Theory of Optical Activity of Crystalline Benzil

Within the limits of a tight‐binding (Frenkel) exciton model, formulas are derived for the optical rotatory dispersion (ORD) of crystals possessing a screw axis of symmetry. It is seen that transitions having a large electric moment may exhibit ORD with a frequency dependence proportional to ${\mathrm{[\omega }}_0^2{\mathrm{\hspace{0.17em}-\hspace{0.17em}\omega }}^2{]}^{\text{−2}}$ and having intensity proportional to the derivative of exciton energy with respect to wave vector. On the other hand, transitions with a weak electric transition moment but possessing larger magnetic dipole transition moments will show ORD spectra with the more familiar frequency dependence proportional to ${\mathrm{[\omega }}_0^0{\mathrm{\hspace{0.17em}-\hspace{0.17em}\omega }}^2{]}^{\text{−2}}$ . It is shown how the rotational strengths of these latter transitions may sometimes arise from purely molecular origins or may sometimes be attributed to configuration interaction among the simple exciton states. The application of the formulas is demonstrated for crystalline benzil, C₆H₅COCOC₆H₅. Pi‐electron wavefunctions are obtained for this molecule within the Pariser–Paar–Pople set of approximations. Exciton wavefunctions and energies are calculated using both dipole–dipole interactions between molecules and also using more complete expressions for the intermolecular interactions. These functions are then used to predict rotational strengths of the various transitions of the crystal. The calculated results are in qualitative agreement with experiment and tentative conclusions are drawn about the mechanism by which the transitions acquire rotational strength. The difficulty in obtaining good wavefunctions for the molecular $\mathrm{n\pi *}$ excited states seems to be the source of the quantitative discrepancy between theory and experiment in this particular case.