Effect of an underdamped vibration with both diagonal and off‐diagonal exciton–phonon interactions on excitation energy transfer

Wang, Yu‐Chen; Zhao, Yi

doi:10.1002/jcc.25611

Cited by 8 publications

(7 citation statements)

References 90 publications

(154 reference statements)

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“…In this way the equilibrium position of the respective vibrational mode is shifted by the excited state displacement. So-called variational approaches relying on the concept of PT ,− involve a shift which does not necessarily correspond to the displacement. Such a variable shift can be introduced in the framework of our approach by adjusting the upper integration boundary in terms of multiplication with the ratio of the intended shift and the displacement.…”

Section: Theorymentioning

confidence: 99%

“…Such a transformation, which is obtained by applying a shift operator , to compensate the displacement of the equilibrium position in excited-state potentials of vibrational modes compared to the ground-state potential, is known as the polaron transformation (PT) . Apart from applications where a quantum mechanical treatment with involvement of vibrational eigenstates was chosen, it has been extensively applied in the context of open quantum systems in the framework of spin-boson models with applications ranging from quantum dots, molecular donor–acceptor complexes, interacting excitonic dimer units, , and light-harvesting complexes , up to bulk materials, such as organic molecular crystals. − In particular, second-order perturbative description of transfer processes in molecular aggregates with separation of reference and interaction Hamiltonian via PT is a widely used application. It has mostly been formulated in the localized basis with basis states corresponding to electronic excitation of a single monomer unit ,,− but also in the exciton basis. − Such a second-order perturbative treatment goes beyond the assumptions entering in Förster- or Redfield type approaches that either the excitonic coupling or the system–bath coupling is sufficiently small to be treated perturbatively. − It is therefore also applicable in cases where neither of them is appropriate, for example, for the treatment of model systems with off-diagonal contributions to the system–bath coupling .…”

Section: Introductionmentioning

confidence: 99%

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Strong Exciton–Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space

Seibt

Kühn

2021

J. Phys. Chem. A

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In Frenkel exciton dynamics of aggregated molecules, the polaron transformation (PT) technique leads to decoupling of diagonal elements in the subspace of excited electronic states from vibrations. In this article we describe for the first time how PT becomes applicable in the framework of the “Hierarchical Equations of Motion” (HEOM) approach for treatment of open quantum systems. We extend the concept of formulating operators in HEOM space by deriving hierarchical equations of PT which lead to a shift in the excited state potential energy surface to compensate its displacement. While the assumption of thermal equilibration of the vibrational oscillators, introduced by PT, results in a stationary state in a monomer, in a dimer under the same assumption nonequilibrium dynamics appears because of the interplay of the transfer process and vibrational equilibration. Both vertical transitions generating a vibrationally hot state and initially equilibrated vibrational oscillators evolve toward the same stationary asymptotic state associated with polaron formation. The effect of PT on the dynamics of this process depends on initial excitation and basis representation of the electronic system. The developed approach facilitates a generic formulation of quantum master equations involving perturbative treatment of polaron dynamics.

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Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strong Exciton–Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space

Seibt

Kühn

2021

J. Phys. Chem. A

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“…In this way the equilibrium position of the respective vibrational mode is shifted by the excited state displacement. So-called variational approaches relying on the concept of PT 13,[21][22][23] involve a shift which does not necessarily correspond to the displacement. Such variable shift can be introduced in the framework of our approach by adjusting the upper integration boundary in terms of multiplication with the ratio of the intended shift and the displacement.…”

Section: B †mentioning

confidence: 99%

“…9 Apart from applications where a quantum mechanical treatment with involvement of vibrational eigenstates was chosen, 10 it has been extensively applied in the context of open quantum systems in the framework of spin-boson models 11 with applications ranging from quantum dots, 12 molecular donor-acceptor complexes, 13 interacting excitonic dimer units 14,15 and light-harvesting complexes 16,17 up to bulk materials, such as organic molecular crystals. [18][19][20][21] In particular, second-order perturbative description of transfer processes in molecular aggregates with separation of reference and interaction Hamiltonian via PT is a widely used application. It has mostly been formulated in the localized basis with basis states corresponding to electronic excitation of a single monomer unit, 9,13,[22][23][24] but also in the exciton basis.…”

Section: Introductionmentioning

confidence: 99%

Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics using the Polaron Transformation in HEOM Space

Seibt,

Kühn

2021

Preprint

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In the context of Frenkel exciton dynamics in aggregated molecules the polaron transformation technique facilitates a treatment where diagonal elements attributed to electronic excited-state populations are decoupled from fluctuations associated with vibrational degrees-of-freedom. In this article we describe for the first time how the polaron transformation can be applied in the context of the "Hierarchical Equations of Motion" (HEOM) technique for treatment of open quantum systems with all vibrational components attributed to an environment. By using a generating function approach to introduce a shift in the excited state potential energy surface, we derive hierarchical equations for polaron transformation in analogy to those for time propagation. We demonstrate the applicability of the developed approach by calculating the dynamics of underdamped and overdamped oscillators coupled to electronic excitation of a monomer without and with previous polaron transformation and study the dynamics of the expectation value of the respective vibrational coordinates. Furthermore, we investigate the dynamics of a dimer with a barrier comparable to the thermal energy between the minima of the lower excitonic potential energy surface. It turns out that the assumption of localization at the monomer unit with energetically higher potential minimum, introduced via polaron transformation, has a substantial influence on the transfer dynamics. Here, it makes a clear difference whether the polaron transformation is performed in the local or exciton basis. This reflects the fact that the polaron transformation only accounts for equilibration of the vibrational, but not of the excitonic dynamics. We sketch an approach to compensate this shortcoming in view of obtaining an initial state for the calculation of emission spectra of molecular aggregates.

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“…Recently, a related model has been studied by Wang and Zhao (2019) who have also investigated the impact of a vibrational mode on energy transfer. Apart from general similarities in the methodology, fundamental differences between the work of Wang and Zhao and this work have to be pointed out.…”

mentioning

confidence: 99%

Intramolecular vibrations enhance the quantum efficiency of excitonic energy transfer

et al. 2020

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We study the impact of underdamped intramolecular vibrational modes on the efficiency of the excitation energy transfer in a dimer in which each state is coupled to its own underdamped vibrational mode and, in addition, to a continuous background of environmental modes. For this, we use the numerically exact hierarchy equation of motion approach. We determine the quantum yield and the transfer time in dependence of the vibronic coupling strength, and in dependence of the damping of the incoherent background. Moreover, we tune the vibrational frequencies out of resonance with the excitonic energy gap. We show that the quantum yield is enhanced by up to 10% when the vibrational frequency of the donor is larger than at the acceptor. The vibronic energy eigenstates of the acceptor acquire then an increased density of states, which leads to a higher occupation probability of the acceptor in thermal equilibrium. We can conclude that an underdamped vibrational mode which is weakly coupled to the dimer fuels a faster transfer of excitation energy, illustrating that long-lived vibrations can, in principle, enhance energy transfer, without involving long-lived electronic coherence.

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Effect of an underdamped vibration with both diagonal and off‐diagonal exciton–phonon interactions on excitation energy transfer

Cited by 8 publications

References 90 publications

Strong Exciton–Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space

Strong Exciton–Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space

Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics using the Polaron Transformation in HEOM Space

Intramolecular vibrations enhance the quantum efficiency of excitonic energy transfer

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