Abstract
The connectivity index chi can be regarded as the sum of bond contributions. In this article, boiling point (bp)-oriented contributions for each kind of bond are obtained by decomposing the connectivity indices into ten connectivity character bases and then doing a linear regression between bps and the bases. From the comparison of bp-oriented contributions with the contributions assigned by chi, it can be found that they are very similar in percentage, i.e. the relative importance of each particular kind of bond is nearly the same in the two forms of combinations (one is obtained from the regression with boiling point, and the other is decided by the constructor of the chi index). This coincidence shows an impersonality of chi on bond weighting and may provide us another interpretation of the efficiency of the connectivity index on many quantitative structure-activity/property relationship (QSAR or QSPR) results. However, we also found that chi's weighting formula may not be appropriate for some other properties. In fact, there is no universal weighting formula appropriate for all properties/activities. Recomposition of some topological indices by adjusting the weights upon character bases according to different properties/activities is suggested. This idea of recomposition is applied to the first Zagreb group index M(1) and a large improvement has been achieved.
Highlights
Since the first topological index – the W index [1] was developed and found useful in finding correlations between property and chemical structures, more and more chemists came to know its merits and tried to propose novel topological indices to construct better QSAR/QSPR models
Different operators on one character can even produce several topological indices, and in this way, more than 400 TIs have been proposed. They have contributed greatly to the widespread use of QSAR/QSPR models, but this indiscriminate proliferation of topological indices has produced some criticisms from skeptics of the use of this approach in chemistry: “This disorientation in the search of such molecular descriptors often produces no good correlation with any property, and looks very convoluted in their definition” [2]
Since the only difference between the definitions of χ and M2 is the weights assigned on the connectivity character bases, at least two conclusions can be drawn: (1) the character bases which describe the molecular structure, and the weighting formula applied on the bases are important for the construction of a topological index, and (2) there are no unified weighting formula for same character bases that will satisfy different regression for different properties well
Summary
Since the first topological index – the W index [1] was developed and found useful in finding correlations between property and chemical structures, more and more chemists came to know its merits and tried to propose novel topological indices to construct better QSAR/QSPR models. A novel interpretation is proposed for the success of the connectivity index χ with its impersonality on the bond weighting formula.
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