**Milan Randic ^{a} and Subhash Basak^{b}**

*On Construction of Optimal Molecular Descriptors*

^{a}Dept. of Mathematics and Computer Science, Drake University,
Des Moines, Iowa

^{b}National Resources Research Insitute, University of Minnesota,
Duluth, Minnesota

We will outline construction of a novel class of molecular descriptors to be used in structure-property-activity studies. In contrast to all descriptors hitheto used in the litersture the novel class of descriptors involve variable part. This allows search for optimal values for the variable parameters such that the standard error in multiple regression analysis (MRA) is minimized. We will describe construction of variable connectivity indices, generalized Hosoya and Wiener index that include variable bond weights, and will in particular describe construction of path numbers involving variable bond weights. We will show use of novel descriptors on set of alcohols and their properties. Besides the boiling points of alcohols we will consider surface cavity area (SCA), log P (water/octanol partition) and log S (solvation). In the cases of SCA and log S the variable descriptors lead to much better MRA statistics then hitherto published alternative approaches, reducing the standard error almost to half of the currently reported values. The optimal values for the variable parametres depend on the number of descriptors used, although not strongly. However, the optimal weights depend more strongly on the property considered. For example, carbon-oxygen bond has weight about x = 2 when boiling points are considered, x = 3 for log S, and x=4 for log P, but for SCA the optimal weight is about x=1/2. The regression results based on novel optimal descriptors will be presented by adopting the orthogonalization procedure that produce stable equations.

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