Kramers−Kronig Transformation for Optical Rotatory Dispersion Studies

The Kramers-Kronig (KK) transform method for deriving optical rotatory dispersion (ORD) from electronic circular dichroism (ECD) has been analyzed. Three different numerical integration methods for the KK transform have been evaluated, and the method proposed by Ohta and Ishida has been used for further calculations. Using this method, the quantum mechanical predictions of electronic circular dichroism (ECD) have been converted to corresponding ORD and compared with that derived from the linear response method. For three molecules exhibiting monosignate ORD in the nonresonant long wavelength region, the KK transform of ECD associated with the lowest energy electronic transition is found to give ORD values close to those obtained with the linear response method. For molecules exhibiting bisignate ORD in the nonresonant long wavelength region, the KK transform method may not provide the correct results. In the resonant region, the KK transform method provides a computationally economical alternative for predicting ORD. While the KK transform method works much like sum-over-states method for ORD, the former offers convenience in transforming the experimental ECD spectrum without the need for spectral curve fitting.