Electrotopological state values

Two sets of molecular descriptors, called intrinsic state pseudoconnectivity indices r, one based on the intrinsic states I and the other on the scaled electrotopological state values , were proposed as [Pogliani, 2000b, 2004] ... 

Topological indices encode the molecular connectivity pattern [65, 66] and quantify features like atom types, numbers of atoms and bonds, and the extent and position of branchings and rings. Furthermore, electrotopological state values [67], molecular shape indices [68] and topological symmetry indices are used. Often, the large number of correlated indices is condensed by principal component analysis (PCA) [69]. 

This pair of delta values is seen as a characterization of the atom in its valence state. The simple delta, 5, describes the role of the atom in the skeleton in terms of its connectedness and count of sigma electrons it could be called the sigma electron descriptor. The valence delta, 8, encodes the electronic identity of the atom in terms of both valence electron count and core electron count. It could be called the valence electron descriptor. The isolated, unbonded atom may be thought of as characterized by its atomic number, Z, and the number of valence electrons, Z. In its valence state, the bonded atom is characterized by 8 and 8. Embedded in the molecular skeleton, the full characterization of the atom in the environment of the whole molecule is given by the topological equivalence value, described in a later section, and the electrotopological state value, presented separately.A representation of the whole molecule is accomplished by the combination of chi, kappa, and topological state indexes. 

FIGURE 7. Electrotopological state values for the methyl and methylene groups in several normal alkanes. Values are omitted for the symmetrically related groups on the right side of the molecule... 

FIGURE 8. Electrotopological state values for the skeletal groups in the butane, pentane and hexane isomers. Values are given only for the symmetry independent groups within each molecule... 

Autocorrelation of Topological Structure Moreau and Broto [24,25] have suggested the autocorrelation vector of a molecular graph as the source for molecular descriptors. This method assumes that each atom i in the graph is uniquely associated with a numeric quantity, qit such as the atomic number, atomic mass, (v)(, (ds), Sv, or electronegativity. The intrinsic atom values of the electrotopological state [26] and the atomic Rd and log Kow parameters [27,28] are other potential atomic descriptors suitable to construct autocorrelation vectors. Generally, the fcth element of the autocorrelation vector is defined as... 

Figure 2.2 Common scaffold, with standardized numbering of atoms for which electrotopological state atom indices (ETSA), sensitive to the perturbations induced by the substituents R1-R5, were calculated and used in QSAR modeling. The study overhastily concluded that phenyl rings A and B must be part of the pharmacophore, explaining anti-Alzheimer activity, because the QSAR study picked the average ETSA values of the atoms within the rings as key descriptors.

Six different weighting schemes are proposed (1) the unweighted case u (yvi = 1 i —, n, where A is the number of atoms for each compound), (2) atomic mass m, (3) the - van der Waals volume v, (4) the Sanderson - atomic electronegativity e, (5) the - atomic polarizability p and (6) the - electrotopological state indices of Kier and Hall 5. All the weights are also scaled with respect to the carbon atom, and their values are shown in Table W-5 moreover, as all the weights must be positive, the electrotopological indices are scaled thus ... 

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. 

These topological indexes, based on the molecular connectivity approach, include three types the ""Xr molecular connectivity chi indexes that characterize the structural attributes of molecules, the ""k kappa indexes of molecular shape, and the topological equivalence state T values that individually characterize atoms and groups in the molecular skeleton and are used primarily to determine chemically equivalent atoms within a molecule. A further development of this approach has led to the electrotopological state atom indexes, which will not be discussed here but will be presented elsewhere. Molecular connectivity chi indexes are discussed in the first part of this paper along with illustrative applications. Then kappa shape indexes are discussed. The topological state index is discussed in the final section. 

Fig. 13.1-5 Intrinsic and electrotopological states, (a) Illustration of intrinsic state values note that these values encode similar information and have equivalent...

The final step in the derivation of the electrotopological state is the combination of the atom intrinsic state expression with the experession for the perturbation by all other skeletal atoms. The perturbing influence on atom i by atom j was assumed to be proportional to the difference between the atom intrinsic values, U — Iy Further, the perturbation falls off as the square of the distance between the two atoms. The distance, in this case, is taken to be the number of atoms in the (shortest) path between atoms i and jj namely Vij. The overall perturbation on atom i, A/ is taken as a sum over all other atoms in the skeleton (molecular graph) ... 

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