Nine Atoms

In the next step, the molecule is fragmented into ring systems and acyclic parts. Ring systems are then separated into small and medium-sized rings with up to nine atoms and into large and flexible systems. 

This simple model allows one to estimate spin densities at eaeh earbon eenter and provides insight into whieh eenters should be most amenable to eleetrophilie or nueleophilie attaek. For example, radieal attaek at the C5 earbon of the nine-atom system deseribed earlier would be more faeile for the ground state F than for either F or F. In the former, the unpaired spin density resides in /5, whieh has non-zero amplitude at the C5 site x=L/2 in F and F, the unpaired density is in /4 and /6, respeetively, both of whieh have zero density at C5. These densities refleet the values (2/L)F2 sin(n7ikRcc/L) of the amplitudes for this ease in whieh L = 8 x Rcc for n = 5, 4, and 6, respeetively. 

Applications of the theory described in Section III.A.2 to malonaldehyde with use of the high level ab initio quantum chemical methods are reported below [94,95]. The first necessary step is to define 21 internal coordinates of this nine-atom molecule. The nine atoms are numerated as shown in Fig. 12 and the Cartesian coordinates x, in the body-fixed frame of reference (BF) i where n= 1,2,... 9 numerates the atoms are introduced. This BF frame is defined by the two conditions. First, the origin is put at the center of mass of the molecule. 

HPPN unit, which is produced after three deacetylation steps, is the main repeating unit in the PH A synthesized from 11-phenoxyundecanoic acid again shows that P. oleovorans prefers repeating units containing eight or nine atoms. 

In our third example (52), dissociative chemisorption of Li2, B2, C2, 02, N2, F2, CO, NO and ethylene on (100)W and Ni surfaces was examined. The metal surfaces are represented by means of nine-atom clusters, arranged as in Fig. 35. Experimental geometry was used for the adsorbates. The standard EHT method was used, i.e. with charge-independent atomic ionization potentials. Charge transfer between adsorbate and surface was explored... 

Figure 8.5 Electronic DOS of bulk quartz from DFT calculations with nine atom supercell that sampled k space with 9x9x9 k points. Energy is defined so the top of the valence band is at 0 eV.

In the past decades, homoatomic polyanions in solid state compounds of group 14 elements have been a powerful starting material toward different kinds of chemical transformations. Recent developments, especially for nine-atom clusters, have been discussed elsewhere [5,125,126] and are not within the scope of this review. Here, we concentrate on neat solvates , which means that in addition to cation and anion... 

Here, only nine-atom cages without sequestering agents like crown ethers or cryptands are listed for an exhaustive overview on Eg compounds, see [5, 125, 126]... 

Fig. 13 Homoatomic polyanions of group 14 elements, which are present in solvate structures (a) tetrahedral (E = Sn, Pb) (b) nine-atom cages Eg" (n = 2-4 E = Si-Pb) (c) trigonal bipyramidal Es (E = Si-Pb)...

Having a closer look at the reported solvate structures of homoatomic polyanions of group 14 elements, it becomes evident that only clusters and no rings or chains are stable in solid state as well as in solution (Fig. 13). Higher reduced polyanions with > 5, equivalent with a charge higher than —1 per atom, are not reported in solution so far. The nine-atom species is quite well established in solutions of ammonia and ethylenediamine. Their interesting reactivity is intensely studied and is discussed elsewhere [5, 125, 126]. The less-understood cluster... 

The tetrahedral Sn2Bi2 ion has been stmcturally characterized by Corbett [72] and studied in solution by Rudolph [23]. The Sn NMR resonance at — 1,574 ppm shows coupling to one other Sn atom with a large, one-bond J( Sn- Sn) = 1,638 Hz. Recent gas phase and theoretical studies on Bi-substituted nine-atom cluster anions suggest that the isoelectronic Sng" analog, SngBis , should be static in solution [31]. 

Scharfe S, Eassler TP (2010) Polyhedral nine-atom clusters of tetrel elements and intermetalloid derivatives. Phil Trans Royal Soc A Math Phys Eng Sci 368 1265-1284... 

Ugrinov A, Sevov SC (2003) [Geg=Geg=Geg=Geg] a linear tetramer of nine-atom germanium clusters, a nanorod. Inorg Chem 42 5789... 

Gupta U, Reber AC, Claybome PA et al (2008) Effect of charge and composition on the structural fluxionality and stability of nine atom tin-bismuth Zintl analogues. Inorg Chem 47 10953-10958... 

Hull MW, Sevov SC (2009) Functionalization of nine-atom deltahedral zintl ions with organic substituents detailed studies of the reactions. J Am Chem Soc 131 9026-9037... 

Further oxidation of the nine-atom clusters to formal [Ge9] leads to linear polymers oi[-Ge9-] with two covalent intercluster bonds (Fig. 2i). Trimers [Ge9=Ge9=Ge9] (Fig. 6a) and tetramers [Ge9=Ge9=Ge9=Ge9] (Fig. 6b) occur via nonclassical bond formation between two neighboring atoms of the triangular prism basis planes of the c/oio-shaped clusters, which results in Ge-Ge-Ge bond angles of 90° and in considerably longer Ge-Ge contacts between the cluster units. Quantum-chemical calculations have shown that the exo-bonds participate in a delocalized electronic system that comprises the whole anion [204]. 

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