Hückel theory and optical activity

Abstract

Optical rotations and rotatory strengths are calculated for achiral, conjugated hydrocarbons with the aim of determining to what extent the sum-over-π → π* rotatory strengths are sufficient to account for nonresonant optical activity. The separability of σ and π electrons might provide a short cut to the interpretation of chiroptical structure-property relations in some cases. It is shown that by restricting the analyses to planar, C(2v)-symmetric π-systems and their one electron HOMO-LUMO excitations, an intuitive understanding of the vexing property of optical activity is forthcoming for the following reasons: Hückel wave functions are simply calculated, and in some cases, they can even be approximated by inspection of structure. Wave functions of planar molecules can be multiplied with one another graphically or, in the mind's eye, to yield transition electric and magnetic moments. The gyration tensors have just one independent component. Transition dipole moments are orthogonal to one another. And, the most optically active directions are found at their bisectors. Throughout, emphasis is on the evaluation of long wavelength optical rotation, consistent with quantum chemical computation, using simple models that are part of the fabric of organic chemistry pedagogy.