Validity of time-dependent trial states for the Holstein polaron

Luo, Bing; Ye, Jun; Guan, Chengbo; Zhao, Yue

doi:10.1039/c0cp00663g

Cited by 51 publications

(71 citation statements)

References 66 publications

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“…Combining such precious information with quantum dynamics simulations could hopefully open new routes for improving our knowledge on radiationless transitions, which control many biochemical and technological processes. Although powerful methodologies capable of handling molecular systems with a large number of degrees of freedom and complex molecular Hamiltonians have been developed [3][4][5][6] their use, is often limited by their algorithmic complexity and high computational costs. There are two possible ways out: i) to employ model Hamiltonians with a small number of 'active' nuclear degrees of freedom, i.e.…”

Section: Introductionmentioning

confidence: 99%

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Borrelli

Peluso

2015

J. Chem. Theory Comput.

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This is the author's final version of the contribution published as:Borrelli, Raffaele; Peluso, Andrea. Quantum dynamics of radiationless electronic transitions including normal modes displacements and duschinsky rotations: A second-order cumulant approach. JOURNAL OF CHEMICAL THEORY AND COMPUTATION. 11 (2) AbstractAn analytical expression for the population dynamics of electronic radiationless transitions has been derived from the second order expansion of the quantum evolution operator in the Liouville space and the cumulant theory. The expression includes the effect of both normal mode displacements and Duschinsky rotations and allows to take into account both equilibrium and non-equilibrium initial conditions. The methodology has been applied to model the electron-transfer process between the accessory bacteriochlorophyll and the bacteriopheophytine in bacterial reactions centers, providing a rate in good agreement with experimental findings.

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Section: Introductionmentioning

confidence: 99%

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Borrelli

Peluso

2015

J. Chem. Theory Comput.

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“…The accuracy of the Davydov Ansätze has been discussed in length in Ref. 37,38 , and it has been shown that for diagonal excitonphonon coupling, the D1 Ansatz has the highest precision in the hierarchy of the Davydov trial states when applied to the solution of Holstein Hamiltonian. The increase in the precision of the D1 Ansatz is achieved mainly by improved sophistication of the phonon wave function 37,38 .…”

Section: A Polaron Dynamics In Lh2 Systemsmentioning

confidence: 99%

“…With the aid of Frenkel-Dirac time-dependent variational method, a hierarchy of variational wave functions has been previously formulated to faithfully describe the dynamics of the Holstein polaron 37,38 . The accuracy of the Davydov Ansätze has been discussed in length in Ref.…”

Section: A Polaron Dynamics In Lh2 Systemsmentioning

confidence: 99%

Excitonic energy transfer in light-harvesting complexes in purple bacteria

Sun

Zhao

et al. 2012

The Journal of Chemical Physics

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Two distinct approaches, the Frenkel-Dirac time-dependent variation and the Haken-Strobl model, are adopted to study energy transfer dynamics in single-ring and double-ring light-harvesting systems in purple bacteria. It is found that inclusion of long-range dipolar interactions in the two methods results in significant increases in intra-or inter-ring exciton transfer efficiency. The dependence of exciton transfer efficiency on trapping positions on single rings of LH2 (B850) and LH1 is similar to that in toy models with nearest-neighbor coupling only. However, owing to the symmetry breaking caused by the dimerization of BChls and dipolar couplings, such dependence has been largely suppressed. In the studies of coupled-ring systems, both methods reveal interesting role of dipolar interaction in increasing energy transfer efficiency by introducing multiple intra/interring transfer paths. Importantly, the time scale ( 4ps) of inter-ring exciton transfer obtained from polaron dynamics is in good agreement with previous studies. In a double-ring LH2 system, dipoleinduced symmetry breaking leads to global minima and local minima of the average trapping time when there is a finite value of non-zero dephasing rate, suggesting that environment plays a role in preserving quantum coherent energy transfer. In contrast, dephasing comes into play only when the perfect cylindrical symmetry in the hypothetic system is broken. This study has revealed that dipolar interaction between chromophores may play an important part in the high energy transfer efficiency in the LH2 system and many other natural photosynthetic systems.

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“…Time-dependent variational parameters which specify the trial state are obtained from solving a set of coupled differential equations generated by the Lagrangian formalism of the Dirac Frenkel variation. Validity of this approach is carefully checked by quantifying how faithfully the trial state follows the Schrödinger equation [24,55,56]. Numerical results show that the D 1 Ansatz is effective and accurate in studying the Holstein polaron dynamics with the diagonal coupling, but fails to describe the case with the off-diagonal coupling.…”

Section: Introductionmentioning

confidence: 99%

Polaron dynamics with a multitude of Davydov D2 trial states

Zhou

Huang

Zhu

et al. 2015

The Journal of Chemical Physics

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122

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We propose an extension to the Davydov D2 Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the "multi-D2 Ansatz" is a linear combination of Davydov D2 trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schrödinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D1 and D2 Ansätze. With an increase in the number of the Davydov D2 trial states in the multi-D2 Ansatz, deviation from the exact Schrödinger dynamics is gradually diminished, leading to a numerically exact solution to the Schrödinger equation.

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Validity of time-dependent trial states for the Holstein polaron

Cited by 51 publications

References 66 publications

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Excitonic energy transfer in light-harvesting complexes in purple bacteria

Polaron dynamics with a multitude of Davydov D2 trial states

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