Kier connectivity index

The last was used by Boelens and Punter (1978) to quantify the odour quality of 16 muguet-smelling materials. These data were then used to derive equation (3), which related the odour similarity (OS) to molecular weight (MW) and the Kier connectivity index (A ). The concept of molecular connectivity was introduced by Randic (1975) and further elaborated by Kier and Hall (1976). It involves the calculation of numerical indices which describe the topology of a molecule. The Kier... 

Weiner index Randic indices Kier and Hall indices Inforanation content Connectivity index Balaban index... 

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. 

Kier and HaU extended the definition of the 5 connectivity index in order to incorporate heteroatoms and multiple bonds in the definition of the connectivity index % [13-15]. They noticed that the 5 connectivity (atom degree) may be expressed as ... 

Kier and Hall proposed a series of connectivity indexes. The zeroth index sums the reciprocal of the square roots of the connection numbers of each individual atom. 

A further extension of this approach was done by Kier and Hall8> so as to provide different values of the connectivity index for molecules depicted by one and the same graph, but differing by the chemical nature of atoms as well as by the presence of single, double or triple bonds. The valency of the atom i (vertex degree), Vj, is replaced by the atom connectivity ... 

Kier and Hall (1976) and Hall et al. (1975) have pioneered the use of the connectivity index as a descriptor of molecular structure. It is an expression of the sum of the degrees of connectedness of each atom in a molecule. Indices can be calculated to various degrees or orders, thus encoding increasing information about the structure. Although the index has been used with success in a number of applications, it is not entirely clear on theoretical grounds why this is so. It appears that the index generally expresses molar volume or area. 

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. 

These are truly structural descriptors because they are based only on the two-dimensional representation of a chemical structure. The most widely known descriptors are those that were originally proposed by Randic (173) and extensively developed by Kier and Hall (27). The strength of this approach is that the required information is embedded in the hydrogen-suppressed framework and thus no experimental measurements are needed to define molecular connectivity indices. For each bond the Ck term is calculated. The summation of these terms then leads to the derivation of X, the molecular connectivity index for the molecule. 

TTie extended edge connectivity indices were defined as a generalization of the edge connectivity index in analogy to the -> Kier-Hall connectivity indices ... 

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 ... 

Balaban distance connectivity index Schultz molecular topological index Kier shape descriptors eigenvalues of the adjacency matrix eigenvalues of the distance matrix Mohar indices Kirchhoff number detour index... 

In analogy with the Kier-Hall - connectivity indices x and the Balaban distance connectivity index J, JJ indices [Randic et al, 1994a] are derived from the Wiener matrix based on the Wiener matrix degrees q, ... 

Kier, L.B. and Hall, L.H. (1991). A Differential Molecular Connectivity Index. Quant.Struct.-Act.Relat., 10,134-140. 

D denotes the degrees of the atoms i and j of a molecular graph, and the sum goes over all adjacent atoms. The exponent was originally chosen by Randic to be -1/2 however, it has been used to optimize the correlation between the descriptor and particular classes of organic compounds. The connectivity index was later extended by Kier and Hall to applications with connected subgraphs [22],... 

Kier and Hall Index is a special form of the connectivity index that allows optimizing the correlation between the descriptor and particular classes of organic compounds. 

Table C6 Values of the first-order Kier-Hall connectivity index for some substituent groups attached to a Carbon atom with a valence vertex degree equal to 3.

Note that the % index of the first line graph Li coincides with the edge connectivity index e. Moreover, the line graph connectivity indices were proposed by analogy with the —> Kier-Hall connectivity indices as... 

Connectivity index The molecular connectivity index is a term used to describe molecular structure in terms of the adjacency of each atom in the molecule. A well-known molecular connectivity index is the y-index of Kier and Hall which basically reflects a weighted count (based on the connectivity of each atom) of bonds and connected sets of bonds in a molecule. 

Molecular connectivity indexes have been widely used to develop QSARs for toxicity and other properties of environmental interest. Hall and Kier investigated the toxicity of substituted phenols to fathead minnow [Pimephales promelasY and have shown that a two-variable equation gives good account of the toxicity data. 

G. Szasz, O. Papp, J. Vamos, K, Hanko-Novak, and L. B. Kier,/. Chromatogr., 269, 144 (1984). Relationships Between Molecular Connectivity Indexes, Partition Coefficients and Chromatographic Parameters. 

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