Topological purely

The localized product-NBO view also makes clear the importance of the non-planarity of the TS in achieving favorable hyperconjugative stabilizations, because interactions of 7t-planar geometry. Indeed, one can see that favorable vicinal n-a or a-7r overlap should primarily involve one end (hybrid) of each NBO, oriented, if possible, in the anti conformation for maximum stabilization. This viewpoint allows one to recognize the importance of angular and orientational factors that would not be evident in a purely topological framework. 

The role of transition metals in the chemical synthesis of corrins is more than just adding a touch of inorganic elegance to organic synthesis- leave elegance to tailors and cobblers , a physicist once said — it is a vital role in the sense that perhaps no synthetic corrin would as yet exist without recourse to metal templates. Beside the purely topological function of arranging the proximity of reaction centres, metal ions have served this purpose as follows ... 

The entropy change upon elongation is a matter of conformations, so purely topological, and is not influenced by temperature. 

We have found recently the topological interpretation of property (34). The stoichiometric constraints (24) can be interpreted in terms of the topological object, the circuit. Existence of the circuit "explains" the appearance of the cyclic characteristic in the constant term of kinetic polynomial. Thus, we can say that in some sense the correspondence between the detailed mechanism and thermodynamics is governed by pure topology. 

To obtain the pure topological enantiomers, the chiral auxiliary was easily replaced by the hexafluorophosphate anion. 

By induction on dim(S). If dim(S) - 0 the theorem is trivially true. Let s assume dim(S) > 0. Since the assertion Is purely topological with respect to S and flatness is preserved under base change, we may assume that S is reduced, irreducible and normal (normalization is a closed mapping and the upper semi-continuity Is equivalent to the fact that the sets... 

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

The various types of reactivity indices can be classified in different ways, for example according to the quantum chemical method used for calculation e.g. purely topological methods (HMO, PMO, FEMO, VBSRT), SCF methods taking into account electron repulsion and other methods, or as related to the structure (energy) of reactant,... 

More recently, correlations of a values with purely topological reactivity indices, vie. structure count ratio and Dewar reactivity number have been extensively studied by v. Szentpaly and Herndon [33, 58], Rather satisfying correlations were obtained the correlation coefficients for obvious reasons (see Sect. 4) being nearly identical for both indices (0.959 and 0.960 respectively, sample size 27). A significant improvement was achieved with Dewar reactivity numbers calculated according to the free electron version of the PMO treatment (correlation coefficient r = 0.973). 

To cast some light on the relative importance of steric effects on the positional reactivities of benzenoid hydrocarbons, correlations of experimental a values of phenanthrene (4), tetrahelicene (5), pentahelicene (<5), and hexahelicene (7) with purely topological reactivity indices (Huckel cation localization energy, Dewar reactivity number and Herndon structure count ratio) have been studied [59],... 

From the efficiency of the MCS model, which is purely topological in nature, it may be concluded that even very complex chemical behaviour of benzenoid hydrocarbons is dominated by molecular topology. 

Liquid extraction was used to make diastereomers, exploiting the high solubility of potassium triflate in water compared with the binaphthylphosphate salts. The two diastereomers have different solubilities and the (+) isomers of knot and anion crystallise together [49, 50], while the laevorotatory knot remains soluble. Counterion exchange with hexafluorophosphate gave the pure topological enantiomers. The optical rotatory power of the copper knots is very high At the sodium D-line (589 nm), the optical rotatory power was 7.000 mol 1 L dm They are beautiful molecules with a remarkable property ... 

The meaning of a complex formation constant is not as clear-cut as one can wish. The behavior of aqua ions which may be either definite species such as Ni(H60)6" or vague representations of the standard solute in dilute solution has already been discussed. One then must discuss the question When is a ligand bound to a central atom Certainly, this problem does not occur for most complexes of multidentate ligands, but weak complexes are not in an easy position. Prue (89) correctly emphasized that without any specific attraction between two molecules, for purely topological reasons, one would find a complexity constant of 0.2 liter/mole from contact charge-transfer spectra in typical conditions. If one finds a smaller formation constant, the two molecules repel each other... 

With our purely topological system (Tables 1 and 2), reactions initially unclear can be easily comprehended and described in the following sections even if in most cases detailed mechanistic knowledge is lacking. This is important because the examples already available show that the complex types — as is also known from the simple types (e.g., [l,2]-eliminations) — can be realized under most different reaction conditions and (apparently) reaction mechanisms. The more precisely the numerous mechanistic alternatives will be explored, the more important the extrapolative potential will be. 

Ultrasonic devulcanization, therefore, causes significant degradation of polymer chains. A simple model based on a purely topological consideration was proposed and simulation of the process was carried out. In the model they have assumed a breakup... 

The dectrotopological state index (Si) is an extension of the purely topological index [55]. Electronic properties (i.e., the charge distribution in the molecule) are also considered. Atoms with identical T may differ in their Si. Electrotopological state indices have been used successfully to predict physico-chemical data, such as basicity (pJCa) or Hpophilicity (logP), as well as for quantitative structure-activity relationship (QSAR) or QSPR studies. 

There is no a priori chemical reason for any system of an even number of electrons to be nonexistent or highly reactive. The MO considerations show that the instability of certain -electron systems has a purely topological background. Our discussion will include only AH with an even number of atoms (and n electrons). For NAH, there are some difficulties which so far remain unsolved 114>. 

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