Valence connectivity values

For the butanoic acid molecule shown in Figure 8.1, the five bond connectivities are the reciprocal square roots of (1 x 3), (1 x 3), (2 x 3), (2 x 1) and (2 X 1), which gives a molecular connectivity value of 2.977. This simple connectivity index is known as the first order index because it considers only individual bonds, in other words paths of two atoms in the structure. Higher order indices may be generated by the consideration of longer paths in a molecule, and other refinements—such as valence connectivity values, path, cluster and chain connectivities—have been introduced. 

Chance correlations may arise from the uncritical combination of a large number of closely interrelated connectivity terms, including normal and valence connectivity values, higher order path and cluster connectivity terms, and squared terms. 

The values 1/V(dj dj) are for the atoms i and j, which make up this bond, and the connectivity index, x, is obtained as the sum of the bond connectivities. In molecules containing heteroatoms, the d values were considered to be equal to the difference between the number of valence electrons (E") and the number of hydrogen atoms (hi). Thus, for an alcoholic oxygen atom, d = 1, and d = 5. The valence connectivity-index, y can then be calculated the use of removes redundancies that can occur through the use of y alone. The calculation of connectivity indices and for the case of two isomeric heptanols is as follows. 

Its counterpart, the first-order ( y") valence molecular connectivity index, is also calculated from the non-hydrogen part of the molecule and was suggested by several authors [103,276,277]. In the valence approximation, non-hydrogen atoms are described by their atomic valence <5 "values, which are calculated from their electron configuration by the following equation ... 

Two basic quantities are tire atomic simple connectivity index 8 and the atomic valence connectivity index 5. These values are tabulated in Bicerano s book (p. 17) for 11 chemical elements, namely C, N, O, F, Si, P, S, Se, Cl, Br, tnd I. Values of 8 and S are also reported for various hybridizations (sp, sp, etc.). 8 is equal to the number of nonhydrogen atoms to which a given atom is bonded. 8" is calculated through ... 

The definition of the valence connectivity indices is related closely to the definition of simple ( ) and valence (I I) value. In the molecular connectivity formalism ... 

Kier, L.B. and Hall, L.H. (1983b). General Definition of Valence Delta-Values for Molecular Connectivity. J.Pharm.ScL, 72,1170-1173. 

In general, values of c < 5 were assumed. The chirality correction was also applied to valence vertex degrees from which valence connectivity indices are derived. 

This chirality descriptor is derived from the Ruch s chirality functions applied to the first-order valence connectivity index. Separate values of the valence connectivity index are calculated for the four atoms/substituents a, h, c, and d bonded to the chiral atom [Lukovits and Linert, 2001]. The chirality correction is calculated by the following function F ... 

Pv Bond valence connectivity index, defined in terms of 8V values. 

The second atomic index [Figure 2.2(b)] is the valence connectivity index 8V, incorporating information on details of the electronic configuration of each non-hydrogen atom. Its value for the lowest oxidation states of the elements will generally be assigned by Equation 2.1 [2], where Zv is the number of valence electrons of an atom, NH is the number of hydrogen atoms bonded to it, and Z is its atomic number (i.e., Z equals Zv plus the number of inner shell electrons). 

As mentioned in a footnote to Table 2.1, the use of 8v=l/3 or 8v=4/9 for silicon atoms, as obtained from the definition of 8V (Equation 2.1), causes the overestimation of the effect of the extra inner shell of electrons in silicon atoms on certain physical properties. Whenever this happens, the replacement Si—>C (i.e., 8V=3 or 4) will be made in calculating the valence connectivity indices to correlate that property. For such properties, the differences between Si and C atoms will be taken into account by introducing an atomic correction term for the number of silicon atoms in the repeat unit. The alternative sets of °%v and values obtained for silicon-containing polymers by making the replacement Si—>C in the hydrogen-suppressed graph of the polymeric repeat unit, are listed in Table 2.3. 

The replacement of silicon atoms by carbon atoms in the calculation of the first-order valence connectivity index (i.e., use of the alternative set of1%v values listed in Table 2.3 for silicon-containing polymers) results in a much better fit than the use of the 1%v values listed in Table 2.2 for these polymers. 

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. 

L.B. Kier, L.H. Hall, General definition of valence delta-values for molecular connectivity, J. Pharm. Sci. 1983, 72, 1170- 3. 

In addition to normal and valence connectivity [372, 373] values, many other topological indices have been defined (for reviews see [52, 158, 287, 369, 371]). 

The bond-clcctron matrix (BE-matrix) was introduced in the Dugundji-Ugi model [39], It can be considered as an extension of the bond matrix or as a mod-ific atinn of Spialter s atom connectivity matrix [38], The BE-inatrix gives, in addition to the entries of bond values in the off-diagonal elements, the number of free valence electrons on the corresponding atom in the diagonal elements (e.g., 03 = 4 in Figure 2-18). 

In connection with a discussion of alloys of aluminum and zinc (Pauling, 1949) it was pointed out that an element present in very small quantity in solid solution in another element would have a tendency to assume the valence of the second element. The upper straight line in Fig. 2 is drawn between the value of the lattice constant for pure lead and that calculated for thallium with valence 2-14, equal to that of lead in the state of the pure element. It is seen that it passes through the experimental values of aQ for the alloys with 4-9 and 11-2 atomic percent thallium, thus supporting the suggestion that in these dilute alloys thallium has assumed the same valence as its solvent, lead. 

To summarize, if the low-lying states connected to the ground state by allowed dipole transition are not valence states but present a predominant Rydberg character, we have to introduce a lot of n) states if not, the value of dynamic polarizability near the first resonance is poor. 

The concept of the molecular connectivity index (originally called branching index) was introduced by Randic [266]. The information used in the calculation of molecular connectivity indices is the number and type of atoms and bonds as well as the numbers of total and valence electrons [176,178,181,267,268]. These data are readily available for all compounds, synthetic or hypothetical, from their structural formulas. All molecular connectivity indices are calculated only for the non-hydrogen part of the molecule [269-271]. Each non-hydrogen atom is described by its atomic 6 value, which is equal to the number of adjacent nonhydrogen atoms. For example, the first-order Oy) molecular connectivity index is calculated from the atomic S values using Eq. (38) ... 

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