Simple connectivity index

Two basic quantities are tire atomic simple connectivity index 8 and the atomic valence connectivity index 5. These values are tabulated in Bicerano s book (p. 17) for 11 chemical elements, namely C, N, O, F, Si, P, S, Se, Cl, Br, tnd I. Values of 8 and S are also reported for various hybridizations (sp, sp, etc.). 8 is equal to the number of nonhydrogen atoms to which a given atom is bonded. 8" is calculated through ... 

P (a) Bond simple connectivity index, defined in terms of 8 values. 

The strongest correlation with N is found for the first-order simple connectivity index x, the second strongest correlation is found for °%, the third strongest correlation is found for °xv, and the weakest correlation is found for 1%v-... 

For the butanoic acid molecule shown in Figure 8.1, the five bond connectivities are the reciprocal square roots of (1 x 3), (1 x 3), (2 x 3), (2 x 1) and (2 X 1), which gives a molecular connectivity value of 2.977. This simple connectivity index is known as the first order index because it considers only individual bonds, in other words paths of two atoms in the structure. Higher order indices may be generated by the consideration of longer paths in a molecule, and other refinements—such as valence connectivity values, path, cluster and chain connectivities—have been introduced. 

The first-order molecular connectivity index has been used very extensively in various QSPR and QSAR studies [269, 272, 273]. Thus, the question of its physical meaning has been raised many times. It has been found, in several studies [103, 178-180, 266, 274, 275], that this particular index correlates extremely well with the molecular surface area. It seems this index is a simple and very accurate measure of molecular surface for various classes of compounds and consequently correlates nicely with the majority of molecular surface dependent properties and processes. 

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. 

The relation between this definition and the mathematical expression of and IIP values (Equation 5.13 and Equation 5.14) can be easily seen. The simple represents the vertex valence (a number of skeletal neighbors for each vertex). It can be presented as both = = k - h, and = - h, after the substitution of the number of valence electrons k with the number of electrons assigned to sigma orbitals . It is evident from Equation 5.15 that the greater the number of skeletal neighbors, the larger the value and the lower the connectivity index. Recently, new arguments were evaluated in support of the thesis that the molecular connectivity indices represent molecular accessibility areas and volumes (Estrada, 2002). 

The aforementioned macroscopic physical constants of solvents have usually been determined experimentally. However, various attempts have been made to calculate bulk properties of Hquids from pure theory. By means of quantum chemical methods, it is possible to calculate some thermodynamic properties e.g. molar heat capacities and viscosities) of simple molecular Hquids without specific solvent/solvent interactions [207]. A quantitative structure-property relationship treatment of normal boiling points, using the so-called CODESS A technique i.e. comprehensive descriptors for structural and statistical analysis), leads to a four-parameter equation with physically significant molecular descriptors, allowing rather accurate predictions of the normal boiling points of structurally diverse organic liquids [208]. Based solely on the molecular structure of solvent molecules, a non-empirical solvent polarity index, called the first-order valence molecular connectivity index, has been proposed [137]. These purely calculated solvent polarity parameters correlate fairly well with some corresponding physical properties of the solvents [137]. 

Note that the total structure connectivity index is the square root of the - simple topological index proposed by Narumi for measuring molecular branching. 

Another series of successfully applied topological descriptors is derived from graph theory using atom connectivity information of a molecule. An example is the connectivity index developed by Randic [21], In the simple form,... 

ETA indices are an extension of the TAU indices (or Topochemically Arrived Unique indices) [Pal, Purkayastha et al, 1992 Pal, Sengupta et al, 1988,1989,1990], which were defined some years before in the framework of a previous version of the Valence Electron Mobile environment (VEM environment). TAU indices are calculated from previous definitions of core count and VEM count and include four indices the composite topochemical index, denoted by T (similar to the composite ETA index), the functionality index, denoted by F, the skeletal index, denoted by Tr, and the simple branching index, denoted by B. In QSAR studies, these indices were used in combination with —> STIMS indices, connectivity indices, and some information indices [Roy, Pal et al, 1999, 2001]. 

Replacing the simple vertex degree by the Yang vertex degree, the Yang connectivity index was proposed [Jiang, Liu et al., 2003]. 

A. Review of Connectivity Index Calculations for Simple Molecules... 

Figure 17.5. Hydrogen-suppressed graph of the a-naphthyl group in (a) poly(a-vinyl naphthalene) and (b) poly(a-naphthyl methacrylate). The simple atomic index 8 (see Chapter 2) is shown at the vertices. The products of pairs of 8 values are shown along the edges. The two graphs differ slightly because the vertex outside the box has 8=3 in (a) and 8=2 in (b), resulting in a small difference between the contributions of the a-naphthyl unit to the first-order connectivity index Both graphs make the same contribution to the zeroth-order index °x-...

HBi is zero for all hydrocarbons and, therefore, was deleted from analyses of BP. Twelve of the TIs were deleted for the analysis of the 140 hydrocarbons as well. These indexes included the third- and fourth-order chain connectivity indexes, which were zero for all chemicals, the fourth- and sixth-order bond and valence corrected cluster connectivity indexes, which were perfectly correlated with the simple cluster connectivity indexes (r = 1.0), and and which were perfectly correlated with 7 for hydrocarbons. 

The simple regression equation using the connectivity index % as the molecular descriptor for the smaller benzenoids is given in Table 26. To improve the regression, Radecki, Lamparczyk, and Kaliszan considered as an additional descriptor the ratio L/B of the length L and the width B of the rectangle within which the molecule... 

The general name for the structural description method utilizing the adjacency relationships of molecular skeletons was selected to be molecular connectivity. The number assigned to a skeleton atom describing its adjacency relationship is called the simple connectivity value (or simple delta value) of the atom. In the development the S values were used for the first-order subgraph (or bond) between atoms i and j. The index for the entire molecule, in this case, the molecular connectivity index of the first order, is designated by the Greek letter chi, is computed as in equation 2,... 

As is known, inequalities can have numerous solutions, so one should look for a simple solution, if there is such. One way to find solutions for a set of inequalities is to test a selection of simple expressions to see if they satisfy the inequalities. In our case, for example, one could consider (m, n) to be m = 1/m and n = 1/n, which is incidentally the choice of (m, ri) values used in the construction of one of the Zagreb indices [11-15]. However, this simple choice is not a solution as one can verify, because it does not satisfy all the seven inequalities. After testing a few similar expressions, it was found that by taking m = 1/Vm and n = 1/Vn all the seven inequalities of Table 6.1 are satisfied. This is the way the new bond additive molecular descriptor, the connectivity index x = 2H/. m n, was bom. The numerical values for the seven inequalities using the weights 1/V(m n) are shown in Table 6.1. In Table 6.2, we show additional solutions of the nine inequalities that offer an alternative form of the connectivity index x, which was more recently found but has not yet been tested. 

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