Clusters linear chains

Single-determinant HF calculations by Ewing and Pfeiffer on C (n = 2 to 6) [227]. MNDO calculations by Bemholc and Phillips for neutral and charged chains and monocyclic rings up to = 25 [228]. For neutral clusters, linear chains were found to be the preferred structures up to n = 9 (as compared with cyclic isomers), with the odd-... 

Dimers and clusters, linear chain and planar magnetic systems... 

In this way we come to class III complexes, i.e. complexes in which the two sites are indistinguishable and the element has a non-integral oxidation state (delocalized valence). Usually one divides this class in two subclasses. In class IIIA the delocalization of the valence electrons takes place within a cluster of equivalent metal ions only. An example is the [NbgCli2] ion in which there are six equivalent metal ions with oxidation state + 2.33. In class IIIB the delocalization is over the whole lattice. Examples are the linear chain compound K2Pt(CN)4.Bro.3o. 3H2O with a final oxidation state for platinum of 2.30, and three-dimensional bronzes like Na WOg. 

Fig. 51. Scanning electron microscope image of different stages of metalization of DNA. (a) Linear chain of separated palladium clusters connecting two gold contacts (b) magnification of (a) showing clusters with diameter > 40 nm (c) continuous coated DNA strand after one development step with a diameter larger than 40 nm. Reproduced with permission from Ref. (175). Copyright 2001, American Institute of Physics.

Although the structure of MAO was analyzed by different methods, such as IR and NMR spectroscopy, mass spectroscopy and lots more, the exact composition and structure of MAO are still not entirely clear or well-understood [27, 28], It is assumed that the structures of MAO include one-dimensional linear chains, cyclic rings that contain triscoordinated A1 centers, and three-dimensional clusters with tetracoordinated aluminum [24] (Fig. 8). 

Fig. 1 Schematic drawing to show the concept of system dimensionality (a) bulk semiconductors, 3D (b) thin film, layer structure, quantum well, 2D (c) linear chain structure, quantum wire, ID (d) cluster, colloid, nanocrystal, quantum dot, OD. In the bottom, it is shown the corresponding density of states [A( )] versus energy (E) diagram (for ideal cases).

In general, incorporation of hydrophobic groups into PIPAAm chains decreases the LCST [29-31]. Hydrophobic groups alter the hydrophilic/ hydrophobic balance in PIPAAm, promoting a PIPAAm phase transition at the LCST, water clusters around the hydrophobic segments are excluded from the hydrophobicaUy aggregated inner core. The resulting isolated hydrophobic micellar core does not directly interfere with outer shell PIPAAm chain dynamics in aqueous media. The PIPAAm chains of the micellar outer shell therefore remain as mobile linear chains in this core-shell micellar structure. As a result, the thermoresponsive properties of PIPAAm in the outer PIPAAm chains of this structure are unaltered [23-27,32]. 

A brief historical note on the structure of the iron-sulfur clusters in ferredoxins is relevant. After the first analytical results revealed the presence of (nearly) equimolar iron and acid-labile sulfur, it was clear that the metal center in ferredoxins did not resemble any previously characterized cofactor type. The early proposals for the Fe S center structure were based on a linear chain of iron atoms coordinated by bridging cysteines and inorganic sulfur (Blomstrom et al., 1964 Rabino-witz, 1971). While the later crystallographic analyses of HiPIP, PaFd, and model compounds (Herskovitz et al., 1972) demonstrated the cubane-type structure of the 4Fe 4S cluster, the original proposals have turned out to be somewhat prophetic. Linear chains of sulfide-linked irons are observed in 2Fe 2S ferredoxins and in the high-pH form of aconitase. Cysteines linked to several metal atoms are present in metallothionein. The chemistry of iron-sulfur clusters is rich and varied, and undoubtedly many other surprises await in the future. 

Let us now consider the relative stability of the two four-atom clusters with symmetric eigenspectra, namely the linear chain and the square. Since ju3 = 0, they have identical first four moments p0, p2, and p3 for ah = ,... 

Figure 4.8 shows that the individual bonds in four-atom s-valent clusters are unsaturated, taking bond orders that are much less than unity. The two end bonds of the linear chain provide the only exception. This reduction in bond order compared to the isolated dimer is, of course, due to a given spherically symmetric s orbital forming bonds with all its neighbours. However, we will see later in Chapter 7 that the angular character of hybrid orbitals allows some sp-valent solids to exhibit saturated bond behaviour. Thus, the concept of the bond order is important because it not only... 

Another aspect that is interesting to note concerns the dependence of the DFT gap on the orientation of the wire, indeed, for each wire size the following relation holds g[100] > g[lll] > Eg [110]. As has been pointed out in Ref. [121], this is related to the different geometrical structure of the wires in the [100], [111] and [110] directions. Indeed the [100], [111] wires appear as a collection of small clusters connected along the axis, while the [110] wires resemble a linear chain. So we expect that quantum confinement effects are much bigger in the [100], [111] wires, due to their quasi zero-dimensionality, with respect to the [110] wires. Further, the orientation anisotropy reduces with the wire width and it is expected to disappear for very large wires, where the band gap approaches that of the bulk material. 

Thus, in the next examples, we comment on supramolecular entities, including linear chains, two-dimensional sheets, and even three-dimensional networks. From them, perhaps the most common structural arrangement is that in which the metals form extended linear systems, usually built from mononuclear units, dinuclear, using polydentate donor ligands and polymetallic units. It is worth mentioning that in this part and also in the following we consider only structures built by gold-heterometal interactions, not bonds thus formal clusters will not be considered. 

The concept of amylopectin forming double helices easily integrates into the currently-accepted cluster model, with the short linear chains of the branches being intertwined into double helices, while the branch points are located in the more amorphous regions between the clusters of double helices. Understanding that parts of amylopectin molecules are capable of forming double helices explains the apparent anomaly that a branched polymer is the source of structural order within granules. 

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