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.

Figures (6)

• Figure 1: Optimized protein-embedded PSII-RC (overall 1331 atoms) with specific segments highlighted: (a) special-pair chlorophylls with Mg centers ($P_{D1}$ and $P_{D2}$), 270 atoms; (b) histidine residues (with backbone) providing axial coordination to the Mg centers of $P_{D1}$ and $P_{D2}$, 68 atoms; (c) accessory chlorophylls with Mg centers ($Chl_{D1}$ and $Chl_{D2}$), 270 atoms; (d) pheophytins with hydrogen-coordinated macrocycles ($Pheo_{D1}$ and $Pheo_{D2}$), 272 atoms; (e) protein-bound plastoquinone cofactors ($Q_A$ and $Q_B$), 218 atoms; (f) surrounding protein scaffold residues (polypeptide backbone), 233 atoms.
• Figure 2: Real-space inverse dielectric functions for the isolated and protein-embedded PSII-RC, evaluated along Cartesian rays from the origin. Panels (a)–(c) show one-dimensional cuts where (a) $|x-x'|$ is varied with $y-y'=z-z'=0$, (b) $|y-y'|$ is varied with $x-x'=z-z'=0$, and (c) $|z-z'|$ is varied with $x-x'=y-y'=0$.
• Figure 3: Polarization-resolved full TDHF@$v_W$ optical spectra for the isolated and protein-embedded PSII-RC systems. Both systems use a transition space of $N_v=200$ and $N_c=400$ orbitals. Laser polarization directions are denoted as $x$-pol, $y$-pol, and $z$-pol.
• Figure 4: The $y$-polarized TDHF@$v_W$ spectra for the isolated and protein-embedded PSII-RC, together with the transition density isosurfaces corresponding to the three dominant absorption peaks in both systems, labeled as (i), (ii), and (iii). Isovalues of $\pm 0.00005$$\text{Bohr}^{-3/2}$ are used for all transition densities with purple used for positive values and grey for negative values.
• Figure 5: Same as Fig. \ref{['fig:densy']}, but for the $z$-polarization and the first absorption peak, labeled as (iv).