Approximate symmetry characteristics using fuzzy-subset theory study for chiral transitions of allene-1,3,-dihalides

Abstract

Based on our study of the application of fuzzy-subset theory to the characterization of imperfect symmetry in some stable molecular systems and simple dynamic molecular systems, we analyze the internal rotation process of allene-1,3- dihalides. Allene-1,3-dihalides (CHX=C=CHY, where X and Y may be the same or different halogen atoms) are optically chiral nonplanar molecules. The two end-groups may internally rotate about the near straight linear C=C=C axis, and the molecule may change its chirality. The internal rotation process may pass through two different planar transition state (TS): cis-TS and trans-TS, which belong to C2v and C2h point groups (as X and Y to be same), respectively. The intrinsic reaction coordinate (IRC) corresponding to the two TS processes is denoted as cis-IRC and trans-IRC. However, for the whole IRC reaction process, only their subgroup C2 well-defined symmetry remains. Other symmetry transformations in C2v and C2h point groups can only be examined in terms of imperfect symmetry, although there appear certain reaction reversal joint point group G(RcC2v) and G(RtC2h) well-defined symmetry in the dynamics through the IRC processes. If X and Y are different, the stable molecule has no conventional nontrivial point group symmetry. The internal rotation processes may pass through two different planar TS’s (cis-and trans-TS). The TS will still be a planar molecule belonging to CS point group with the molecule plane as its symmetry plane. Other states in the IRC may belong to certain reaction reversal joint point groups, G(RM)C and G(RM)T. We have thus examined the approximate symmetry of MO’s related to C2 point group. Moreover, we have also analyzed the membership functions, representation components, and their relationships shown in the MO fuzzy main representation correlation diagrams.