Valence connectivity

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. 

Inasmuch as (ambi)valence connects with medical alchemy (exemplified by Paracelsianism in the sixteenth century), it stands at odds with philosophical alchemy (anti-Paracelsianism). But of course, valence in the sense 1 am using here is only one of a number of possible registers. In philosophical alchemy (ex-plicidy defined as non-practice), the corresponding term to valence might be virtue. 

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 ... 

Differential connectivity indices are defined as differences between connectivity indices "x d -> valence connectivity indices [Hall and Kier, 1986 Kier and Hall, 1991] ... 

It is a solvent polarity index defined [Kier and Hall, 1986] as the first-order valence connectivity index divided by the number Nf of discrete, isolated functional groups in order to account for multiple interaction sites as ... 

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 ... 

Relative chirality indices and chirality correction factors forthe two enantiomers shown below, together with valence vertex degrees and first-order valence connectivity index of the functional groups. 

Differential connectivity indices (or coimectivity differences) are defined as the difference between connectivity indices and valence connectivity iruiices" x [Hall and Kier, 1986 Kier... 

To account for nondispersive force effects, the relative valence connectivity indices to nonpolar compounds were defined as... 

By replacing the vertex degree 5 by the —> valence vertex degree 5 in the formulas reported above, similar valence connectivity indices were proposed [Kier and Hall, 1981,1983b], denoted by able to account for the presence of heteroatoms in the molecule as well as double and triple bonds (Table C6). 

Table C7 Some connectivity and valence connectivity indices for the data set of phenethylamines (Appendix C- Set 2).

Vukicevic, D. and Graovac, A. (2004c) Valence connectivity versus Randic, Zagreb and modified Zagreb index a linear algorithm to check discriminative properties of indices in acyclic molecular graphs. Croat. Chem. Acta, 77, 501-508. 

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). 

Figure 2.3. Illustration of calculation of zeroth-order and first-order valence connectivity...

As shown in figures 2.5-2.8, the zeroth-order and first-order connectivity indices correlate quite strongly with N, and thus also with each other. The correlations of N with the valence connectivity indices °%v and are both much weaker than the correlations of N with x and... 

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. 

Weight factors of 10/J(group) were used in developing the correlation for J. The best fit possible without using any atomic or group correction terms was obtained when the number of hydrogen atoms NH in the repeat unit and the zeroth-order valence connectivity index °%v were... 

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