ON CHARACTERIZATION OF MOLECULAR SHAPES

We consider the problem of characterization of molecular shape. In par ticular we consider shapes of planar objects derived by fused regular hexagons, i.e., shapes that can be embedded on a regular hexagonal gri d. We have introduced binary codes for the representation of molecular shapes and have limited our attention to planar benzenoidal forms of a constant perimeter. The form of the code depends on the selection of the starting bond and the sense of circling around the molecular peri meter. We selected as the canonical code one that results in the small est binary number for the periphery code. The binary canonical codes o ffer a systematic catalog of all possible shapes defined on the graphi te lattice. The binary codes also fully reflect the symmetry of shapes , while chiral structures show different codes for their mirror forms. Finally, we discussed similarity of shapes (using Hamming distance be tween the codes as the measure of dissimilarity). The numerical magnit ude of the similarity of codes depends on the length of the fragment o f the code to be compared. With more entries (longer the local sequenc es of comparison) a better discrimination between similar objects is o btained. Calculating similarity by comparing codes using a longer ''wi ndow'' (longer local subsequence) was accomplished by a computer progr am written for that purpose (in FORTRAN).