Bonding topological methods

Simple branching equation (SB) A topological method for describing steric effects which takes into account the order of branching by using as parameters the number of atoms other than H that are bonded to the i-th atoms of the substituent. 

Once the alcohol or at least the cluster contains a soft ionization or fluorescence chromophore, a wide range of experimental tools opens up. Experimental methods for hydrogen-bonded aromatic clusters have been reviewed before [3, 19, 175]. Fluorescence can sometimes behave erratically with cluster size [176], and short lifetimes may require ultrafast detection techniques [177]. However, the techniques are very powerful and versatile in the study of alcohol clusters. Aromatic homologs of ethanol and propanol have been studied in this way [35, 120, 121, 178, 179]. By comparison to the corresponding nonaromatic systems [69], the O—H - n interaction can be unraveled and contrasted to that of O—H F contacts [30]. Attachment of nonfunctional aromatic molecules to nonaromatic alcohols and their clusters can induce characteristic switches in hydrogen bond topology [180], like aromatic side chains [36]. Nevertheless, it is a powerful tool for the size-selected study of alcohol clusters. 

This method is thus about equivalent in accuracy to the bond contribution method, but the connectivity index does contain information about molecular configuration or topology which is absent from the simple bond contribution method. It thus is inherently more likely to express differences between isomers. Its primary disadvantage is the need to deduce the indices, which can be difficult to the uninitiated. The indices lack physical meaning, which is worrisome to those who seek to understand fully the inherent nature and principles of the estimation method. 

A theoretical study on the reaction mechanism for the Bergman cyclization from the perspective of the Electron Localization Function and Catastrophe Theory has been reported.175 The authors argue that topological analysis of electron localization function can be used to complement the molecular orbital- or valence bond-based methods. 

Cremer and Gauss " estimated the C-C and C-H bond energies based on the topological method. First, they obtained the quantity N(A,B) by integrating the density over the surface between the two bonded atoms A and B. 

Meylan, W., Howard, PH. (1991) Bond contribution method for estimating Henry s law constants. Environ. Toxicol. Chem. 10,1283-1293. Meylan, W., Howard, P.H., Boethling, R.S. (1992) Molecular topology/fragment contribution method for predicting soil sorption coefficient. Environ. Sci. Technol. 26(8), 1560-1567. 

The bulk structures of silicas are classified as crystalline and amorphous polymorphs. More than 35 well-defined crystalline silicas are known, which are well-characterized by the Si-O length, the Si-O-Si bond angle, and the Si-O bond topology and coordination (10). Some of the crystalline polymorphs are collected in Table I. Because of the lack of sufficiently precise methods to assess the long-range structural order, amorphous silicas remain poorly characterized. They can be loosely discriminated according to their dispersity, bulk density, and type of pore structure. 

Recently, Cioslowski and Mixon proposed a method for obtaining bond orders that is more in tune with the spirit of the topological method. Their method eliminates the need for any empirical parameters or arbitrary choice of molecules to serve as a model set and thus can apply to any pair of bonded atoms. 

A full description is beyond the scope of this review, but it is noted that the topological method identifies other chemical features in the electron density. The union of all bond paths gives a bond path network that is normally in a 1 1 correspondence with the chemical bond network drawn by chemists. The bond paths for bonds in strained rings are curved, reflecting their bent nature. In Figure 6, we show the gradient paths in the molecular plane of cyclopropane. The C—C bond paths are distinctly bent outward. The value of the Laplacian at the bond critical point discriminates between ionic and covalent bonding." Maps of the Laplacian field reveal atomic shell structure, lone pairs, and sites of electrophilic and nucleophilic attack. The ellipticity of a bond measures the buildup of density in one direction perpendicular to the... 

Figure 7 Comparison of the surfaces separating bonded atoms according to (a) the topological method and (b) the projected density method.

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