Kramers-Kronig transformation of experimental electronic circular dichroism: application to the analysis of optical rotatory dispersion in dimethyl-L-tartrate.

When a limited region of the experimental electronic circular dichroism (ECD) spectrum is subjected to Kramers-Kronig (KK) transformation, the resulting optical rotatory dispersion (ORD) may or may not reproduce the experimentally measured ORD in the long-wavelength nonresonant region. If the KK transform of experimentally measured ECD in a limited wavelength region reproduces the experimentally measured ORD in the long-wavelength nonresonant region, then that observation indicates that the ORD in the long-wavelength nonresonant region should be satisfactorily predicted from the correspondingly limited number of electronic transitions in a reliable quantum mechanical calculation. On the other hand, if the KK transform of experimentally measured ECD in a limited region does not reproduce the experimentally measured ORD in the long-wavelength nonresonant region, then it should be possible to identify the ECD bands in the shorter wavelength region that are responsible for the differences between experimentally observed ORD and KK-transformed ECD. This approach helps to identify the role of ECD associated with higher energy-excited states in the nature of ORD in the long-wavelength nonresonant region. These concepts are demonstrated here by measuring the experimental ECD and ORD for dimethyl-L-tartrate in different solvents. While ECD spectra of dimethyl-L-tartrate in different solvents show little variation, ORD spectra in the long-wavelength nonresonant region show marked solvent dependence. These observations are explained using the difference between experimental ORD and KK-transformed ECD. Quantum mechanical predictions of ECD and ORD are also presented for isolated (R, R)-dimethyl tartrate at the B3LYP/aug-cc-pVDZ level.