Kier-Hall

Some further topological descriptors are the Kier-Hall connectivity indices [13] and the electrotopological state index (or -state index) [14]. A comprehensive overview of topological molecular desaiptors is given by Todeschini and Consonni [15]. 

The Randic-Kier-Hall Molecular Connectivity Indices... 

Kier and Hall noticed that the quantity (S -S) jn, where n is the principal quantum number and 5 is computed with Eq. (2), correlates with the Mulliken-Jaffe electronegativities [19, 20]. This correlation suggested an application of the valence delta index to the computation of the electronic state of an atom. The index (5 -5)/n defines the Kier-Hall electronegativity KHE and it is used also to define the hydrogen E-state (HE-state) index. 

The E-state indices are atomic descriptors composed of an intrinsic state value I and a perturbation AI that measures the interactions with all other atoms in a molecule. The Kier-Hall electronegativity is the starting point in the definition of the intrinsic state of an atom, which encodes its potential for electronic interactions and its connectivity with adjacent atoms. The intrinsic state of an atom i is [19, 21] ... 

The Kier-Hall electronegativity is used to define the HE-state index HS [19] ... 

Graph theory indices Randic indices Kier-Hall indices Ad hoc indices... 

JJ indices derived from the - Wiener matrix were proposed as a generalization of the Balaban index in analogy with the Kier-Hall -> connectivity indices. 

Kier and Hall defined [Kier and Hall, 1986 Kier and Hall, 1977b] a general scheme based on the Randic index to calculate also zero-order and higher-order descriptors, thus obtaining connectivity indices of m th order, usually known as Kier-Hall connectivity indices. They are calculated by the following ... 

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

Table E-7. Valence vertex degrees 6, vertex degrees 6, their differences, and Kier-Hall electronegativity values for different atoms.

Kier-Hall connectivity indices Burden eigenvalues BCUT descriptors... 

Kier-Hall connectivity indices connectivity indices ofmth order -> connectivity indices... 

Kier-Hall connectivity matrix - weighted matrices... 

Kier-Hall solvent polarity index - electric polarization descriptors... 

Therefore, the Kier-Hall electronegativity was proposed based on the difference between valence and simple vertex degree, as ... 

Another important connectivity matrix is obtained weighting each bond i-j by the -+ edge connectivity (6,- bj) b being the - vertex degree of the atoms. This matrix is known as the Kier-Hall connectivity matrix or sparse x matrix ... 

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, ... 

Topological 2D structural formula (Kier-Hall indices, extent of branching)... 

The chiral connectivity indices were calculated by analogy with the Kier-Hall connectivity indices by using vertex degrees modified by a chirality correction c = 1 [Xu, Zhang et al., 2006]. 

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.

Moreover, generalized coimectivity indices are a generalization of the Kier-Hall cormectivity indices in terms of a variable exponent X as ... 

By summing these local connectivity indices over all the nonhydrogen atoms, the Kier-Hall connectivity indices are reproduced. 

By analogy with Kier-Hall cormectivity indices. Topological Distance Connectivity Indices (TDCIs), also called Topological Distance Measure Connectivity Indices (TDMCIs), were also defined by using the reciprocal distance sum RDS in place of the —> vertex degree 6 [Balaban, Ciubotariu et al., 1990 Ciubotariu, Medeleanu et al., 2004] ... 

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