B800-to-B850 relaxation of excitation energy in bacterial light harvesting: All-state, all-mode path integral simulations

Abstract

We report fully quantum mechanical simulations of excitation energy transfer within the peripheral light harvesting complex (LH2) of Rhodopseudomonas molischianum at room temperature. The exciton–vibration Hamiltonian comprises the 16 singly excited bacteriochlorophyll 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 of the excitation energy transfer following photoexcitation of various electronic eigenstates are performed using the numerically exact small matrix decomposition of the quasiadiabatic propagator path integral. We find 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 that 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 an 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, which is in good agreement with experimental results.

Tight inner ring architecture and quantum motion of nuclei enable efficient energy transfer in bacterial light harvesting

“…The rate obtained from the path integral calculations is in good agreement with the experimental value of 1.08 ps (49). Furthermore, the total ring population curves are nearly identical to those obtained with eigenstate initial conditions (50). Snapshots and molecular illustrations of excited pigment populations are shown in Figs.…”

Excitation Energy Transfer in Bias-Free Dendrimers: Eigenstate Structure, Thermodynamics, and Quantum Evolution

“…It uses two parameters, the QuAPI memory length L and the entanglement r max . Recent work has shown 48 that the entanglement of the path integral variables may be considerably shorter than the memory length, facilitating convergence in very challenging situations. Representative convergence tests are shown for some of the most challenging cases presented in section 5.…”

“…Feynman’s path integral formulation − offers unique capabilities for treating large numbers of vibrational degrees of freedom at any temperature. Real-time path integral methods developed in our group − were recently used to investigate EET through all-mode exciton–vibration calculations in the LH2 complex of purple bacteria, ,, in J aggregates of perylene bisimide − (PBI), in cofacial porphyrin dimers, as well as the coupled spin dynamics of Ising chains interacting with model harmonic baths . Even though generic characteristics such as decoherence, equilibration, and some aspects of spectral characteristics , and density evolution are common to all these systems and captured through simplified system-bath models, , the striking finding of such all-state, all-mode path integral studies (where the exciton-vibration parameters were treated with their specific molecular values without simplification) is the complexity of the ensuing dynamics and the diversity of observed behaviors …”

Quantum State-to-State Rates for Multistate Processes from Coherences

“…This is an exact, analytically derived decomposition of the quasi-adiabatic propagator path integral (QuAPI) which allows iterative propagation with small, n 2 × n 2 matrices, thereby obviating the tensor storage of the iterative QuAPI algorithm. , The real-time path integral , is an exact, fully quantum mechanical formulation of time-dependent quantum mechanics that allows an analytical treatment of harmonic bath degrees of freedom without approximation . The SMatPI algorithm employs two convergence parameters, the memory length L and the entanglement length r max , which in many situations is shorter than the memory induced by the bath. , The coupled kinetic equations were solved using the numerical differential equation solver of Mathematica…”

“…39 The SMatPI algorithm employs two convergence parameters, the memory length L and the entanglement length r max , which in many situations is shorter than the memory induced by the bath. 33,40 The coupled kinetic equations were solved using the numerical differential equation solver of Mathematica. 41 Figures 2−5 the rates obtained from the imaginary parts of the coherences, for several multistate model systems.…”