Spectral broadening of interacting pigments: polarized absorption by photosynthetic proteins.

Excitonic interaction between pigment molecules is largely responsible for the static and dynamic spectroscopic properties of photosynthetic pigment-proteins. This paper provides a new description of its effect on polarized absorption spectroscopy, in particular on circular dichroism (CD). We investigate excitonic spectra of finite width and use "spectral moments" to compare 1) inhomogeneously broadened excitonic spectra, 2) spectra that are (homogeneously broadened by vibrations or electron-phonon interaction, and 3) spectra that are simulated by applying convolution after the interaction has been evaluated. Two cases are distinguished. If the excitonic splitting is smaller than the width of the interacting absorption bands, the broadening of the excitonic spectrum can be approximated by a convolution approach, although a correction is necessary for CD spectra. If the excitonic splitting exceeds the bandwidth, the well-known exchange narrowing occurs. We demonstrate that this is accompanied by redistribution of dipole strength and spectral shifts. The magnitude of a CD spectrum is conveniently expressed by its first spectral moment. As will be shown, this is independent of spectral broadening as well as dispersive shifts induced by pigment-protein interactions. Consequently, it provides a simple tool to relate the experimental CD spectrum of a pigment complex to the excitonic interactions from which it originates. To illustrate the potential of the presented framework, the spectroscopy of the LH2 pigment-protein complex from purple bacteria is analyzed and compared for dimer-like and ring-like structures. Furthermore, it is demonstrated that the variability of the CD of chlorosomes from green bacteria can be explained by small changes in the structure of their cylindrical bacteriochlorophyll c subunits.