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WIREs Comput Mol Sci
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Theoretical study of excitation energy transfer and nonlinear spectroscopy of photosynthetic light‐harvesting complexes using the nonperturbative reduced dynamics method

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Abstract The highly efficient excitation energy transfer (EET) processes in photosynthetic light‐harvesting complexes have attracted much recent research interests. Experimentally, spectroscopic studies have provided important information on the energetics and EET dynamics. Theoretically, due to the large number of degrees of freedom and the complex interaction between the pigments and the protein environment, it is impossible to simulate the whole system quantum mechanically. Effective Hamiltonian models are often used, in which the most important degrees of freedom are treated explicitly and all the other degrees of freedom are treated as a thermal bath. However, even with such simplifications, solving the real‐time quantum dynamics could still be a difficult task. A particular challenging case in simulating the EET dynamics and related spectroscopic phenomena lies in the so‐called intermediate coupling regime, where the intermolecular electronic couplings and the electronic–vibrational couplings are of similar strength. In this article, we review theoretical studies of linear and nonlinear spectroscopic signals of photosynthetic light‐harvesting complexes, using the nonperturbative hierarchical equations of motion (HEOM) approach. Simulations were performed for the EET dynamics, various types of linear spectra, two‐dimensional electronic spectra, and pump–probe spectra. Benchmark tests of several approximate methods related to the HEOM approach were also discussed. The results show that the nonperturbative HEOM approach is an effective method in simulating the EET dynamics and spectroscopic signals of photosynthetic light‐harvesting complexes. Important insights into EET pathways, quantum effects including quantum delocalization, and quantum coherence in photosynthetic light‐harvesting complexes were also obtained through such simulations. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Theoretical and Physical Chemistry > Spectroscopy Software > Simulation Methods
Relation between the HEOM and several related approximate methods. GQME, generalized quantum master equation39,132; HEOM, hierarchical equations of motion37,38; HTA, high temperature approximation37,38,74; MHTA, modified high temperature approximation69,133; QFPE, quantum Fokker–Planck equation38,134; SLE, Stochastic Liouville Equation38,69; TL, time local; TNL, time nonlocal; ZE, Zusman equation73,74,134
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Simulated isotropic pump–probe signal ΔAiso(t) and anisotropy decay r(t) for a dimer model consisting of pigment 3 and 4 of FMO complex.125 The frequency of the undamped vibrational mode is 700 cm−1. Results with different values of the Huang–Rhys factors (HRFs) are shown. Three of the curves are for laser pulses with FWHM width of 87 fs, which is the value used in the experiment in Reference 124. Two other curves are for laser pulses with FWHM of 30 fs
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Comparison of simulated (left) and experimental (right) results of the FMO complex at 19 K: (a) Polarized absorption difference ΔA(t) and ΔA(t), (b) Isotropic absorption difference, (c) Polarization anisotropy decay125
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Simulated pump–probe polarization anisotropy signals for three model dimer systems featuring different types of quantum coherence: (a) The isotropic pump–probe signal ΔAiso(t), (b) The anisotropy decay signal r(t)125
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Simulated two‐color 2DES of the LHCII complex at 298 K.104 The horizontal and vertical axis correspond to the pump frequency ωτ(ω1) and the probe frequency ωt(ω3), respectively
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Evolution of the amplitude of the 2D spectra of the FMO complex from C. tepidum for diagonal peaks corresponding to exciton 1 (DP1) and exciton 3 (DP3), and the lower off‐diagonal peak between excitons 1 and 3 (CP13)70
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Simulated absorptive part of the 2D spectra for the FMO complex from C. tepidum.70 The populations times T are 0, 200, 600, and 1 ps, respectively
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Absorption spectra of a symmetric J‐type dimer model indicating the problem with second‐order TNL‐GQME.72 γ = 0.3J, η = J, and βJ = 1
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2D electronic spectra for a model dimer calculated using different methods69: (a) HEOM, (b) TNL2, (c) TL2, (d) SLE, (e) HTA, and (f) MHTA
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Simulated absorption and emission spectra of the B850 ring of the LH2 complex from the purple bacterium Rps. acidophila at 300 K67
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Distributions of coherence length Lρ defined in Equation (31) of the B850 ring in the LH2 complex from the purple bacterium Rps. acidophila at 300 K. The static disorder is considered by adding random shifts to the transition energies from a Gaussian distribution. (a) without the electronic–vibrational coupling, (b) with the electronic–vibrational coupling67
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Absorption spectra of a symmetric J‐type dimer simulated using the HEOM method.72 The parameters are η = J, βJ = 1, and different bath characteristic frequencies: γ = 0.1J (solid line), γ = 0.3J (dashed line), γ = 0.5J (dash dot line), and γ = J (dash dot dot line)
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Laser excited population dynamics of LHCII complex at 298 K.104 The excitation pulse is centered at 15,385 cm−1 with a time duration of 42 fs. (a) The Chlb states. (b) The Chla states. (c) Sum of the population of all the Chlb and Chla manifolds
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Double side Feynman diagrams for the calculation of rephasing and nonrephasing signals in the 2DES.69 They can be classified into ground state bleaching (GSB), excited stimulated emission (ESE), and excited‐state absorption (ESA) contributions
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Simulated population dynamics of the B800 and B850 manifolds in the LH2 complex, driven by two consecutive independent 30 fs pump pulses.102 The time delay is Δt = 102 fs between the pulse centers, and the phase difference is Δϕ = 0
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Simulation of the population dynamics in a seven‐site model of the FMO complex using the HEOM method, starting from initial excitations on two different Bchl molecules94
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Software > Simulation Methods
Theoretical and Physical Chemistry > Spectroscopy
Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics

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