Modelling the bacterial photosynthetic reaction center. VI. Use of density-functional theory to determine the nature of the vibronic coupling between the four lowest-energy electronic states of the special-pair radical cation

Abstract

It is now over ten years since the first FTIR spectra were recorded of the radical cation of the special-pair, a dimer of bacteriochlorophyll molecules that forms the primary electron donor responsible for primary charge separation in bacterial photosynthesis. While spectra of this type promise to reveal much concerning the role of the special pair electron donor in photosynthesis, attempts to model and interpret them have been limited by poor knowledge of the vibrationally specific aspects of the electron–phonon coupling and have thus been restricted to crude model calculations only. We develop techniques through which density-functional theory can be employed to evaluate most of the unknown properties. This includes symmetric-mode displacements, antisymmetric-mode vibronic coupling constants, and interstate electronic couplings evaluated for interactions between the four lowest-energy states of the special-pair cation radical: the ground state, the primary hole-transfer state, and states involving these two combined with SHOMO to HOMO transitions. Geometry optimizations are performed for all four states of the dimer while vibrational analyses are obtained for the first two; vibronic coupling constants are extracted from analysis of stolen infrared transition moments using Herzberg–Teller theory. Quantitatively, these results are employed in the subsequent paper in this series to simulate the observed spectra. Qualitatively, these results indicate that: (1) vibronic coupling occurs through a large number of antisymmetric modes of the dimer rather than through a small number of strongly active modes, (2) the role of symmetric vibrational motions of the dimer is only minor, (3) that the active symmetric modes are significant in number and low in frequency, (4) that vibronic coupling between the hole-transfer state and the SHOMO to HOMO state is relatively weak and influences spectra only near resonance, and (5) that the calculated electronic couplings are qualitatively realistic and may provide an explanation for the much weaker coupling observed in chlorophyll-containing reaction centers.