Analysis of optical activity in terms of bonds and lone-pairs: The exceptionally large optical rotation of norbornenone

Norbornenone, which has both a C=O and a C=C chromophore in a rigid bicyclic hydrocarbon framework, exhibits optical rotation (OR) an order of magnitude larger than that of similar molecules with only one of these chromophores (e.g., α-pinene). Its OR is also very sensitive to approximations in electronic structure calculations. The present study demonstrates a novel approach to interpret optical rotation using familiar concepts of chemical bonding, aided by first-principles calculations. A theoretical procedure is developed for analyzing the OR tensor components of a molecule in terms of individual bonds and lone pairs. The link between the chemists bond and quantum mechanics is provided by localized molecular orbitals obtained from density functional theory (DFT) calculations. Delocalization of π orbitals is shown to play a crucial role in the large OR of norbornenone, as hinted by the DFT delocalization error inherent in many standard functionals and confirmed by detailed analysis. The OR contributions generated by the double bond in α-pinene are even stronger than that of norbornenone. The isotropic average, observed in solution or in gas phase, is small as a result of cancellation of tensor components with opposite signs. The electronic coupling and delocalization of the C=C π bond and the C=O oxygen π lone pair in norbornenone selectively enhance one of the OR tensor components, resulting in the exceptionally large negative isotropic OR.