Cluster models structural transitions

The underlying motivation of the work presented in this paper is to provide a theoretical understanding of basic physical and chemical properties and processes of relevance in photoelectrochemical devices based on nanostructured transition metal oxides. In this context, fundamental problems concerning the binding of adsorbed molecules to complex surfaces, electron transfer between adsorbate and solid, effects of intercalated ions and defects on electronic and geometric structure, etc., must be addressed, as well as methodological aspects, such as efficiency and reliability of different computational schemes, cluster models versus periodic ones, etc.. 

The combination of the cluster model approach and modem powerful quantum chemistry techniques can provide useful information about the electronic structure of local phenomena in metal oxides. The theoretical description of the electronic states involved in local optical transitions and magnetic phenomena, for example, in these oxides needs very accurate computational schemes, because of the generally very large differential electron correlation effects. Recently, two very promising methods have become available, that allow to study optical and magnetic phenomena with a high degree of precision. The first one, the Differ-... 

H, Me, r-Bu, or Ph or R = H and R = Me, r-Bu, or Ph), was performed. Two possible reactions were investigated (a) the reactions suitable for the gas-phase interactions, which start from a 1 1 Br2-alkyne r-complex and do not enter into a 2 1 Br2-alkyne jt-complex and (b) the processes passing through a 2 1 Br2-alkyne 7r-complex, which appear more realistic for the reactions in solutions. The structures of the reactants and (g) the final products and also the possible stable intermediates have been optimized and the transition states for the predicted process have been found. Both trans- and cw-dibromoalkenes may ensue without the formation of ionic intermediates from a n-complex of two bromine molecules with the alkyne (solution reactions). The geometry around the double bond formed in dibromoalkenes strongly depends on the nature of the substituents at the triple bond. The cluster model was used for the prediction of the solvent influence on the value of the activation barrier for the bromination of the but-2-yne.35... 

We emphasize two natural limitations of the finite cluster model. It does not allow to make a statement about the dependence of essential parameters such as adsorption and transition energies on the level of surface coverage, and it does not account adequately for charge delocalization or surface relaxation phenomena. Further, it excludes by definition any information about the modification of the surface band structure as a consequence of the organic molecule adsorption. The following case study of 1-propanol on Si(001) - (2 x 1) is intended to clarify how these elements can be consistently incorporated into the description of the Si surface interaction with organic species. 

It therefore seems quite natural to choose silica, silica aluminas, and aluminium oxide as the objects of the first systematical quantum-chemical calculations. These compounds do not contain transition elements. They are built of the individual structural fragments primary, secondary, etc. This enables one to find the most suitable cluster models for quantum-chemical computations. The covalent nature of these structures again makes quite efficient a comparatively simple method of taking into account the boundary conditions in the cluster calculations. Finally, these systems demonstrate clearly defined Bronsted and Lewis acidity. This range of questions comprises the subject of the present review. This does not by any means imply that there are no quantum-chemical computations on the cluster models of the surface active sites of transition element oxides. It would be more proper to say that the few works of this type represent rather preliminary attempts, being far from systematic studies. Also, many of them unfortunately include some disputable points both in the statement of the problem and in the procedure of calculations. In our opinion, the situation is such that it is still unreasonable to try to summarize the results obtained, and therefore this matter is not reviewed in the present article. 

For carbon, it is of course also tempting to study clusters of clusters, namely aggregation of C60 fullerenes [67-69]. This is not really a molecular cluster application since the inner structure of the fullerene, leading to dependence of the particle interaction on relative particle orientation, is largely or completely ignored. The Pacheco-Ramalho empirical potential is used frequently, and fairly large clusters up to n=80 are studied. There appears to be agreement that small fullerene clusters are icosahedral in this model. In contrast to LJ clusters, however, the transition to decahedral clusters appears to occur as early as at n=17 the three-body term of the potential is found to be responsible for this [67]. 

High-quality ab initio calculations of various cluster models, were in favor of the view that water is only physisorbed on the zeolite and found that the proton-transferred hydronium ion structure is a transition state between two minima corresponding to the water H-bonded to the acid site (cf. Fig. 5). 

Additional information on electronic structure may be obtained from the x-ray emission spectra of the SiOj polymorphs. As explained in Chapter 2, x-ray emission spectra obey rather strict selection rules, and their intensities can therefore give information on the symmetry (atomic or molecular) of the valence states involved in the transition. In order to draw a correspondence between the various x-ray emission spectra and the photoelectron spectrum, the binding energies of core orbitals must be measured. In Fig. 4.12 (Fischer et al., 1977), the x-ray photoelectron and x-ray emission spectra of a-quartz are aligned on a common energy scale. All three x-ray emission spectra may be readily interpreted within the SiO/ cluster model. Indeed, the Si x-ray emission spectra of silicates are all similar to those of SiOj, no matter what their degree of polymerization. Some differences in detail exist between the spectra of a-quartz and other well-studied silicates, such as olivine, and such differences will be discussed later. 

Next we study the effects of the cluster size on DOS. When the cluster size is increased, the interactions between neighboring atoms with long distances are taken into account, then the electronic state approaches that of btilk. Figure 12 compares DOS of the clusters Nig, Nij3, Nijj and Ni j, as well as bulk crystaP by a band structure calculation. Usually the band structure of the bulk crystal can be rather well reproduced if we take several ten atoms in the model cluster for transition elements, though the small cluster model provides somewhat narrower d band. In the case of the element with a d band which is almost completely occupied, for example the case of silver, the size effect is not very large, but a small cluster already well represents the band structure of bulk as shown in Fig. 13. 

Another example is the extensive study by Haase and Sauer, whose calculations were carried out for a methanol molecule with a number of cluster models, the most sophisticated of which was sufficiently large to represent a portion of the faujasite lattice formed by three 4-R rings and one 6-R. All structures were fully optimized at the SCF and/or MP2 level. The authors found that, for all cases studied, the IP complex was a transition state, whereas the HB complex corresponded to a minimum on the PES of the system. However, the adsorption energies for both structures were very close to one other, with a barrier for proton transfer of only a few kilojoules per mole. A strong H-bond between the Bronsted proton and the O atoms of methanol, and a long and weak H-bond between the H atom of the molecule and the O atom of the zeolite... 

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