Electrotopological State Indices

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]. 

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],... 

The electrotopological state 5, of the /th atom in the molecule, called the fl-state index (or electrotopological state index) gives information related to the electronic and topological state of the atom in the molecule and is defined as [Kier and Hall, 1990a Kier and Hall, 1999] ... 

HE-state index hydrogen electrotopological state index - electrotopological state indices... 

Aboushaaban, R.R., Alkhamees, H.A., Abouauda, H.S. and Simonelli, A.R (1996). Atom Level Electrotopological State Indexes in QSAR Designing and Testing Antithyroid Agents. Pharm.Res., 13,129-136. 

Hall, L.H. and Kier, L.B. (1992a). Binding of Salicylamides QSAR Analysis with Electrotopological State Indexes. Med.Chem.Res., 2, 497-502. 

Kier, L.B. and Hall, L.H. (1990a). An Electrotopological-State Index for Atoms in Molecules. Pharm.Res 7, 801-807. 

Llorente, B., Rivero, N., Carrasco, R. and Martinez, R.S. (1994). A QSAR Study of Quinolones Based on Electrotopological State Index for Atoms. Quant.Struct.-Act.Relat, 13, 419-425. 

Tsantilikakoulidou, A., Kier, L.B. and Joshi, N. (1992b). The Use of Electrotopological State Indexes in QSAR Studies. J.Chim.PhysPhys-Chim.Biol.,89,1729-1733. 

Kier LB, Hall LH. An electrotopological-state index for atoms in molecules. 

H -state index = hydrogen electrotopological state index electrotopological state indices > heteroatom-corrected extended adjacency matrix —> extended adjacency matrices... 

It can be noted that the definition of this local vertex invariant is very similar to that of the electrotopological state index Si, but this is based on absolute values of the perturbation terms Ij — Ii, with the consequence that the sum of A/j over all the vertices is different from zero. Absolute values were introduced to avoid the sum of the matrix off-diagonal elements results in zero for any weighting scheme w considered. 

The final graph theoretical index popularised by Kier and Hall that we shall consider is the electrotopological state index [Hall et al. 1991], Unlike the molecular connectivity and shape indices this is determined for each atom (including the hydrogen atoms, if so desired). This index depends upon the intrinsic state of an atom, which for an atom i (in the first row of the periodic table) is given by ... 

In the development of the electrotopological state index, Kier and Hall viewed each atom as possessing an intrinsic state which is modified through interaction with the field... 

E-State descriptors of potential internal hydrogen bond strength (7 = 2-10) Electrotopological state index values for atoms types ... 

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