Topology of Reaction

Nevertheless, sometimes it is possible to point the reaction rate constant that is limiting for the relaxation in the following sense. For known topology of reaction network and given ordering of reaction rate constants we find such a constant (ergodicity boundary) that... 

Figure 7 Phase relationships in the system MgO-Si02-H20 for bulk composition bci (Figure 6 60% olivine, 40% orthopyroxene, with 40% serpentization of the olivine), showing the stable mineral assemblages as a function of pressure and temperature. Stability fields and topology of reaction boundaries after Ulmer and Trommsdorff (1999).

Figure 5 Zefirov topologies of reactions on three to six atoms...

HORACE used alternating phases of classification (which topological or physicochemical features are required for a reaction type) and generalization (which features are allowed and can be eliminated) to produce a hierarchical classification of a set of reaction instances. 

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 selection rules for cycloaddition reactions can also be derived from consideration of the aromaticity of the transition state. The transition states for [2tc -f 2tc] and [4tc -1- 2tc] cycloadditions are depicted in Fig. 11.11. For the [4tc-1-2tc] suprafacial-suprafacial cycloaddition, the transition state is aromatic. For [2tc -F 2tc] cycloaddition, the suprafacial-suprafacial mode is antiaromatic, but the suprafacial-antarafacial mode is aromatic. In order to specify the topology of cycloaddition reactions, subscripts are added to the numerical classification. Thus, a Diels-Alder reaction is a [4tc -f 2 ] cycloaddition. The... 

As mentioned in the Introduction, it is necessary but not sufficient for isotopically discriminating reactions to occur if isofractionation is to be observed in any particular body component. Whether the isofractionation incurred in a particular reaction in the pathway leads to a measurable effect in a body pool component depends on the pattern or topology of the metabolic fluxes. Three basic cases are considered here for illustrative purposes. 

Abstract In general, asymmetric catalysts are based on the combination of a chiral organic ligand and a metal ion. Here we show that future research should also focus on complexes in which the chirality resides only at the metal center, as the result of a given topology of coordination of achiral ligands to the metal ion. Here we make a brief presentation of the methods available for preparing such compounds as well as the very few examples of enantioselective reactions catalyzed by chiral-at-metal complexes. 

The branched polymers produced by the Ni(II) and Pd(II) a-diimine catalysts shown in Fig. 3 set them apart from the common early transition metal systems. The Pd catalysts, for example, are able to afford hyperbranched polymer from a feedstock of pure ethylene, a monomer which, on its own, offers no predisposition toward branch formation. Polymer branches result from metal migration along the chain due to the facile nature of late metals to perform [3-hydride elimination and reinsertion reactions. This process is similar to the early mechanism proposed by Fink briefly mentioned above [18], and is discussed in more detail below. The chain walking mechanism obviously has dramatic effects on the microstructure, or topology, of the polymer. Since P-hydride elimination is less favored in the Ni(II) catalysts compared to the Pd(II) catalysts, the former system affords polymer with a low to moderate density of short-chain branches, mostly methyl groups. 

Closely related to the approach considered here are the formal frameworks of Feinberg and Clarke, briefly mentioned in Section II. A. Though mainly devised for conventional chemical kinetics, both, Chemical Reaction Network Theory (CRNT), developed by M. Feinberg and co-workers [79,80], as well as Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83], seek to relate aspects of reaction network topology to the possibility of various... 

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