Topological factor

In the case of TGT structures which are acyclic or which contain isolated rings, the disconnection of non-ring bonds must be examined to identify those disconnections which may be most effective on topological grounds. However, for such acyclic disconnections the topological factors may be overshadowed by other structural considerations. For instance, if a powerful stereosimplifying disconnective transform, such as stereospecific organometallic addition to carbonyl... 

The same inertness holds for many inoperative cyclization paths that would have given highly quinoid systems such as 104 (cf 44 and 45), 105 (cf 86). 106(cf 87) and 107 c 88). Under certain circumstances such topological factors can not only modify the AO coefficients at the reacting atoms but can also result in an interchange of the usual topmost occupied MO and lowest unoccupied MO with other orbitals which prevent the photocyclization altogether. This situation has been deduced for the pentahelicenes series (Table In this series, (Table 20) benzo... 

The combination of the electronic and topological factors within this approach yields high correlations with thermodynamic properties of molecules. 

These coherent results simultaneously gained by kinetic, electrochemical, and photophysical studies strongly suggest that the kinetic and electronic properties of the knots and their unknotted analogs are not governed by the topological factors... 

We see that the Diagrams I and IV and Diagrams II and III respectively, give us the same contributions. The topological factor according to rule 7 is equal to Hence, the total expression becomes... 

Then, adding up these contributions and multiplying them with the topological factor i we arrive at the final expression... 

The functional and morphological heterogeneity of a lamellar system of chloroplasts indicates that pH values in different compartments (in granal and intergranal thylakoids) differ. This type of structure makes it difficult to measure local pH values at different sites. Therefore, mathematical models taking into account the spatial structure of chloroplasts provide a tool for studying the effect of diffusion restrictions on pH distributions over the thy lakoid on the rates of electron transport, proton transport, and ATP synthesis. The rate of ATP synthesis depends on the osmotic properties of a chloroplast-incubation medium and, therefore, on topological factors. 

These results strongly suggest that the electrochemical properties of the knots are not governed by the topological factors alone. They are obviously also very sensitive to structural parameters which become prevailing when switching from the aliphatic flexible spacers between two phenanthroline units to the more rigid 1,3-phenylene spacer in knot CuCu.l4 +. 

Narumi, H. and Hosoya, H. (1980). Topological Index and Thermodynamics Properties. II. Analysis of Topological Factors on the Absolute Entropy of Acyclic Saturated Hydrocarbons. Bull. Chem.Soc.Jap., 53,1228-1237. 

Waychunas, G. A., Davis, J. A., and Euller, C. C., 1995, Geometry of sorbed arsenate on ferrihydrite and crystalline EeOOH Re-evaluation ofEXAES results and topological factors in predicting sorbate geometry, and evidence for monodentate complexes Geochimica et Cosmochimica Acta, v. 59, p. 3655-3661. 

Under this general heading we wish to draw attention to the importance of geometrical and topological factors which have a direct bearing not only on the details of molecular and crystal structures but also on the stability and indeed existence of some compounds. In spite of their relevance to structural problems, some of the factors we shall mention seem to have been completely ignored. 

This is a natural generalization of the Woodward-Hoffmann (W-H) rules 155,158) A similar approach was also discussed by Salem 157>. The extraordinary success of the W-H rules shows that in some cases purely topological factors govern the course of chemical reactions 158>. An interesting approach was also developed by Dewar and advocated by him for twenty years 159>. He established the following set of rules, now known as the Dewar-Evans (D-E) rules 160> ... 

When considering reactions in the solid state, it is important to draw distinctions between reactions in crystals and reactions in amorphous solids, since the controlling factors are quite different in these two situations. Reactions in the crystalline state are controlled primarily by topological factors, such as the distances and the relative orientation of potentially reactive groups. Trans-cinnamic acid undergoes photochemical dimerization when the distance between adjacent double bonds in the crystal is shorter than 4 A (Table 2.5 ). Irradiation of 2,5-distyrylpyrazine (DSP) which has two double bonds per molecule leads to a linear high... 

This decisive topological factor largely accounts for the fact that, at equivalent degree of crosslinkings, the swelling abilities of the products of post-crosslinking linear polystyrene in solution or swollen styrene—DVB copolymer are much higher than that of conventional gel-type... 

A dozen measurements of Dg on concentrated polymer solutions have been carried out with well-characterized polymers in solvents of different quality, with the aim of checking the concentration dependence predicted by scaling arguments (eq 2.35 for 0 solvents and eq 2.37 for good solvents) as well as the molecular weight dependence. As can be seen from Tirrell s review [2], it was evident already in 1984 that the topological factor Fg as a function of c does not follow a simple power law, while its M dependence appears to be consistent with the reptation theory over a wide range of c. However, it was... 

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