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.

The Importance of Motions that Accompany Those Occurring Along the Reaction Coordinate

“…Indeed, the missing bands remained unobserved for 50 years until we pioneered techniques employing quantitative vibronic coupling analyses, [101] paralleled by the development of the first-ever technique permitting analytical inversion of observed MCD and absorption spectral data to yield the critically required state polarization information. [105] Both of these methods allow for quantitative identification of all expected bands, verifying the vibronic coupling hypothesis. Another significant obstacle that was overcome concerned the interpretation of many highly influential spectra, measured over 30 years, of chlorophyll-a in ether at low temperature.…”

Putting David Craig’s Legacy to Work in Nanotechnology and Biotechnology

“…2b. This scenario leads naturally to three diabatic electronic states, the ground state G, the singly excited state S, and the doubly excited state D. Antisymmetric vibrations couple G to S in analogy to what happens in electron transfer, but the same vibrations necessarily also couple S to D. Therefore there exists one low-lying conical intersection seam for the G to S interaction and the process can be considered as a pseudo Jahn-Teller effect, [19,[94][95][96] but there also exists a second seam linking S to D. This seam changes to properties of S significantly, just as the first seam affects G and S, and hence by an indirect mechanism D influences G. If one assumes that the vibronic coupling between S and D is the same as that between G and S (in practice small differences arise owing to the effects of electron correlation), then a renormalization of the full set of coupled equations is possible that allows the properties of the groundstate to be re-represented in terms of a simple two-state model analogous to electron-transfer theory. [180] This tells why twostate models involving only one conical intersection seam have been so successful in numerical applications, but it also indicates that the parameters appearing in such approaches get renormalized from a more basic set of parameters in different ways.…”

“…We showed that one of these unknowns can be determined based on other assumptions already used in the analysis, and that it was possible to construct a second unknown whose value acts to rescale component spectra but not significantly change their shape. [95] The result is a general method that can be used to get critical polarized bandshape information from MCD experiments. Had Gouterman had these simple equations in 1962, he would no doubt have immediately correctly assigned the spectrum of Chl-a.…”

“…For it, a simple model with just two or three parameters could qualitatively describe a wide range of spectroscopic and kinetics properties. [180] Analogous quantitative treatments of chemical properties based on say pseudo Jahn-Teller approaches [19,[94][95][96] have been very successful but require parameterization, often based on accurate ab initio calculations, for each property of interest. These approaches focus on two diabatic surfaces and the conical intersection that links them, by analogy to electron-transfer theory, but the deduced parameters are not transferrable either for the evaluation of different properties of the same system or else between similar systems.…”

“…Two data analysis methods were developed to reveal them, a computational method for fitting the observed spectra to Gouterman's model appropriate for very strong coupling, [47] and an experimental method providing a new way of qualitatively interpreting data coming from MCD experiments. [95] Both approaches identified the missing bands in all species, with the fitting procedure delivering quantitative information concerning the unperturbed location of the Q x origin (the property deduced by electronic-structure calculations such as CAM-B3LYP), the Q x intensity, and the vibronic coupling strength between Q x and Q y . These results were in excellent agreement with the previous CAM-B3LYP calculations, and so a new assignment of the spectrum of Chl-a was established.…”