Structural transitions topological

The development of metallaborane chemistry in recent years has led to the discovery of some metallaborane structures containing the so-called isocloso deltahedra, which have a transition metal atom (e.g., Ru, Rh, Ir) located at a degree 6 vertex. Such isocloso metalla-borane dehahedra, except for the 11-vertex structures, are topologically different from the closo borane deltahedra foimd in the simple boranes and the... 

Up to this point, we have emphasized the stereochemical properties of molecules as objects, without concern for processes which affect the molecular shape. The term dynamic stereochemistry applies to die topology of processes which effect a structural change. The cases that are most important in organic chemistry are chemical reactions, conformational changes, and noncovalent complex formation. In order to understand the stereochemical aspects of a dynamic process, it is essential not only that the stereochemical relationship between starting and product states be established, but also that the spatial features of proposed intermediates and transition states must account for the observed stereochemical transformations. 

The second difference is related to the structure of the lamellar phase. The Euler characteristic has been assumed zero in the whole lamellar phase by Gompper and Kraus [47], whereas we show that it fluctuates strongly in the lamellar phase between the transition line and the topological disorder fine. The notion of the topological disorder line has not appeared in their paper. We think that the topological disorder line is much closer to the transition... 

For diffuse and delocahzed interfaces one can still define a mathematical surface which in some way describes the film, for example by 0(r) = 0. A problem arises if one wants to compare the structure of microemulsion and of ordered phases within one formalism. The problem is caused by the topological fluctuations. As was shown, the Euler characteristic averaged over the surfaces, (x(0(r) = 0)), is different from the Euler characteristics of the average surface, x((0(r)) = 0), in the ordered phases. This difference is large in the lamellar phase, especially close to the transition to the microemulsion. x((0(r)) =0) is a natural quantity for the description of the structure of the ordered phases. For microemulsion, however, (0(r)) = 0 everywhere, and the only meaningful quantity is (x(0(r) = 0))-... 

What does the set of possible state transition graph topologies for families of structurally similar graphs look like ... 

As suggested at the beginning of tiiis subsection, we can by reversing the above reasoning process - partially infer the topological structure of the global state transition graph, Qc-... 

In the case of n-butene isomerization it was demonstrated (Figure 2) that the ideal micro-pore topology led to retardation of the C8 dimer intermediate and that the catalyst based on the ferrierite structure was close to optimal in this respect [1). For selective isodewaxing a one-dimensional pore structure which constrained the skeletal isomerization transition state and thereby minimized multiple branching such as the SAPO-11 structure was found to meet these criteria. Clearly, these are ideal systems in which to apply computational chemistry where the reactant and product molecules are relatively simple and the micro-porous structures are ordered and known in detail. 

Investigations of cyanides and cyano complexes of Cd and Hg have augmented tremendously since about 1990, after detection of inclusion compounds of Cd(CN)2. A thorough review on transition-metal cyanides especially emphasizes the chemistry of inclusion compounds of both the Hofmann type (frameworks dominated by planar Ni(CN)4 building blocks) and the cyanocad-mate type (frameworks with tetrahedral Cd(CN)4 units).87 The structures of these inclusion compounds, but also of cyanides themselves, often topologically resemble the structures of minerals this aspect ( mineralomimetic chemistry ) is dealt with in a simultaneous survey.88 A more generic review of framework structures, with a section on cyanide inclusion compounds, is also to be mentioned.90... 

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