Kier-Hall index

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

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

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]. 

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

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 ... 

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

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 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... 

Kier-Hall solvent polarity index —> electric polarization descriptors > Kier molecular flexibility index flexibility indices... 

A set of extended Wiener-Hosoya indices " Vj [Li, 2002 Li, Li et al, 2003] was proposed by combining the original definition of the Wiener index as the sum of the products N j, x Njj, with the definition of —> Kier-Hall connectivity indices and the approach for the Hosoya Z index calculation ... 

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... 

Geometry optimizations were carried out by using the PM3 or AM 1 approaches. Satisfactory linear correlations with normal boiling points for 53 alkenes were obtained (r = 0.984, s = 5.6 °C) with the Q( ) and D/ q) indices [in the last case, 8 q) values are replaced by values], as well as with the Kier-Hall 2D-index x abetter... 

The Wiener index [86] can be expressed in terms of the distance matrix [87] and equals the half-sum of all distance matrix entries. Randi(5 [88] and Kier and Hall indices of order 0-3 [89] are calculated from coordination numbers of atoms or from values of atomic connectivity. The Kier shape index (order 1-3) [90] depends on the number of skeletal atoms, molecular branching, and the ratio of the atomic radius and the radius of the carbon atom in the sp hybridization state. The Kier flexibility index [90] is derived from the Kier shape index. The Balaban index depends on the row sums of the entries of the distance matrix and the cyclomatic number [92,93]. The information content index and its derivatives (order 0-2) are based on the Shannon information theory [95]. Modifications of the information content index are structural information content, complementary information content, and bond information content [96],... 

Chi indices for the various isomers of hexane. (Figure adapted in part from Hall L H and L B Kier 1991. The ir Connectivity Chi Indexes and Kappa Shape Indexes in Structure-property Modeling. In Lipkowitz K B and id (Editors) Reviews in Computational Chemistiy Volume 2. New York, VCH Publishers, pp. 367-422.)... 

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

LH Hall, LB Kier. The molecular connectivity chi indexes and kappa shape indexes in structure-property modeling. In KB Lipkowitz, DB Boyd, eds. Reviews in Computational Chemistry, Vol. 2. New York VCH, 1991, pp 367-422. 

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

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

Another set of particularly useful 2D-based topological descriptors are the so-called electrotopological state index (E-state) descriptors developed by Kier and Hall [36],... 

Lowell H. Hall and Lemont B. Kier, The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure-Property Modeling. 

A system of molecular connectivity indices was developed and extensively exploited by Kier and Hall [102-104,113], Hall and Kier [108,109,115,120,125] and Kier [107]. The zero-order (°y) and second-order (2y) molecular connectivity indices are the closest members to the l index described above. The... 

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. 

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