The use of cross-correlation functions in the analysis of circular dichroism spectra

Following Gordon, we show that the circular dichroism (CD) spectrum is proportional to the imaginary part of the Fourier transform of the cross-correlation function of the electric dipole moment and of the magnetic dipole moment. Such a result is useful in the study of CD band shapes, and also in obtaining a spectrum from a classical trajectory calculation, as was done for absorption by Noid, Koszykowski, and Marcus. For ergodic and multiperiodic regimes, the formula reduces to the Fourier cross spectrum of the two moment functions. As an application, we have run classical trajectories calculations for two coupled CH stretchings belonging to a chiral HCCH fragment, in the fixed partial charge approximation. Two sets of results are presented, relative to low and high total energy: Comments are made about the spectroscopic manifestation of normal, local, and chaotic modes.