Continuous chemical topology

Continuous Chemical Topology Chemical Bonding and Functional Analysis... 

The broad landscape of chemical topology and topoisomerism has been summarized in comprehensive reviews [2-5], The accomplishments of Schill, Walba, Sauvage, Stoddart, and others are landmarks in organic synthesis. This chapter describes a personal odyssey in which the focus is on statistical approaches - tinged by polymer science in their continual reference to the flexibility of chains. Some early laboratory efforts, and the technical considerations which led to them, are discussed, as is more recent activity. 

It is beyond the scope of this chapter to discuss the range of structure-based methods that chemists can use for molecular afignment. This field of research has been, and continues to be, very active. One algorithm, called TGSA, will be presented here in some detail, however, because of its popularity in molecular quantum similarity studies. Structure-based techniques differ from the aforementioned techniques in several respects. First, they not attempt to maximize the MQSM for a pair of molecules. Second, they do not make a specific reference to molecular quantum similarity as such, they are aimed at a wider range of applications. Third, they are not based on electron density in a formal way, but instead they take a more familiar approach based on chemical topology. Consequently, they apply well-known concepts such as chemical bonds and try to overlap the most similar and largest common structure elements in both molecules. 

Interlocked rings (catenanes) continue to occupy a privileged position in chemical topology. They still exert a real fascination on synthetic chemists as witnessed by their recent development [22,42] de.spite the long standing interest of numerous laboratories in these compounds. [9,10]... 

A typical chemical plant flowsheet has a mixture of multiple units connected both in series and in parallel. As noted in the previous chapter, the common topology consists of reaction sections and separation sections. Streams of fresh reactants enter the plant by being fed into the reaction section (or sometimes into the separation section) through a heat exchanger network. Here the chemical transformations occur to produce the desired species in one or more of a potentially wide array of reactor types continuous stirred tank, tubular, packed bed, fluidized bed, sparged, slurry, trickle bed, etc. 

An elastically active network chain is active in the equilibrium elastic response of the network to deformation. From the topological point of view, an EANC is a chain between two active branch points. An active branch point is a imit from which at least three paths issue to infinity. In the case under consideration, only some of the chemically tetrafunctional diamine units can become active branch points. If the polyepoxide were more than bifunctional, it would also contribute to the number of EANC s. In analogy with Eq. (14), the pgf for the numbo- of bonds with infinite continuation issuing from a diamine unit T,(z) is given by... 

Domain 1 is at the N terminus, but spatially is the central of three domains. It is an antiparallel j3 barrel that is superficially reminiscent of the viral capsid fold, but actually has completely different topology (Fig. 7 see Color Insert). In the jelly roll, the /3 strands alternate between the two opposing sheets of the barrel. In E protein they zigzag up and down the same sheet, with the following exception. Strand B, which in chemical sequence falls between strands A and C of the outermost sheet, actually forms the end strand of the inner sheet. So, the strand order is ACDEF for the outer sheet, and BIHG for the inner. Strands F and G are hydrogen bonded, but there is no direct continuation of the sheets across the AB strand gap. 

These theories are based on the classical theories of rubber elasticity of macromolecular solids, wherein permanent chemical crosslinks connect segments of molecules, forcing them to move together. This central idea can be applied to polymeric liquids. However in this case, the interactions between molecules are assumed to be localized at junctions and are supposed to be temporary. Whatever their nature, physical or topological, these crosslinks are continually created and destroyed but, at any time, they ensure sufficient connectivity between the molecules to give rise to a certain level of cooperative motion. 

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