Comparative rotatory power of bent and twisted polyynes

Abstract

Linear polyynes of the formula C18H2 (symmetry D∞h) were bent in silico by progressively introducing CCC angles less than 180°. The bent structures (symmetry C2v) were then twisted by introducing torsion angles across the CCCC segments by as much as 60°. The gyration tensors of these 19 structures (linear, bent, and twisted) were computed by linear response methods. Bending is massively generative of optical activity in oriented structures, even achiral structures, whereas twisting in conjunction with bending, serves to linearize the molecules and diminish maximally observable optical activity. This computational exercise is intended to unbind the infelicitous linkage of optical activity and chirality, which is only meaningful in isotropic media. Although bent structures are not optically active in solution—the spatial average of the optical activity is necessarily zero—solution measurements that deliver the spatial averages are a special class of measurements, albeit the overwhelmingly most common chiroptical measurements, that prejudice our common understanding of how π‐conjugated structures generate gyration. Bending is far more effective than twisting at generating optical activity along some directions for oriented structures. The respective contributions from the transition electric dipole–magnetic dipole polarizability and the transition electric dipole–electric quadrupole polarizability are compared.

Computed Gyration Tensors of Knotted Chiral and Achiral Topological Stereoisomers of C60 Cyclocarbons

“…We showed that curvature is generative of OA, even for planar, bent carbon chains C 18 H 2 . [75] 4 1 may be more responsive than 3 1 because it has a larger integrated curvature. Increased curvature supports larger magnetic dipole transition moments.…”

“…The electric dipole-magnetic dipole contribution dominates as we have seen before in extensively π-conjugated systems. [32,33,36,75] Although the approximately S 4 symmetric 4 1 is achiral in its ground state, it has OA when oriented. The absolute eigenvalues of the gyration are nearly twice as great as those of 3 1 , its chiral stereoisomer, equating to a comparable OA.…”