Valence connectivity Kier—Hall index

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 ... 

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.

Over the past almost four decades, the connectivity index has received considerable attention. For most of its early recognition, clear responsibility goes to Kier and Hall [16,17], who were very much interested in both structure-property and structure-activity studies. Besides hydrocarbons, they paid attention to compounds involving oxygen, nitrogen, fluorine, chlorine, bromine, sulfur, and more. Kier and Hall immediately realized a need to differentiate among atoms of different kinds, which brought them to formulate a modification of the connectivity index known as the valence connectivity indices [18], which, from the start in 1976, have continued to play an important role in QSAR even today. 

The valence connectivity indices not only represent, strictly speaking, an ad hoc solution for discrimination of heteroatoms, even if plausible, but indirectly presume that there are universal valence weights characteristic for individual heteroatoms and valid for all their molecular properties. That the latter assumption is questionable follows from the already mentioned few regression equations of Kier and Hall in which the classical connectivity index x produced better correlations than the corresponding valence connectivity index. Recognition that different molecular properties may require different heteroatom weights led to the idea of the variable connectivity index. 

Kier and Hall used the valence 5 index from Eq. (3) to define the family of molecular connectivity indices "Xt [13-15] ... 

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. 

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. 

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