Environment-Induced Exciton Renormalization in the Photosystem II Reaction Center

Abstract: Protein electrostatics tune excitation energies in the Photosystem II reaction center (PSII-RC), yet a fully quantum-mechanical many-body description of how the surrounding protein environment renormalizes excitons has remained computationally inaccessible. The Bethe-Salpeter equation (BSE) within many-body perturbation theory accurately describes excitonic physics through an explicit electron-hole interaction, but is prohibitively expensive for systems containing thousands of valence electrons. Here, we show that for sufficiently large systems the BSE becomes simpler to solve when treated with modern stochastic sampling techniques, as atomistic interactions self-average. In this regime, the effective electron-hole interaction mediated by the environment is governed by collective $k$-dependent polarization. These insights enable an ab initio study of the PSII-RC in which all six chlorins forming the hexameric dye core are treated explicitly together with a roughly seven Angstrom local protein environment. We directly compare the low-lying optical excitations of the isolated chromophore hexamer (1276 valence electrons) and the protein-dye cluster (3238 valence electrons). For $Q_y$ excitations near 680 nm, inclusion of the protein environment induces polarization-dependent energy shifts, redistributes spectral weight, and alters exciton delocalization and pigment character. Lateral and transverse asymmetries in the low-lying excited states are captured at the BSE level of theory. These results establish that we now have the tools for many-body calculations of biological nanostructures.