Delocalized Electronic Excitations and their Role in Directional Charge Transfer in the Reaction Center of Rhodobacter Sphaeroides

In purple bacteria, the fundamental charge-separation step that drives the conversion of radiation energy into chemical energy proceeds along one branch - the A branch - of a heterodimeric pigment-protein complex, the reaction center. Here, we use first principles time-dependent density functional theory (TDDFT) with an optimally-tuned range-separated hybrid functional to investigate the electronic and excited-state structure of the primary six pigments in the reaction center of \textit{Rhodobacter sphaeroides}. By explicitly including amino-acid residues surrounding these six pigments in our TDDFT calculations, we systematically study the effect of the protein environment on energy and charge-transfer excitations. Our calculations show that a forward charge transfer into the A branch is significantly lower in energy than the first charge transfer into the B branch, in agreement with the unidirectional charge transfer observed experimentally. We further show that inclusion of the protein environment redshifts this excitation significantly, allowing for energy transfer from the coupled $Q_x$ excitations. Through analysis of transition and difference densities, we demonstrate that most of the $Q$-band excitations are strongly delocalized over several pigments and that both their spatial delocalization and charge-transfer character determine how strongly affected they are by thermally-activated molecular vibrations. Our results suggest a mechanism for charge-transfer in this bacterial reaction center and pave the way for further first-principles investigations of the interplay between delocalized excited states, vibronic coupling, and the role of the protein environment of this and other complex light-harvesting systems.