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WIREs Comput Mol Sci
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The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials

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A number of non‐Markovian stochastic Schrödinger equations, ranging from the numerically exact hierarchical form toward a series of perturbative expressions sequentially presented in an ascending degrees of approximations are revisited in this short review, aiming at providing a systematic framework which is capable to connect different kinds of the wavefunction‐based approaches for an open system coupled to the harmonic bath. One can optimistically expect the extensive future applications of those non‐Markovian stochastic Schrödinger equations in large‐scale realistic complex systems, benefiting from their favorable scaling with respect to the system size, the stochastic nature which is extremely suitable for parallel computing, and many other distinctive advantages. In addition, we have presented a few examples showing the excitation energy transfer in the Fenna‐Matthews‐Olson complex, a quantitative measure of decoherence timescale of hot exciton, and the study of quantum interference effects upon the singlet fission processes in organic materials, since a deep understanding of both mechanisms is very important to explore the underlying microscopic processes and to provide novel design principles for highly efficient organic photovoltaics. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Structure and Mechanism > Computational Materials Science
Plots of time‐evolving populations at BChl 1, 2, 3, and 4 for a seven‐site subunit of FMO complex, under four different parameter sets with the specific values given at the top of every panel. The reorganization energy is fixed at λ = 35cm−1. The initial population is located at BChl 1
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Population evolution of SF with (a) Vex = 20 meV, (b) Vex = −40 meV and (c) Vex = 90 meV, as well as TT state population from only one SE state pathway (dashed line). (d) the SF rates in terms of Vex in dimer (solid line) and 10 monomer (dashed line) models. (Reprinted with permission from Reference . Copyright 2017 American Chemical Society)
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Schematic SF processes in J‐ and H‐aggregates in terms of Equation 49 (Reprinted with permission from Reference . Copyright 2017 American Chemical Society)
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A schematic diagram for the five electronic states and the couplings among them. The signs of couplings marked with red are alterable, whereas the couplings marked with black are fixed to be positive (Reprinted with permission from Reference . Copyright 2017 American Chemical Society)
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(a) The time‐evolving exciton population of PBDTTPD at room temperature. (b) The corresponding contour map of the coherence length sequence {Lk(t)} (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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The frequency dependence of mode‐specific reorganization energy for PBDTTPD (frequencies between 3,000 and 3,300 cm−1 are not shown because the peaks are too weak to display). The molecular structure of PBDTTPD and its component unit is embedded (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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(a) The energy relaxation dynamics corresponding to two different exciton–phonon interaction (weak: λ = 0.4 and strong: λ = 4.0, respectively). (b) The dephasing process of the averaged coherent length . (c) The dephasing time (td) and the fast energy relaxation time (t1) with respect to the varying reorganization energies. The initial wavepacket is generated by a laser pulse with the parameters (2Vi, i ±1 above the bottom of the energy band), ΔE = 0.008, and ωc = 1, β = 10 (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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Plots of time‐evolving populations for a full 24‐site FMO complex, under four different parameter sets with the specific values given at the top of every panel. The reorganization energy is fixed at λ = 35cm−1. The initial population is located at BChl 1 within one subunit out of a homotrimer. For the purpose of a better visualization, only those corresponding to the most‐populated eight BChls are displayed
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Transform of initial distribution from the energy representation to the site representation. The energy band ranges from −2Vi, i ±1 to 2Vi, i ±1 as the excitonic energies {ɛn} are all set as zero (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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Plots of the time‐evolving populations at site 1 in a dimer model system, subjected to various reorganization energies λ[(1) − (4)] and two different energy biases [ΔE = E1 − E2 = 0 and ΔE = 100cm−1] at both high and low temperatures [T = 300 K and T = 50 K]. The initial population is put at site 1. Other parameters are set as: The excitonic coupling V = 100cm−1, in the Debye spectral density function Equation 25
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Structure and Mechanism > Computational Materials Science
Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics

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