First-order connectivity index

Four types of indexes can be identified path-labeled, cluster-labeled, path/ cluster, and chain-labeled, denoted., respectively, by "Xp, Xc- ""Xp/cj and "ich- All calculations reported here are based on the zeroth- and first-order connectivity indexes, Xj x and x, x respectively, for the entire repeat unit and these are defined as ... 

Another important consideration is that all results reported here are based on the calculation of zero- and first-order connectivity indexes only. It is possible that die inclusion of higher-order indexes, which in turn means more detailed... 

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-...

For the pentanol shown in Figure 1, the five bond connectivities are the reciprocal square roots of (1 x 2), (2 x 3), (3 x 1), (3 x 2), and (2 x 1), which gives a molecular connectivity of 2.808. This process is known as a first-order connectivity index because it considers only individual bonds in the structure, that is, paths of two atoms only. Fligher order indices may be generated by taking longer paths and other variations including valence connectivity values, path, cluster, and chain connectivities. ... 

Figure 1. Loadings of molecular descriptors and sensory sweet score on two PlS factors. 1 = log k, 2 = Kovats index on OVIOI and (3) Caibowax-20M, 4 = molecular weight, S = dipole moment, 6 = ionization potential, 7 = electron energy, 8 = heat of formation, 9 = zero-order connectivity, 10 = first-order connectivity, 11 = first-order connectivity/n Y = sensory sweet score.

First-order connectivity indices computed for predefined positions on molecular fragments in congeneric series [Takahashi et al, 1985]. By superimposition of all congeneric compounds, a template structure is derived whose vertices define the positions for the FMC indices the vertices of the common parent structure are not considered in defining the positions. For a k th position the corresponding fragment connectivity index is defined as ... 

The two Zagreb indices are strictly related to zero-order °x and first-order - connectivity indices, respectively. The 1 Zagreb index M (also called Gutman index) is also related to the - Platt number F and the - connection number Na by the relationship ... 

Table 3.5. Experimental amorphous densities p (g/cc) and molar volumes V (cc/mole) at room temperature, "correction index" NMV used in correlation for V, and fitted values of V and p, for 152 polymers. Zeroth-order connectivity indices °x and °xv and first-order connectivity indices X and 1xv- all of which are also used in the correlation, are listed in Table 2.2. The alternative set of °xv and 1 %v values listed in Table 2.3 is used for the silicon-containing polymers. 

Strkcttire inflkence. The specificity of interphase transfer in the micellar-extraction systems is the independent and cooperative influence of the substrate molecular structure - the first-order molecular connectivity indexes) and hydrophobicity (log P - the distribution coefficient value in the water-octanole system) on its distribution between the water and the surfactant-rich phases. The possibility of substrates distribution and their D-values prediction in the cloud point extraction systems using regressions, which consider the log P and values was shown. Here the specificity of the micellar extraction is determined by the appearance of the host-guest phenomenon at molecular level and the high level of stmctural organization of the micellar phase itself. 

On the basis of data obtained the possibility of substrates distribution and their D-values prediction using the regressions which consider the hydrophobicity and stmcture of amines was investigated. The hydrophobicity of amines was estimated by the distribution coefficient value in the water-octanole system (Ig P). The molecular structure of aromatic amines was characterized by the first-order molecular connectivity indexes ( x)- H was shown the independent and cooperative influence of the Ig P and parameters of amines on their distribution. Evidently, this fact demonstrates the host-guest phenomenon which is inherent to the organized media. The obtained in the research data were used for optimization of the conditions of micellar-extraction preconcentrating of metal ions with amines into the NS-rich phase with the following determination by atomic-absorption method. 

The concept of the molecular connectivity index (originally called branching index) was introduced by Randic [266]. The information used in the calculation of molecular connectivity indices is the number and type of atoms and bonds as well as the numbers of total and valence electrons [176,178,181,267,268]. These data are readily available for all compounds, synthetic or hypothetical, from their structural formulas. All molecular connectivity indices are calculated only for the non-hydrogen part of the molecule [269-271]. Each non-hydrogen atom is described by its atomic 6 value, which is equal to the number of adjacent nonhydrogen atoms. For example, the first-order Oy) molecular connectivity index is calculated from the atomic S values using Eq. (38) ... 

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. 

Its counterpart, the first-order ( y") valence molecular connectivity index, is also calculated from the non-hydrogen part of the molecule and was suggested by several authors [103,276,277]. In the valence approximation, non-hydrogen atoms are described by their atomic valence <5 "values, which are calculated from their electron configuration by the following equation ... 

For molecular connectivity indices with orders higher than 2, it is also necessary to specify the subclass of index. There are four subclasses of higher order indices path, cluster, path/cluster, and chain. These subclasses are defined by the type of structural subunits they are describing, a subunit over which the summation is to be taken when the respective indices are calculated. Naturally, the valence counterparts of all four subclasses of higher order indices can be easily defined by analogy, described above for the first-order valence molecular connectivity index. 

The main characteristic of cluster-type indices is that all bonds are connected to the common, central atom (star-type structure). The third-order cluster molecular connectivity index (3yc) is the first, simplest member of the cluster-type indices where three bonds are joined to the common central atom [102-104, 111-113,152-154,166,167,269]. The simplest chemical structure it refers to is the non-hydrogen part of ferf-butane. This index is then calculated using Eq. (43) ... 

Meylan et al. (1992) described another attempt to extend MCI-Koc relationships to polar compounds. This method uses the first order molecular connectivity index (Jy) and a series of statistically derived fragment contribution factors for polar compounds. To develop the model, they performed two separate regression analyses. The first related log Koc to for... 

Calculate the first order molecular connectivity index for anthracene. 

The calculation of the first-order valence molecular connectivity index ( CP) is demonstrated for 2,3-dimethylpentanol, which differs from 2,3-dimethylhexane only by 1 oxygen atom (replacing the carbon atom at the first position) ... 

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]. 

Go el and Madan [117] investigated the 8AR of the antiulcer activity of these compounds with Wiener s topological index (Wiener number of chemical graph, W(G)) [118] and the first-order molecular connectivity index ( x) [119] using a typical classification procedure. In the case of Wiener s... 

To derive these equations, log P (hydrophobic parameter), MR (molar refrac-tivity index), and MV (molar volume) were calculated using software freely available on the internet (wwwlogP.com, www.daylight.com). The first-order valence molecular connectivity index of substituents was calculated as suggested by Kier and Hall [46,47]. In these equations, is cross-vahdated obtained by the leave-one-out jackknife procedure. Its value higher than 0.6 defines the good predictive ability of the equation. The different indicator variables in these equations were defined as follows. 

It is a solvent polarity index defined [Kier and Hall, 1986] as the first-order valence connectivity index divided by the number Nf of discrete, isolated functional groups in order to account for multiple interaction sites as ... 

If the atomic property is the vertex degree, the obtained LOVIs correspond to twice the first order - local connectivity indices. Moreover, the Randic-Razinger index is defined as ... 

This matrix is a special case of —> distance degree matrices obtained by the parameter combination a = 0, (3 = 0, y=l. The row sum of the additive adjacency matrix is the —> extended connectivity of first-order EC defined by Morgan. This local invariant was used to calculate the eccentric adjacency index. A modification of this matrix, which accounts for heteroatoms, is the additive chemical adjacency matrix. 

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