Cluster models relaxation

Figure 2 Structural models for the (a) S11H4, (b) Si5H12, (c) SiioHi6, (d) S129H36 and (e) S135H36 clusters at relaxed geometry in the ground- (left panels) and excited-state (right panels) configuration.

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. 

Table 12-3. Comparison of calculated structural parameters for the kaolinite(O)—H2O system obtained from geometry optimizations of a cluster model (ONIOM(B3LYP/SVP PM3 method) and the periodic DFT(PW91) approach) (static relaxation and MD simulation) [73], Bond lengths and interatomic distances are in A, angles are in degrees. Superscript w stands for water, subscripts distinguish O and H atoms of three different surface OH groups...

Structural parameter Cluster model Static relaxation MD... 

Figure 8.11. Cluster models for surface relaxation of Ca(OH>2 due to removal of one OH group (A) No vacancy (without surface relaxation), (B) One OH vacancy (without surface relaxation), (C) One OH vacancy (with surface relaxation).

Fig. 6.32. Calculated energy levels for an MoS/ cluster as a model for MoSj obtained using the MS-SCF-Ya method. Alongside (a) the x-ray photoelectron spectrum of MoSj are shown (b) the results of a non-self-consistent calculation on a MoSf, cluster, (c) a self-consistent calculation for a MoS/ cluster, and (d) a self-consistent calculation for a MoS/ cluster including relaxation effects for the five highest energy orbitals (after de Groot and Hass, 1975 reproduced with the publisher s permission).

The question of cluster structure arises from the preceding observations. In order to study this problem, an apparatus was built in Orsay. Thanks to it and to the construction of cluster models, the structure of Ar clusters containing from a few atoms to several thousand atoms is now completely elucidated. A description of the experiment is given in Section II. The construction of noncrystalline models is presented in Section III, and their relaxation, together with structural transitions, is studied in Section IV. Section V discusses other intermediate models and gives a brief comparison with metallic clusters. Finally, Section VI deals with the structure of clusters made of several polyatomic molecules. 

A similar situation arises in recently reported DFT calculations by Byskov et al. [70, 71] that show that if vacancies are introduced in a large cluster model of a MoSj surface by removing sulfur atoms, and relaxation is allowed taking into account several layers of the solid, a spontaneous surface reconstmction process takes place through migration of sulfide ions from the bulk to the surface, so as to fill the empty sites. Thus, although the distinction may be rather subtle, the idea of latent or potential vacancies in a resting state rather than actual physically empty sites around electron rich areas of space seems like an adequate and useful evolution ofthe classical concept of anionic vacancies in HDS catalysts. 

Notably stronger structural relaxation should accompany the formation of sites on the MgO(OOl) surface that are characterized by a reduced coordination number of ions, such as point (vacancy) or extended (step, edge, comer, etc.) defects [87]. This new situation is adequately reproduced by DF cluster models. For instance, for the edge formed by the intersection of (001) and (100) surfaces of MgO, a notable inward (into the substrate) displacement of Mg and O ions from the bulk-terminated position was computed in the [101] direction, by 15 and 12 pm, respectively [95]. Comer three-coordinated Mgsc cations are predicted to move even further, 32 pm, along the [111] direction, "down" to the three O anion neighbors [60], Opposite displacements of the Mg and O ions, to partly restore the bulk-terminated geometry, take place when an adsorbate effectively repairs the reduction of coordination numbers at these defects on clean MgO surface, e.g. Refs. 60 and 95. 

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