were interested in studying transition metal impurities in NiAl alloys, so they considered a TMAl cluster embedded in a periodic self-consistent crystal field appropriate for bulk p -NiAl. The field was calculated via calculations, as was the cluster itself The idea was to provide a relatively inexpensive alternative to supercell DET calculations. 

Gutdeutsch U, Birkenheuer U, Kruger S and Rdsch N 1997 On cluster embedding schemes based on orbital space partitioning J. Chem. Phys. 106 6020... 

Gutdeutsch U, Birkenheuer U and Rdsch N 1998 A strictly variational procedure for cluster embedding based on the extended subspace approach J. Chem. Phys. 109 2056... 

Kruger S, Birkenheuer U and Rdsch N 1994 Density functional approach to moderately large cluster embedding for infinite metal substrates J. Eleotron Speotroso. Relat Phenom. 69 31... 

Fig. 16.9 (a) Partial structure of the extended Na5RbCu4(As04)4Cl2 lattice showing the [Cu40i2] clusters embedded in the salt lattice containing, rarely seen, NagOg (5-8 type) clusters, (b) The crown-... 

The above methods all assume that a clear spatial distinction can be made between toxic and nontoxic compounds. However, it is sometimes found that toxic compounds form a cluster embedded in a milieu of nontoxic compounds. In such cases, a different technique, embedded cluster modeling, can be used [77]. Cronin [78] has used the technique to model eye irritation data. 

Rotating culture vessels such as simulated microgravity systems are primarily used to study 3-D tumor growth and differentiation. However, mixed cell populations combined with matrix proteins can be used to generate a complex microenvironment in which cell-cell interactions and invasion can be measured (95). A similar system has also been described for the coculture of endothelial cells, myofibroblasts, and tumor cell clusters embedded in Matrigel . Differential labeling of the cell populations enables their invasion and the effects of inhibitors to be measured (96). 

Cobalt clusters embedded in silver display giantmagnetoresistance (GMR), with an increase in resistance of up to 20%, and are used for magnetic recording and data storage. 

The clearest use of ONIOM-PCM is for solute-solvent clusters embedded in a continuum. The method can also be used to partition the solute itself into layers that are each treated at a different level of theory. An example is the study of NMR shielding in a merocyanine in solution (Figure 4.10) [41], We looked at the shielding on the nitrogen center. Nuclear shielding is a relatively local property, and previous gas-phase studies showed that ONIOM can accurately reproduce target values [43], We investigated several... 

The detailed magnetic behavior of Fe clusters has been studied for the films with Fe clusters embedded in Ag [34]. In UHV conditions, preformed Fe clusters with a mean diameter of 3 nm from a gas-aggregation source were deposited in conjunction with atomic Ag vapor. In such films clusters can come into direct contact and interact via exchange. Films containing Fe cluster volume fraction from < 1 % (isolated clusters) to 100% (pure clusters with no matrix) have been studied at temperatures ranging from 2 to 300 K by magnetometry and field-cooled (FC)/zero-field-cooled (ZFC) measurements. 

Kliiner et al. [19] has analyzed the bimodal velocity distributions observed in NO desorption from NiO(0 01) shown in Fig. 24 by calculating a full ab initio potential energy surface (PES) for an excited state in addition to the PES for the ground state. Calculation of the electronically excited state uses a NiOj cluster embedded in a semi-infinite Madelung potential of point charges 2. The excited state relevant for laser-induced desorption is an NO -like intermediate, where one electron is transferred from the cluster to the NO molecule. 

A particular scheme of introducing the pseudo-atom A depends both on the type of a quantum-chemical method and on a specified set of experimental properties whose reproduction is assumed to be the most important in the forthcoming investigations. This set of properties can also include, instead of experimental values, the values obtained by a more rigorous theoretical method (extended cluster, embedded or periodic cluster, band approach). In the scope of ZDO-type methods, the following parameters of pseudo-atom A can in principle be adjusted (77). 

A crucial feature of the metal/oxide interface is that it combines the extended nature of the support with the limited size of the supported metal particles - a feature that is common to the study of defects in solids. Such systems pose special problems for realistic modelling. The requirements of defining computationally tractable, as well as accurate models are of particular importance. Three different approaches are common, namely bare clusters, embedded clusters and periodic slab models. All three are associated with approximations, and the best choice must be defined by the correct compromise between cost and accuracy. 

Three clusters were chosen (I) MggOg embedded in the field of the first cationic coordination sphere (each anion of the cluster has coordination number 6) (II) MggOg embedded in the whole first coordination sphere of the cluster plus the second cationic sphere (III) is obtained from (II) by deleting all the pseudoatoms attached above the upper plane of the MggOg cluster. Embedded clusters (I) and (II) could be considered as models of the MgO bulk, whereas (Ill)as modeling the MgO surface. The number of embedding centers is 21, 58, and 41 in (I), (II), and (III), respectively. 

Table 6. Mulliken charges on anions (Qo)y the gap, and the maximal splitting of the core O Is levels (Aeoi ). calculated for the MggOg cluster embedded in three different surroundings (clusters I, II and III, see text above)...

In order to calculate the binding energy and bulk modulus of the MgO crystal, we have used the smallest cluster, namely, the diatomic MgO unit, embedded into two coordination spheres, whose nodes have effective potentials described by Eq. 20. Table 7 compares our results with the experimental data and the results of other calculations. One could see that even the smallest cluster embedded in the pseudopotential environment allows a decent reproduction of the bulk properties. Let us note that we have used also the smallest basis consisting of the numerical HFS orbitals of the 0 and Mg ions. 

Numerical integration schemes allow an opportunity to test the numerical nonempirical pseudopotentials without their fit by analytical functions, which can lead to a considerable reduction in computational efforts. Employment of atomic pseudopotentials only at some selected atoms of a system while treating the rest all-electronically makes an impression of the consistency and reliability of such a combined approach. The results obtained for the MgO clusters embedded in some effective pseudopotential surroundings demonstrate a promise of the approach for compensation of broken bond effects. Specifically, the approach offers a tool for a substantial reduction of the artificially introduced nonequivalence of partial densities and the effective charges for atoms equivalent in the lattice. It is worth to mention that our approach can be modified further in many ways because numerical integration schemes can be easily applied/adapted even in those cases where the analytical methods become too complicated. 

Fig 10. Theoretical XPS valence band spectrum of a P4O12 cluster fAJ and that of a PO.f cluster embedded into a P40i. cluster (B) calculated by using the DV-Xa cluster MO method, in comparison with the experimental valence band spectrum (Cj of the (NaPOs) (n>3) sample (Ref 28). 

A DV-Xa calculation for a S04 cluster of Td symmetry B DV-Xa calculation for a Li8S04 cluster embedded into the potential field of neighboring ions C all electron "ab initio" calculation using split valence (6-3IG ) GTOs as basis. Note that the experimental values presented here arc referenced to the Fermi level, so the work fimction of the sample material (ca 3-4 eV) should be subtracted for the correct comparison with the theoretical data being referenced to the vacuum level. 

Gaudry M., Lerme J., Cottancin E., Pellarin M., Vialle J.L., Broyer M., Prevel B., Treilleux M. and Melinon P., (2001) Optical properties of (AuxAgl-x)(n) clusters embedded in alumina Evolution with size and stoichiometry Phy, Rev. B 64 085407. 

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