Role of electronic polarization in the primary charge-transfer states of the purple bacteria reaction center: A polarizable QM/MM study with the integral-exact direct reaction field method

A hybrid QM/MM study with the integral-exact direct reaction field (IEDRF) polarizable embedding scheme developed in the companion paper is performed on the purple bacteria reaction center of Rhodobacter sphaeroides in order to investigate how polarization induced in the protein matrix helps to stabilize the primary charge-transfer state relative to the exciton states of the special pair. The protein environment is represented by point charges and induced dipoles that are coupled to the QM region via the integral-exact direct reaction field Hamiltonian, which can simultaneously describe differential solvation of multiple electronic states of different polarities. Treating the special pair, $P=P_L P_M$, and one of the bacteriopheophytins ($H_L$ or $H_M$) quantum-mechanically, we compare excitation energies computed at the $\omega$PBEh time-dependent density functional theory level for charge-transfer states along the active and inactive branches. Thermal fluctuations on the electronic-state energies are included by extracting snapshots from a molecular dynamics trajectory. With IEDRF embedding, the reaction field induced in the protein matrix stabilizes long-range charge-transfer (CT) states by over 1.0 eV, shifting them below the exciton states. The protein environment favors charge separation along the active $L$ branch. With only electrostatic embedding, the CT states are found $>$0.5 eV above the exciton states, and asymmetry between the branches is diminished. The polarization in the protein is largely dictated by the secondary structure, with induced dipoles pointing along the axes of $\alpha$-helices. The relaxation of dipoles on the excited state provides similar stabilization of both branches, however the ground state polarization, captured by IEDRF, screens $P^+ H_L^-$ more than $P^+ H_M^-$ and is thus key to directing the CT towards the active branch. The different ground-state dielectric environment of the two branches is confirmed by computing relative local fields at key carbonyl probes. With IEDRF embedding, we find the local fields to be in near quantitative agreement with the interpretations of recent vibrational Stark-effect experiments, while the agreement is diminished for electrostatically embedded QM/MM calculations. These results caution against QM/MM calculations with electrostatic embedding alone, because CT states in a rigid, dense protein matrix are mostly stabilized by the fast electronic polarization of the surrounding medium.