An analytical data inversion method for magnetic circular dichroism spectra dominated by the "B-term"

Abstract

A simple procedure is developed enabling the analytical inversion of an (unpolarized) absorption spectrum combined with a Magnetic Circular Dichroism (MCD) spectrum to resolve two overlapping bands of orthogonal polarization. This method is appropriate when (i) the overlapping transitions are well isolated from other bands, and (ii) when their electronic spacing is large enough so that the "A-term" and "C-term" contributions to the MCD spectrum can be ignored and hence only the "B-term" contribution need be considered. We apply this procedure to assign the Q-band system of chlorophylls, though similar challenges also commonly arise throughout both conventional and X-ray MCD (XMCD) spectroscopy. Analytical data inversion has not previously been possible as the inversion process is two-fold underdetermined. We show that the assumptions of isolated spectra and "B-term" dominance yields one generally valid constraint, leaving only one quantity unspecified by the experimental data. For some systems, an approximation leading to equal but opposite sign B-term magnitudes of the two components may be reasonable, but for chlorophyllides we find this constraint to be inappropriate. Instead, we constrain a bounded variable controlling the relative absorption strengths. Derived spectral bandshapes of the individual components are shown to be insensitive to its particular value, allowing weak spectral components of one polarization overlapped by intense components of the other to be immediately exposed. This is demonstrated for the chlorophylls, molecules for which the failure to detect such weak features historically led to incorrect proposals for the Q-band assignments.