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.

Chiroptical structure‐property relations in cyclo[18]carbon and its in silico hydrogenation products

“…However, chiral molecules have twisted wave functions that are hard to reckon in the mind's eye. Recently, we have shown that planar π‐conjugated molecules with symmetries supporting optical activity when oriented, facilitate structure‐property correlations because their π electronic structure can be intuitive . Once the wave functions of optically active compounds can be rendered in a plane, in our experience, the mechanism of optical activity becomes transparent.…”

TDDFT Study of the Optical Spectra of Free and Supported Binary Coinage Metal Hexamers: Effect of Doping and Support

“…The electronic transition involves donor orbitals of highest occupied molecular orbital (HOMO) – 1 or HOMO type, whereas acceptor orbitals are lowest unoccupied molecular orbital (LUMO), LUMO + 1, or LUMO + 2. In most clusters, a significant number of transitions are involved, with small individual contributions, a feature typical of realistic complex systems. , Exceptions are the Au 3 Ag 3 and Au 3 Cu 3 clusters. Finally, only a limited number of electronic transitions lies below 3 eV, mostly with low intensities ( f < 0.1).…”

Optical Activity Anisotropy of Benzil

“…The third Cartesian direction is about zero. Interpreting this tensor in terms of a small number of excited states is difficult because unlike simple hydrocarbons investigated previously, 96,97 a great number of states contribute to the long wavelength value of benzil. For instance, the g xx tensor element for one molecule which has a value of 9.8 bohr 4 , requires summing the contributions from 100 excited states at a minimum.…”