The Variable Connectivity Index

In Table 6.12, we illustrate variations of the connectivity indices x(x, y), x, y), and y) for 1-aminohexane as a function of the weights for nitrogen atoms while assuming x = 0 for carbons atoms. In this example, we assumed x = 0 for carbon atoms and varied only the weights y for nitrogen in the interval [0.50, -0.95]. As one can see, in this way, one obtains a set of values for the connectivity indices to choose from. 

In Table 6.14, we show the variable connectivity index y(x, y), the experimental boiling points (bp), the calculated bp, and their difference for the regression of the boiling points of amino-alkanes. The final regression eqnation, 

Variation of the Standard Error for Different Weights for Carbon (x) and Nitrogen (y) in Smaller Amino-Alkanes 

The Optimal Variable Connectivity Index, Experimental and Calculated Boiling Points and Their Difference 

FIGURE 6.5 Correlation of the experimental boiling points of 16 primary amines versus the calculated boiling points using the variable connectivity index. 

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Randic M, Pompe M (2001a) The variable connectivity index %f versus the traditional molecular descriptors A comparative study of against descriptors of CODESSA. J. Chem. Inf. Comput. Sci. 41 631-638. 

Randic, M. and Basak, S.C. (2001c) On use of the variable connectivity index in QSAR toxicity of aliphatic ethers. /. Chem. Inf. Comput. Sci., 41, 614-618. 

Hence, the variable connectivity index is a function of several variables and can assume numerical values only after particular values for x,y, and z are selected. In contrast, if we set x = 0,y = 0, and z = 0, we obtain the rigid index x for tryptophan. The variable vertex connectivity index remained overlooked... 

QSAR, as the acronym implies, is about quantitative structure-activity relationships and not about quantitative mechanistic-activity relationships We will comment on few of the errors on the list of 21 types of error, which, in our view, are not errors and on a few questions for which have been offered answers for those interested in considering them. It is not our aim here to critically review the paper How Not to Develop a Quantitative Structure-Activity or Structure-Property Relationship by Dearden et al but to make our contribution to How to Develop a Quantitative Structure-Activity or Structure-Property Relationship. One particular matter that we will address is, in our view, a misrepresentation in the article by Dearden et al. of the connectivity index and the variable connectivity index. 

Quarter Century Symposium to celebrate 25 years of the publication of the article on the connectivity index. The symposium was attended by some 25 scientists for a two-day meeting offering an opportunity to participants to present some more recent results for the connectivity index [20]. Equally, as a significant development, one may mention various generalizations and extensions of the connectivity index, one of which is the variable connectivity index, which is discussed later in this chapter. 

They are ordered from left to right and from top to bottom relative to their hypotensive activity (experimental EDjo values in pg/kg) obtained from dose-response curves following intravenous administration to anaesthetized, nonmotentive rats, that is, in vivo effective doses which produce anesthesia in 50% of the population. These compounds were used to illustrate construction of the variable connectivity indices in the seminal paper on the variable connectivity index [109]. All the data has been taken from particularly detailed research by Timmermans and Van Zweiten [110], who studied a set of 27 hypotensive imidazolidines, which in addition to the 17 choro derivatives considered here, include nine additional compounds having other heteroatoms fluorine, bromine, nitrogen, and oxygen. In the report that we selected, these compounds were excluded because they represent too small a sample to allow one to determine with acceptable certainty their relative weights for the construction of the variable connectivity indices. 

The optimal variables found were the following for carbon, the optimal weight was 1.27 for chlorine, the optimal weight -0.235 for bromine, the optimal weight -0.653 and for iodine, the optimal weight was -0.8005. It is known from the early calculations with the variable connectivity index that small positive values for optimal weights have little influence on affecting bond contributions to the overall... 

The variable connectivity index has also been waiting for greater attention since 1991, when it was first briefly outlined [6]. It has received some attention, having a few citations short of 100, but in our view, it deserves at least having a few citations short of 1000, if not 10,000. You decide whether this speculation is sound or unsound. What makes the variable connectivity index unique, and this holds for other variable indices, is the following ... 

Here the sign y(x, y) is the symbol for the variable connectivity index. The slight increase of the variable parameters for carbon atoms suggests a lesser role of carbons in comparison with halogen atoms on the boiling points of these compounds. 

The valence connectivity indices not only represent, strictly speaking, an ad hoc solution for discrimination of heteroatoms, even if plausible, but indirectly presume that there are universal valence weights characteristic for individual heteroatoms and valid for all their molecular properties. That the latter assumption is questionable follows from the already mentioned few regression equations of Kier and Hall in which the classical connectivity index x produced better correlations than the corresponding valence connectivity index. Recognition that different molecular properties may require different heteroatom weights led to the idea of the variable connectivity index. 

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