Molecular connectivity indices values

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) ... 

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 ... 

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. 

Equations 15 and 16 obtained for the analogues of 10 exhibited the parallel correlations for the two activities, indicating that for both the activities the hydrophobic property and electron-donating nature of the R-substituents will be crucial. The Am moiety was shown to affect both the activities through its size dehneated by the molecular connectivity index Vim- qs. 15 and 16, however, 7rR and Vim shown to have parabolic correlations with the activities, each with an optimum value as shown in the equations. 

A variety of parameters are included into the QSAR equation. Log P is a commonly used parameter and is obtained from Medchem or estimated using the CLOGP3 computer program. Molecular weight is calculated. In interspecies models the LD50 or LC50 value is incorporated as a typical parameter. Molecular connectivity indexes, electronic charge distributions, and kappa environmental descriptors have been proven as powerful predictors of toxicity. The efficacy of these values lies in the fact that each of these parameters describes a molecule in a fashion similar to that actually seen by the molecular receptors that initiate a toxic response. Substructural keys are identified with the help of the MOLSTAC substructural key system. MOLSTAC consists of five classes of descriptors ... 

Several other models have been proposed to account for retention in reversed phase chromatography of these two have found some degree of popularity and include the concepts of molecular connectivity and interaction indexes . The value of the molecular connectivity index has been shown to be proportional to the capacity ratio and the solubility of the solute in water (Karger et al., 1976). 

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,... 

A rehable model for predicting values is the one proposed by Meylan et al. [25], which is based on the first order molecular connectivity index of the compound. Meylan et al. [25] report that their model accounts for 96% of the variation in measured log vdues for the training set (189 chemicals) and 86% of the variation for the validation set (205 chemicals). 

Some electronic, geometric, and topological parameters are taken into consideration for the mathematic modeling, they are Log P (hydrophobic constant), square of Log P, a (Hammett constant), Ej Taft values), MR (molar refractivity), (valence molecular connection index). 

Zi is the atomic number. The chi molecular connectivity indices are obtained by summing )ns of these delta values. Thus the chi index of order zero is defined as follows ... 

Values for hydrocarbons other than alkynes and alkadienes can be predicted by the method of Suzuki et al. The best model includes the descriptors T, P, the parachor, the molecular surface area (which can be approximated by the van der Waals area), and the zero-order connectivity index. Excluding alkynes and alkadienes, a studv for 58 alkanes, aromatics, and cycloalkanes showed an average deviation from experimental values of about 30 K. 

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 formerly proposed and the most important of this series of topological indices is the Baiaban distance connectivity index J (also called distance connectivity index or average distance sum connectivity). It is one of the most discriminating - molecular descriptors and its values do not increase substantially with molecule size or number of rings it is defined in terms of sums over each ith row of the - distance matrix D, i.e. the vertex distance degree o [Baiaban, 1982 Baiaban, 1983a]. It is defined as ... 

Other molecular descriptors based on atom eccentricity values combined with other —> local vertex invariants are the eccentric connectivity index, the —> eccentric distance sum, the connective eccentricity index, the eccentric adjacency topochemical indices, the superadjacency index, and the —> eccentricity-hased Madan indices. 

In the molecular connectivity method, numerical indexes are developed to represent and characterize molecular structure. The indexes are suitable for use in structure-property relationships that may be developed by standard regression methods, producing equations for estimation of property values. The indexes are also used as a basis for pattern recognition and discriminant analysis. ... 

These topological indexes, based on the molecular connectivity approach, include three types the ""Xr molecular connectivity chi indexes that characterize the structural attributes of molecules, the ""k kappa indexes of molecular shape, and the topological equivalence state T values that individually characterize atoms and groups in the molecular skeleton and are used primarily to determine chemically equivalent atoms within a molecule. A further development of this approach has led to the electrotopological state atom indexes, which will not be discussed here but will be presented elsewhere. Molecular connectivity chi indexes are discussed in the first part of this paper along with illustrative applications. Then kappa shape indexes are discussed. The topological state index is discussed in the final section. 

The key to useful topological state values is an appropriate form for the r, values. Hall and Kier have shown that simple forms, such as the graph distance d,j, are not useful because they fail to indicate proper topological equivalence. To ensure representation of topological equivalence, two features of the paths must be encoded (1) atomic identity and (2) the sequence of atoms in each path. It has been shown that both these characteristics can be encoded as follows. Atomic identity can be encoded using the molecular connectivity valence delta value, 8. The discussions concerning chi indexes and related quantities have shown the validity of the valence delta value as a characterization of atoms. 

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. 

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