A site-dependent spectral density system–bath model of the Fenna–Matthews–Olsen (FMO) pigment–protein complex is developed using results from ground-state molecular mechanics simulations together with a partial charge difference model for how the long-range contributions to the chromophore excitation energies fluctuate with environmental configuration. A discussion of how best to consistently process the chromophore excitation energy fluctuation correlation functions calculated in these classical simulations to obtain reliable site-dependent spectral densities is presented. The calculations reveal that chromophores that are close to the protein–water interface can experience strongly dissipative environmental interactions characterized by reorganization energies that can be as much as 2–3 times those of chromophores that are buried deep in the hydrophobic protein scaffolding. Using a linearized density matrix quantum propagation method, we demonstrate that the inhomogeneous system–bath model obtained from our site-dependent spectral density calculations gives results consistent with experimental dissipation and dephasing rates. Moreover, we show that this model can simultaneously enhance the energy-transfer rate and extend the decoherence time. Finally, we explore the influence of initially exciting different chromophores and mutating local environments on energy transfer through the network. These studies suggest that different pathways, selected by varying initial photoexcitation, can exhibit significantly different relaxation times depending on whether the energy-transfer path involves chromophores at the protein–solvent interface or if all chromophores in the pathway are buried in the protein.

Influence of Site-Dependent Pigment–Protein Interactions on Excitation Energy Transfer in Photosynthetic Light Harvesting B

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on Thermo Field Dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. The solution of Thermo Field Dynamics equations with a novel technique for the propagation of Tensor Trains (Matrix Product States) is implemented and discussed. The methodology is applied to the study of the exciton dynamics in the Fenna-Mathews-Olsen complex using a realistic structured spectral density to model the electron-phonon interaction. The results of the simulations highlight the effect of specific vibrational modes on the exciton dynamics and energy transfer process, as well as call for careful modeling of electron-phonon couplings.

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Simulation of Quantum Dynamics of Excitonic Systems at Finite Temperature: an efficient method based on Thermo Field Dynamics.

The Dirac-Frenkel time-dependent variational approach with Davydov Ansatze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrodinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansatze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.

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Finite-temperature time-dependent variation with multiple Davydov states.

The coupled quantum dynamics of excitonic and vibrational degrees of freedom is investigated for high-dimensional models of the Fenna-Matthews-Olson (FMO) complex. This includes a seven and an eight-site model with 518 and 592 harmonic vibrational modes, respectively. The coupling between local electronic transitions and vibrations is described within the Huang-Rhys model using parameters that are obtained by discretization of an experimental spectral density. Different pathways of excitation energy flow are analyzed in terms of the reduced one-exciton density matrix, focussing on the role of vibrational and vibronic excitation. Distinct features due to both competing time scales of vibrational and exciton motion and vibronically-assisted transfer are observed. The question of the effect of initial state preparation is addressed by comparing the case of an instantaneous Franck-Condon excitation at a single site with that of a laser field excitation.

Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) Approach to the Correlated Exciton-Vibrational Dynamics in the FMO Complex

Correlated Protein Environments Drive Quantum Coherence Lifetimes in Photosynthetic Pigment-Protein Complexes

The coupled exciton-vibrational dynamics of a three-site model of the Fenna–Matthews–Olson complex is investigated using the numerically exact multilayer multiconfiguration time-dependent Hartree approach. Thereby the specific coupling of the vibrational modes to local electronic transitions is adapted from a discretized experimental spectral density. The solution of the resulting time-dependent Schrodinger equation including three electronic and 450 vibrational degrees of freedom is analyzed in terms of excitonic populations and coherences. Emphasis is put onto the role of specific ranges of vibrational frequencies. It is observed that modes between 160 and 300 cm–¹ are responsible for the sub-picosecond population and coherence decay. Further, it is found that a mean-field approach with respect to the vibrational degrees of freedom is not applicable.

O. Kühn

Papers

Explicit Correlated Exciton-Vibrational Dynamics of the FMO Complex B