Cluster models crystallographic symmetry

Fig. 3.21 R4O cluster bonding (reprinted with permission from [137, 140]) and the reconstruction models for the O-Rh(lll) [118, 133] and the 0-Ru(0001) surfaces of C3V symmetry [119, 120]. a At o < 1/4 ML coverage, 0 locates in the center of one of the four tetrahedral sites to form one bond with the atom labeled 1. The 0 induees and pushes the dipoles labeled 2 radially away and the C3V symmetry remains, producing the clusters of STM jrotrusion. b At o S 1/2 ML, O evolves into by forming another bond with a surface R atom labeled 1. The lone pairs sustain the dipoles (labeled 2). The dipole and ionic row move closer toward the sites without adsorbates, which generates the pairing-STM protrasion-depression patterns, c At o <1-0 ML, H-Uke bonds dominate at the surface. Two lone pairs polarize each surface R atom (1/2) which donates meanwhile one electron to other adsorbate. Formation of the H-like bonds restores the reduced work function and lowers the STM protrusions. The entire surface network is stabilized and becomes unreconstructed and restores the 3 crystallographic symmetry (reprinted with permission from [1])...

Structural models of zeolite with faujasite topology (A) crystallographic unit cell with the Fd3 m symmetry containing 576 atoms (192 T atoms) (B) a smaller rhombohedral lower-symmetry unit cell with 144 atoms (48 T) (C) a cluster model containing sixT-atoms (D) representing a local structure of a single cation site and a respective hybrid 12 T cluster embedded in the rhombohedral faujasite unit cell (E) (adapted from Ref. [28]). 

Both show a greater number of vibrational modes than predicted for pure Tj symmetry, but show good correspondence with the expected distribution for a distorted D2d cube (24,43). This finding Is In agreement with the x-ray crystallographic results which Indicate that the 4Fe-4S clusters In these two proteins, as well as In a number of model compounds, have a compressed tetragonal structure with 4 short and 8 long Fe-S bonds (41,45). 

The recent electron spectrometer provides highly resolved spectrum for valence state XPS, which supplies us with very useful information for discussion on chemical bonding, when combined with an appropriate theoretical analysis as mentioned above. Therefore, an accurate calculation of electronic state is required for such a purpose. The DOS calculated by DV-Xa method has been demonstrated to reproduce well the valence state XPS for some oxyanions compared with other theoretical calculations. The calculation was made using a simple model cluster XO4 " with T symmetry, thus the theoretical analysis was insufficient for the valence structure in details. This has significantly been improved by a careful analysis with more realistic model clusters which are determined from crystallographic data for those oxyanions. The comparison of the theoretical and experimental spectra for PO4 ions is shown in Fig.8. The agreement is very good even for the fine structure in the valence band. 

In the earlier crystallographic work carried out with the trimer crystals of the Synechococcus sp. reaction center at 6 Aresolution , 21 tubular structures could be identified in the electron-density map and were attributed to transmembrane a-helices in the PS-I reaction-center monomer. In more recent work at 4.5 A resolution and later at 4 A resolution, however, 29 and 31 transmembrane a-helices could be observed in the respective electron-density maps. In the model shown in Fig. 6 (A), based on the 4.5 A study the 29 a-helices are depicted as rods of different shades. The three iron-sulfur clusters, FeS-X and FeS-A/B, are shown immediately above the shaded rods. Another perspective may be obtained by viewing the structure in (A) from the stroma side of the membrane, as shown in Fig. 6 (B). Here the rods representing the helices belonging to PsaA and PsaB are shown confined inside the dashed areas. The symmetry axis is shown by a dot at the PsaA/PsaB interface. 

Quasicrystals or quasiperiodic crystals are metallic alloys which yield sharp diffraction patterns that display 5-, 8-, 10- or 12-fold symmetry rotational axes - forbidden by the rules of classical crystallography. The first quasicrystals discovered, and most of those that have been investigated, have icosahedral symmetry. Two main models of quasicrystals have been suggested. In the first, a quasicrystal can be regarded as made up of icosahedral clusters of metal atoms, all oriented in the same way, and separated by variable amounts of disordered material. Alternatively, quasicrystals can be considered to be three-dimensional analogues of Penrose tilings. In either case, the material does not possess a crystallographic unit cell in the conventional sense. 

In the molecular-cluster approach a crystal with a surface is modeled by a finite system consisting of the atoms on the surface and of some atomic planes nearest to it. The diperiodicity of the surface is not taken into account. The symmetry of such a model is described by one of the crystallographic point groups. 

Nineteen-atom [MXgMi2] clusters (M=Ti, V X = C, N Fig. 6.2) were used as the models of initial matrices in the MWH calculations carried out. All possible arrangements of H atoms in various high-symmetry nonequivalent crystallographic sites of the crystals were studied. In the case of an ideal binary phase, these are tetrahedral interstitial sites, which can be described by [MXeMi2 -I- H] clusters. H-H interactions may be taken into account, when considering [MXgMi2 + H2] clusters. Typical results for the TiN-H system are presented in Fig. 6.3. 

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