We have performed fully quantum mechanical simulations of excitation energy transfer within the peripheral light harvesting complex (LH2) of Rhodospirillum molischianum at room temperature. The exciton-vibration Hamiltonian comprises the 16 singly excited bacteriochlorophyll (BChl) states of the B850 (inner) ring and the 8 states of the B800 (outer) ring with all available electronic couplings. The electronic states of each chromophore couple to 50 intramolecular vibrational modes with spectroscopically determined Huang-Rhys factors and to a weakly dissipative bath that models the biomolecular environment.
Simulations following photoexcitation of various electronic eigenstates were performed using the small matrix path integral (SMatPI), a numerically exact decomposition of the quasiadiabatic propagator path integral (QuAPI). We found that the energy relaxation process in the 24-state system is highly nontrivial. When the photoexcited state comprises primarily B800 pigments, a rapid intra-band redistribution of the energy sharply transitions to a significantly slower relaxation component which transfers 90% of the excitation energy to the B850 ring. The mixed character B850* state lacks the slow component and equilibrates very rapidly, providing an alternative energy transfer channel. This (and also another partially mixed) state has anomalously large equilibrium population, suggesting a shift to lower energy by virtue of exciton-vibration coupling. The spread of the vibrationally dressed states is smaller than that of the eigenstates of the bare electronic Hamiltonian. The total population of the B800 band is found to decay exponentially with a 1/e time of 0.5 ps, in good agreement with experimental results.