Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex

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We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first-and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and systembath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx

Section: Discussionmentioning

confidence: 99%

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

Tanimura

2015

128

237

“…This is a challenging benchmark problem for electronically nonadiabatic dynamics and allows our method to be compared with other mapping approaches, 16,41,64,66 as well as to numerically exact results obtained via the hierarchical equation of motion (HEOM) approach. [67][68][69][70][71]…”

Section: Application To the Fenna-matthews-olson Modelmentioning

confidence: 99%

Generalized spin mapping for quantum-classical dynamics

Runeson

Richardson

2020

207

We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system and a spin-1/2 particle. In the present paper, we generalize this method to describe the dynamics of N -level systems. This is done via a mapping to a classical phase space that preserves the SU (N )-symmetry of the original quantum problem. The theory reproduces the standard Meyer-Miller-Stock-Thoss Hamiltonian without invoking an extended phase space, and we thus avoid leakage from the physical subspace. In contrast with the standard derivation of this Hamiltonian, the generalized spin mapping leads to an N -dependent value of the zero-point energy parameter that is uniquely determined by the Casimir invariant of the N -level system. Based on this mapping, we derive a simple way to approximate correlation functions in complex nonadiabatic molecular systems via classical trajectories, and present benchmark calculations on the seven-state Fenna-Matthews-Olson complex. The results are significantly more accurate than conventional Ehrenfest dynamics, at a comparable computational cost, and can compete in accuracy with other state-ofthe-art mapping approaches.

“…Despite current attention to fine effects of underdamped intramolecular vibrational modes [24][25][26][27][28] and to details of spectral density shapes [29], and despite recent efforts to introduce a paradigm shift in understanding of the origin of the photosynthetic EET efficiency [30][31][32], the overall picture of this process, as drawn by the master equations of the Förster and Redfield types, remains valid [33] (see e. g. [34] for quantitative results). Recent theoretical advances enabling exact numerical solutions of some types of energy transfer problems e.g.…”

Section: Introductionmentioning

confidence: 99%

Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories

Seibt

Mančal

2017

We derive equations of motion for the reduced density matrix of a molecular system which undergoes energy transfer dynamics competing with fast internal conversion channels. Environmental degrees of freedom of such a system have no time to relax to quasi-equilibrium in the electronic excited state of the donor molecule, and thus the conditions of validity of Förster and Modified Redfield theories in their standard formulations do not apply. We derive non-equilibrium versions of the two well-known rate theories and apply them to the case of carotenoid-chlorophyll energy transfer. Although our reduced density matrix approach does not account for the formation of vibronic excitons, it still confirms the important role of the donor ground-state vibrational states in establishing the resonance energy transfer conditions. We show that it is essential to work with a theory valid in strong system-bath interaction regime to obtain correct dependence of the rates on donor-acceptor energy gap.