Molecular Shapes and Chirality

In this report we consider quantitative characterization of molecular chirality based on the binary code that describes the shape of the molecular periphery. We have limited our attention to chirality in two-dimensional space and consider benzenoid forms that are chiral and have constant perimeter P, i.e., we consider planar structures constructed from fused regular hexagons. The binary codes used assign either zero or one to CC bonds on the molecular periphery depending on whether we turn right or left, respectively, at each branching site of graphite lattice as we move around the molecular periphery. We have examined all benzenoid structures having molecular perimeter of 22 and fewer CC bonds (over 30 pairs of chiral structures). Since enantiomers have distinct codes, we based our quantitative measure of chirality on the degree of dissimilarity between the codes for a structure and its mirror image. As discussed in the text, the measure of dissimilarity depends on the length of the segments of the codes...

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