Molecular connectivity indexes

Correlation methods discussed include basic mathematical and numerical techniques, and approaches based on reference substances, empirical equations, nomographs, group contributions, linear solvation energy relationships, molecular connectivity indexes, and graph theory. Chemical data correlation foundations in classical, molecular, and statistical thermodynamics are introduced. 

Molecular Connectivity Indexes and Graph Theory. Perhaps the chief obstacle to developing a general theory for quantification of physical properties is not so much in the understanding of the underlying physical laws, but rather the inabiUty to solve the requisite equations. The plethora of assumptions and simplifications in the statistical mechanics and group contribution sections of this article provide examples of this. Computational procedures are simplified when the number of parameters used to describe the saUent features of a problem is reduced. Because many properties of molecules correlate well with stmctures, parameters have been developed which grossly quantify molecular stmctural characteristics. These parameters, or coimectivity indexes, are usually based on the numbers and orientations of atoms and bonds in the molecule. 

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. 

Kier and Hall developed an interesting concept termed molecular connectivity, in which the molecular-connectivity index, x, was defined as... 

Kier and coworkers found that the molecular connectivity-index and such molecular properties as polarizability, molecular volume," and partition coefficients between water and octanol"" show very good correlation. Because all of these properties could be correlated with biological activity. 

Estimation from molecular connectivity index/fragment contribution method (Meylan et al. 1992, Lohninger 1994) ... 

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) ... 

Koch, R. Molecular connectivity index for assessing ecotoxicological behaviour of organic compounds, Toxicol. Environ. Chem., 6(2) 87-96, 1983. 

Applications of Molecular Connectivity Indexes and Multivariate Analysis in Environmental Chemistry... 

Recently, Tichy investigated 41) the dependencies of the steric constants, Es, v, L, Bj, B4, MV (molar volume), [P] (parachor), MR (molar refraction), MW (molecular weight), and % (molecular connectivity index) on lipophilicity, as it is measured by n 42) and f43) constants. The data were treated by factor analysis methods. 

The solvophobic model has been used to deduce a functional form for a Henry s constant correlation based on molecular connectivity index and polarizability (42). Accurate predictions are reported over a span of seven log units in Henry s constant. A reliable solvophobic model of aqueous solubility has also been reported (45,46). 

Method 3 Molecular Connectivity Index Method of Nirmalakhandan and Speece (1988) and Nirmalakhandan et al. (1997)... 

More recently, Brennan et al. (1997) compared five methods for estimating KAW, namely the vapor pressure/solubility ratio, the group or bond contribution method, linear solvation energy methods, and molecular connectivity. The authors compared the methods by application to a common set of 150 chemicals and concluded that the Meylan and Howard (1991) bond contribution method and the molecular connectivity index method of Nirma-lakhandan and Speece (1988) are comparably accurate, having standard deviations of, 0.29 and 0.34 log units, respectively. 

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. 

Biodegradation by metabolic processes Molecular connectivity index (topological indices - shape) Molar refractivity Field constants atomic charges... 

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