Spectral Moments of the Edge-Adjacency Matrix of Molecular Graphs. 2. Molecules Containing Heteroatoms and QSAR Applications

A novel substructural approach to structure−property and structure−activity relationships studies is proposed. The method is based on the computation of spectral moments of the edge-weighted adjacency matrix. In the present work, bond distances are used as bond weights in the diagonal entries of edge matrix. Spectral moments of the edge-weighted adjacency matrix are expressed in terms of structural fragments present in molecules via algebraic expressions. Boiling points of 58 alkyl halides were well described by the present approach, and this property was expressed as a linear combination of structural fragments of the studied molecules. QSAR applications of the novel approach are explored by studying the antifungal activity of benzyl alcohols. An equation expressing contributions of each substituent in benzyl alcohols to the antifungal activity is obtained. The methodology proposed here permits the rational design of novel compounds with improved activity, which is illustrated for benzyl alcohol derivatives.