Hierarchy of equations to calculate the linear spectra of molecular aggregates: Time-dependent and frequency domain formulation

Zhang, Pan Pan; Li, Zeng-Zhao; Eisfeld, Alexander

doi:10.1002/qua.25386

Cited by 3 publications

(8 citation statements)

References 31 publications

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“…Many groups have considered the impact of vibronic coupling on the UV–vis absorption and PL spectral line shapes in molecular aggregates ,,,,,− beginning with the seminal works of McRae − and Fulton and Gouterman. , In this section, we review the progress made on interpreting the steady-state optical spectra of J- and H-aggregates using the Holstein-style Hamiltonians based on eq . For most of this section, vibronic coupling is limited to a single symmetric intramolecular mode, which in the case of π-conjugated oligomers and polymers is the ubiquitous progression-building vinyl-stretching (or aromatic-quinoidal) mode with energy ω vib in the range of 150–180 meV.…”

Section: Absorption and Photoluminescence In Vibronically Coupled H- ...mentioning

confidence: 99%

“…Kasha and co-workers recognized that increasing the strength of the excitonic coupling in a molecular aggregate should eventually lead to vibronic decoupling, as noted in a qualitative discussion in ref . However, it was Fulton and Gouterman’s numerical treatment of molecular dimers, , which showed in much greater detail how the vibronic fine structure responds to the magnitude and especially the sign of the Coulomb coupling that laid the groundwork for an enduring fascination for the impact of vibronic coupling on molecular aggregate photophysics, ,,,,,− that has culminated in some recent, rather sophisticated non-Markovian treatments of aggregate–bath interactions. , …”

Section: Introductionmentioning

confidence: 99%

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Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

2018

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The electronic excited states of molecular aggregates and their photophysical signatures have long fascinated spectroscopists and theoreticians alike since the advent of Frenkel exciton theory almost 90 years ago. The influence of molecular packing on basic optical probes like absorption and photoluminescence was originally worked out by Kasha for aggregates dominated by Coulombic intermolecular interactions, eventually leading to the classification of J- and H-aggregates. This review outlines advances made in understanding the relationship between aggregate structure and photophysics when vibronic coupling and intermolecular charge transfer are incorporated. An assortment of packing geometries is considered from the humble molecular dimer to more exotic structures including linear and bent aggregates, two-dimensional herringbone and "HJ" aggregates, and chiral aggregates. The interplay between long-range Coulomb coupling and short-range charge-transfer-mediated coupling strongly depends on the aggregate architecture leading to a wide array of photophysical behaviors.

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Section: Absorption and Photoluminescence In Vibronically Coupled H- ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

2018

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“…All calculations are performed using the formalism described in Ref. 40 , section 3.1. In particular, in the following we plot the frequency dependence of the transition strength (Eq.…”

Section: A Example 1: Calculation Of Absorption Spectramentioning

confidence: 99%

“…( 5) of Ref. 40 ), which we will denote in the following simply by 'absorption'. Recall that there is no stochasticity involved in the calculation of the absorption spectra.…”

Section: A Example 1: Calculation Of Absorption Spectramentioning

confidence: 99%

Flexible scheme to truncate the hierarchy of pure states

Zhang

Bentley

Eisfeld

2018

The Journal of Chemical Physics

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The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

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“…In this work, however, we focus on the response of an open quantum system beyond the perturbative regime, with respect to the system environment interaction, at the price of using demanding approaches such as HEOM − or NMQSD/HOPS. − On the one hand, these methods are capable of determining the full nonlinear response directly, by solving the reduced dynamics including the probe driving. On the other hand, for a weak probe signal we can apply Kubo’s linear response theory to efficiently obtain spectra of strongly damped systems.…”

Section: Introductionmentioning

confidence: 99%

Open Quantum System Response from the Hierarchy of Pure States

Hartmann

Strunz

2021

J. Phys. Chem. A

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The spectral properties of a quantum system are essential when probing theoretical predictions against experimental data. For an open quantum system strongly interacting with its environment, spectral features are challenging to calculate. Here we demonstrate that the stochastic Hierarchy of Pure States (HOPS) approach is well suited to calculate the response of an open quantum system to a, possibly strong, coherent probe driving. For weak driving, where Kubo’s linear response theory is applicable, it turns out that the HOPS method is highly efficient since fluctuations inherent to the stochastic dynamics cancel for the response function and, thus, allow us to obtain the susceptibility easily. Our results are in agreement with experimental data for a strongly damped spin system showing that the transition from oscillatory to overdamped motion is also reflected by the transmission spectrum. As a further application we demonstrate that the susceptibility, quantifying the amplitude of the response, as a function of temperature exhibits a maximum which is the hallmark of stochastic resonance. Beyond the linear regime, the exact open system dynamics shows the asymptotic Floquet state. We use the topic of probe driving and response to present the HOPS approach in a novel and self-contained way. This includes the importance sampling scheme which yields the nonlinear HOPS as well as the stochastic treatment of a thermal initial environmental state within the zero temperature formalism. Special attention is given to the exponential representation of the algebraic Ohmic bath correlation function and the truncation condition for the hierarchy.

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Hierarchy of equations to calculate the linear spectra of molecular aggregates: Time-dependent and frequency domain formulation

Cited by 3 publications

References 31 publications

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

Flexible scheme to truncate the hierarchy of pure states

Open Quantum System Response from the Hierarchy of Pure States

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