On computation of optimal parameters for multivariate analysis of structure‐property relationship

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Abstract
We outline a search for optimal parameters involving heteroatoms for use in multivariate regression analysis in structure‐property and structure‐activity studies. The problem consists of determining optimal numerical values for the diagonal elements of the adjacency matrix in graphs with atoms of different kind. In particular we consider weighted paths as the basic molecular descriptors and search for optimal parameters for carbon atom and oxygen atom in a correlation of molecular structure with isomeric variations in the boiling points of hexanols. Standard error is taken as the criterion for the selection of the optimal parameters. The weighting algorithm restricts the diagonal entries to values greater than −1. The selection of positive diagonal values leads to reducing the path numbers and the negative values lead to enlarging the role of path numbers relative to the zero diagonal values implied by simple graphs in which heteroatoms are not discriminated. A systematic search for optimal parameters for alcohols gave for carbon atom and oxygen atom diagonal entries: x = 1.50 and y = −0.85 respectively when a single path number is used as a descriptor and x = −0.15 and y = −0.94 when two path numbers are used. The parameters derived for 17 hexanols have been successively applied to 37 heptanols demonstrating thus transferability of the parameters.

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