APPLICATIONS OF THE RADIUS DIAMETER DIAGRAM TO THE CLASSIFICATION OF TOPOLOGICAL AND GEOMETRICAL SHAPES OF CHEMICAL-COMPOUNDS

The shape coefficient (I) of a chemical compound is defined as the ratio (D - R)/R, where R is the generalized radius and D is the generalized diameter. Chemical compounds have both a graph-theoretical and a geometrical-shape coefficient, and the properties of these coefficients are examined in this paper. The graph-theoretical bivariate repartition of the (R,D) pairs, named here the "radius-diameter diagram", has been computed for members of a large file of compounds derived from the Chemical Abstracts Services Registry File. This analysis shows many shapes and structural formulas to be absent and suggests that, prior to 1978, organic chemistry had evolved in only a few specialized directions.