Comparative rotatory power of bent and twisted polyynes

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 C_2v) 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.