Pith. sign in

REVIEW 2 major objections 4 minor 46 references

Characterizing the Role of Peierls Vibrations in Singlet Fission with the Adaptive Hierarchy of Pure States

T0 review · 2 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Peierls vibrations accelerate singlet fission in EP-PDI by breaking a coupling anti-symmetry so that charge-transfer-mediated pathways interfere constructively.

desk verdict Genuine method advance (adHOPS for Peierls couplings) with a plausible mechanism that, as the authors admit, depends on uncorrelated baths; worth peer review and a correlated-bath test. read the letter →

arxiv 2505.02292 v2 pith:INQGM3NE submitted 2025-05-04 physics.chem-ph

Jacob K. Lynd , Doran I. G. B. Raccah This is my paper · ORCID
classification physics.chem-ph
keywords singletfissionPeierlsvibrationsadaptiveHierarchyofPureStatescharge-transfer-mediatedcouplingconstructiveinterferenceEP-PDItriplettransportelectron-phonon
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that Peierls vibrations—intermolecular vibrations that modulate electronic couplings rather than site energies—accelerate singlet fission in the perylene diimide EP-PDI. The acceleration operates through the charge-transfer-mediated route: the vibrations break the anti-symmetric relation $V_{HL} = -V_{LH}$ between the two CT–triplet couplings, generating correlated effective couplings between the two neighboring singlet states and their shared triplet-pair state. When the singlet is delocalized across the pair, those correlated couplings add constructively and triplet formation speeds up. The same mechanism accelerates singlet-mediated triplet transport in a 100-site linear chain, where removing the Peierls vibrations slows triplet diffusion by half. The paper also extends the exact adaptive Hierarchy of Pure States method to Peierls couplings and shows that the calculation remains size-invariant at mesoscale.

What carries the argument

The load-bearing object is the mediated coupling $\hat{V}_{\mathrm{med}}$ between singlet states and the triplet-pair state, assembled from the pair of high-energy charge-transfer states $|A_n C_{n+1}\rangle$ and $|C_n A_{n+1}\rangle$ that bridge them. Without vibrations the bridge is anti-symmetric: the two CT–TT couplings satisfy $V_{HL} = -V_{LH}$, so the mediated couplings of the two singlets to the shared triplet pair are equal in magnitude and opposite in sign. Peierls vibrations enter as fluctuations in these couplings that break the anti-symmetry and make the two mediated couplings correlated in the complex plane; that correlation is what converts destructive interference into constructive addition. The computational machinery is the generalized adaptive Hierarchy of Pure States (adHOPS), a formally exact open-quantum-system trajectory method in which auxiliary wavefunctions are kept or discarded by a bounded-error criterion, extended here from diagonal to general Hermitian system-bath coupling operators so that Peierls vibrations can be treated exactly while cost scales with excitation delocalization length rather than chain length.

What would settle it

Repeat the EP-PDI dimer simulation with a single shared harmonic bath for the CT and TT states of each molecule, keeping the same spectral density and reorganization energies. If the correlated effective couplings shown in Fig. 4a shrink and the triplet-formation rate drops back toward the rate without vibrations, the uncorrelated-bath assumption is load-bearing; if the acceleration persists, the mechanism survives shared baths.

Watch

Extended reading notes

Core claim

The paper's central discovery is that Peierls vibrations change the interference pattern of the charge-transfer-mediated fission pathway rather than simply adding energetic noise. In the dimer model, the pair of charge-transfer states $|A_n C_{n+1}\rangle$ and $|C_n A_{n+1}\rangle$ couple to the triplet pair $|T_n T_{n+1}\rangle$ with equal magnitude and opposite sign ($V_{HL} = -V_{LH}$), so in a static molecule the two singlet states have mediated couplings to the triplet pair that are equal and opposite and largely cancel. Peierls vibrations that modulate the CT–TT couplings break this anti-symmetry; because the same two CT states mediate both singlet couplings, the effective couplings of $|e_n\rangle$ and $|e_{n+1}\rangle$ to $|T_n T_{n+1}\rangle$ become correlated in both magnitude and phase. An in-phase delocalized singlet then couples to the triplet pair constructively, gaining a factor of $\sqrt{2}$ in effective coupling, and triplet formation accelerates by roughly 30% relative to a single-site singlet. In a 100-site linear chain, the same effect accelerates singlet-mediated triplet diffusion; without the Peierls vibrations the transport slows by 50%. Methodologically, the paper claims that the adaptive Hierarchy of Pure States, generalized to non-diagonal system-bath operators, reproduces exact HOPS dynamics and reaches size-invariant cost by $N \approx 50$ even with simultaneous Holstein and Peierls vibrations.

Load-bearing premise

The load-bearing assumption is that each electronic state is coupled to its own fully independent vibrational bath, even though the charge-transfer and triplet-pair states physically inhabit the same molecules, so the correlated effective couplings that drive constructive interference could change if those baths were shared.

Editorial extensions

If this is right

  • In EP-PDI, vibrational engineering should target modes that modulate charge-transfer–triplet couplings; modes that modulate the direct singlet–triplet coupling are predicted to have little effect on fission rate.
  • The same uncorrelated-bath mechanism predicts that a J-aggregate sign of the effective singlet coupling is required for acceleration; in an H-aggregate the anti-symmetry breaking would promote rather than impede fission, as the paper notes.
  • Because triplet mobility limits photovoltaic efficiency, the predicted acceleration of singlet-mediated triplet transport makes Peierls vibrational character a relevant design handle for organic solar cells.
  • The exact, size-invariant adHOPS extension permits mesoscale singlet-fission models with simultaneous Holstein and Peierls baths, moving beyond rate-equation parametrizations of triplet transport.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A clean test of the mechanism is to rerun the dimer with a single shared harmonic bath for each molecule's CT and TT states; if the correlated effective couplings weaken and the constructive-interference acceleration disappears, the uncorrelated-bath assumption is carrying the result.
  • The predicted correlation between the two mediated couplings might be observable spectroscopically: two-dimensional electronic spectroscopy on EP-PDI should show the triplet-forming pathway acquiring a J-type delocalized character in phase with the CT-modulating vibrational mode.
  • The mechanism's sign-dependence suggests a broader design rule: the same Peierls vibration can accelerate or impede fission depending on aggregate packing, so vibrational-mode engineering and crystal-structure engineering are coupled, not independent, design levers.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper generalizes the adaptive Hierarchy of Pure States (adHOPS) method to open quantum systems with non-diagonal (Peierls) system-bath couplings in addition to the previously supported diagonal (Holstein) couplings. The new method is validated against non-adaptive HOPS in a 7-site Peierls chain and shown to exhibit size-invariant scaling by N=30. The authors then apply the method to a model of singlet fission in EP-PDI dimers and linear chains, with parameters taken from prior literature. Their central finding is that Peierls vibrations modulating the CT-TT couplings break the anti-symmetry V_HL = -V_LH, generating correlated effective couplings V_med between two singlet states and their shared triplet pair, which support constructive interference and accelerate singlet fission. They further report that Peierls vibrations accelerate singlet-mediated triplet diffusion in a 100-site chain and that the method remains size-invariant in these more complex models. The paper closes with an explicit statement of limitations, including the questionable assumption of fully uncorrelated vibrational baths for states that physically share the same molecules.

Significance. The methodological contribution is significant: extending adHOPS to general Hermitian system-bath couplings broadens the class of problems accessible to formally exact, reduced-scaling simulations, and the authors provide code and data via Zenodo, convergence checks against non-adaptive HOPS, and reproducible analysis scripts. The mechanistic claim, if correct, identifies a concrete symmetry-breaking route by which intermolecular vibrations accelerate singlet fission and directly challenges the earlier Redfield-based attribution of the effect to direct-coupling modulation (Ref. 13). The diagnostics are thoughtful: the V_med distribution analysis, the singlet-removal control, and the phi_s delocalization measure together build a plausible case for constructive interference, and the 100-site transport demonstration is an impressive use of the method. However, as the authors themselves note, the central mechanism relies on the assumption of fully uncorrelated baths for states and couplings that physically involve the same molecules; this assumption is not tested and may determine whether the reported acceleration is real or largely an artifact of the model.

major comments (2)
  1. [Final paragraph and model description (Table 1, Fig. 3 bottom row)] The central mechanistic claim—that Peierls vibrations break the anti-symmetry V_HL = -V_LH and thereby generate correlated CT-mediated couplings that support constructive interference—depends on assigning each CT-TT coupling (V_HL and V_LH) its own independent harmonic bath. The authors explicitly acknowledge in the final paragraph that "the assumption that each state possesses a totally uncorrelated bath is at odds with the fact that the CT and TT states physically inhabit the same molecules." This is a load-bearing limitation: if the physical intermolecular mode modulates both couplings from a shared coordinate in a way that preserves the anti-symmetry (e.g., a symmetric stretch that simply scales the common orbital overlap), the constructive-interference acceleration, the tripled |V_med|, and the ~50% triplet-diffusion acceleration would likely not survive. The manuscript should include a correlated-bath test (for example, a shared bath coordinate for V_HL and V_LH with the appropriate symmetry) or, failing that, should substantially temper the generality of the conclusions and present the results as specific to the independent-bath model.
  2. [Fig. 4b and the singlet-removal control] The evidence for constructive interference rests on a comparison between the full dimer and a truncated model in which |e2> is removed from the Hamiltonian. This deletion also removes all couplings of |e2> to the CT states and the effective singlet-singlet coupling V_NN (section S6.A of the SI), so the observed ~30% rate reduction could reflect a reduction in the number of pathways or a change in energy denominators rather than the loss of constructive interference specifically. The phi_s analysis in Fig. 4b demonstrates that the singlet is delocalized, but it does not separate the interference effect from the increased number of pathways. A cleaner control would be to keep the full dimer Hamiltonian and compare dynamics initialized in a localized state |e1> with dynamics initialized in |J+>, or to artificially decorrelate or sign-flip one of the two V_med couplings. As written, the claim that 'constructive interference accelerates SF' is not uniquely supported by this calculation.
minor comments (4)
  1. [Table 1] The sign convention for the electronic couplings is not stated; the table gives absolute values for |V_HH|, |V_LL|, |V_HL|, and |V_LH|, yet the argument that V_HL = -V_LH is anti-symmetric and the constructive-interference mechanism both depend on the relative signs. Please state the sign convention explicitly.
  2. [References 35 and 43] References 35 and 43 are identical duplicated footnotes describing CPU time measurements; please merge them or renumber appropriately.
  3. [Abstract and Introduction] The phrase "formally exact, reduced-scaling" may confuse readers because HOPS is formally exact while the adaptive approximation introduces controlled error bounds; please clarify that exactness refers to the convergence of the adaptive truncation in the limit of zero error bounds.
  4. [Data Availability Statement] The statement that 'All calculations were run with an intermediate version of our code, also available in the Zenodo' is vague; please specify the exact version or the Zenodo record identifier so that results can be reproduced.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: SF rates and transport results are unfitted simulation outputs, and the generalized adHOPS method is benchmarked against exact non-adaptive HOPS; self-citations are methodological and not load-bearing.

full rationale

The derivation chain is not circular. The central claims—Peierls vibrations accelerate singlet fission and singlet-mediated triplet diffusion in EP-PDI—are obtained from population dynamics and mean-squared-displacement simulations, not from fitting the target observables. The model parameters (Table 1) are taken from the independent prior work of Renaud and Grozema (Ref. 13), and the diabatic-state/coupling pattern follows Refs. 12, 15, and 37; no parameter is extracted from the present dynamics to force the reported rates. The generalized adHOPS method is validated against non-adaptive HOPS (δA = δS = 0) in Fig. 1b, so the method's exactness does not rest solely on the authors' earlier papers; the CPU-time scaling in Fig. 1c is a direct measurement. The V_med analysis (Figs. 3b and 4a) is an interpretive decomposition of the same Hamiltonian used in the dynamics, not a definition of the rates; the acceleration is independently evidenced by the full triplet-population dynamics and by the control calculation that removes |e2>, which is a model manipulation rather than a renamed target. The paper's stated limitation that the uncorrelated-bath assumption conflicts with the shared molecular identity of CT and TT states is a physical modeling caveat, not a circular reduction: it affects the realism of the Hamiltonian but does not make any output equal to an input by construction. Self-citations (Refs. 30–34) concern the adHOPS formalism and are supported by external benchmarks and available code (MesoHOPS, Zenodo), so they are not load-bearing. No step was found in which a prediction is defined in terms of a fitted quantity or in which a claimed first-principles result is equivalent to its input.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The model is an open quantum system with a fixed Hamiltonian and Drude-Lorentz baths. All electronic and vibronic parameters come from prior literature or are chosen for the model, and the central mechanism depends on the anti-symmetric CT-TT couplings and the independent-bath assumption. No new physical entities are postulated.

free parameters (8)
  • ES - ETT = 2200 cm^-1
    Energy gap between singlet and triplet-pair states; taken from the EP-PDI dimer model of Ref 13.
  • ECT - ETT = 9800 cm^-1
    Charge-transfer state energy above the triplet pair; taken from Ref 13.
  • V2e = -3.39 cm^-1
    Direct two-electron singlet-TT coupling; taken from Ref 13.
  • VHH, VLL, VHL, VLH = magnitudes 968 to 1170 cm^-1 with VHL = -VLH
    One-electron couplings between singlet, CT, and TT states; taken from Ref 13 and orbital geometry.
  • lambda_H (Holstein reorganization) = 621 cm^-1
    Intramolecular vibrational reorganization energy for each electronic state; taken from Ref 13.
  • lambda_P^2e = 0.726 cm^-1
    Peierls reorganization energy modulating the direct singlet-TT coupling.
  • lambda_P^HL = 217 cm^-1
    Peierls reorganization energy modulating CT-TT HOMO-LUMO couplings; central to the acceleration mechanism.
  • Bath timescales and Drude-Lorentz parameters = gamma_H, gamma_P (values in SI Table S2)
    Spectral density widths for Holstein and Peierls baths; the spectral density shape is known to affect dynamics (Ref 13).
assumptions (5)
  • domain assumption The full Hamiltonian is a system Hamiltonian plus independent harmonic baths linearly coupled to the system (Eq. 2).
    Standard open quantum system model; assumed throughout the paper.
  • domain assumption Each vibrational bath is described by a Drude-Lorentz spectral density.
    Used for all baths; the authors acknowledge that the spectral density shape significantly impacts dynamics (Ref 13).
  • domain assumption Each electronic state and each coupling is coupled to a totally independent, uncorrelated harmonic bath.
    This assumption is explicitly flagged by the authors as at odds with the fact that CT and TT states physically inhabit the same molecules; it underpins the correlated CT-mediated coupling distributions.
  • domain assumption The CT-TT couplings VHL and VLH are anti-symmetric (VHL = -VLH) in the static Hamiltonian due to orbital geometries.
    Follows Ref 15 and defines the baseline whose breaking is claimed to drive the acceleration.
  • domain assumption Electronic states are diabatic HOMO/LUMO states with a CT-mediated mechanism; the direct two-electron coupling is weak.
    Model defined following Refs 12 and 37; central to identifying which coupling matters.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Characterizing the Role of Peierls Vibrations in Singlet Fission with the Adaptive Hierarchy of Pure States." pith.science (2026). https://pith.science/paper/INQGM3NE

@misc{pith2026250502292,
  author       = {Pith},
  title        = {Pith review of: Characterizing the Role of Peierls Vibrations in Singlet Fission with the Adaptive Hierarchy of Pure States},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/INQGM3NE}},
  note         = {Machine review of arXiv:2505.02292}
}
read the original abstract

Singlet fission, a phenomenon in which a singlet exciton is converted to two triplet excitons, is sensitive to vibrations that perturb couplings between electronic states (i.e., Peierls vibrations). In singlet fission models larger than dimers, the inconvenient scaling of exact simulations has limited treatment of Peierls vibrations to approximate methods. In this letter, we generalize the formally exact, reduced-scaling adaptive Hierarchy of Pure States (adHOPS) method to account for both Holstein and Peierls vibrations and study singlet fission in N,N'-Bis(2-phenylethyl)-3,4,9,10-perylenedi-carboximide (EP-PDI). We find that Peierls vibrations accelerate singlet fission by generating correlated charge transfer-mediated pathways that support constructive interference. Finally, we extend this singlet fission model to a linear chain of EP-PDI to demonstrate that Peierls vibrations can accelerate singlet-mediated triplet transport on the 100-nm scale.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

46 extracted references · 45 canonical work pages

  1. [13]

    Renaud, N.; Grozema, F. C. Intermolecular Vibrational Modes Speed Up Singlet Fission in Perylenediimide Crystals. J. Phys. Chem. Lett. 2015, 6, 360--365

    work page 2015

  2. [1]

    Bandlike Motion and Mobility Saturation in Organic Molecular Semiconductors

    Fratini, S.; Ciuchi, S. Bandlike Motion and Mobility Saturation in Organic Molecular Semiconductors. Phys. Rev. Lett. 2009, 103, 266601

    work page 2009

  3. [2]

    Modeling Charge Transport in High-Mobility Molecular Semiconductors: Balancing Electronic Structure and Quantum Dynamics Methods with the Help of Experiments

    Nematiaram, T.; Troisi, A. Modeling Charge Transport in High-Mobility Molecular Semiconductors: Balancing Electronic Structure and Quantum Dynamics Methods with the Help of Experiments. J. Chem. Phys. 2020, 152, 190902

    work page 2020

  4. [3]

    A General Charge Transport Picture for Organic Semiconductors with Nonlocal Electron-Phonon Couplings

    Li, W.; Ren, J.; Shuai, Z. A General Charge Transport Picture for Organic Semiconductors with Nonlocal Electron-Phonon Couplings. Nat. Commun. 2021, 12, 4260

    work page 2021

  5. [4]

    Studies of Polaron Motion: Part I

    Holstein, T. Studies of Polaron Motion: Part I. The Molecular-Crystal Model. Ann. Phys. 1959, 8, 325--342

    work page 1959

  6. [5]

    G.; Venuti, E

    Girlando, A.; Grisanti, L.; Masino, M.; Bilotti, I.; Brillante, A.; Della Valle, R. G.; Venuti, E. Peierls and Holstein Carrier-Phonon Coupling in Crystalline Rubrene. Phys. Rev. B 2010, 82, 035208

    work page 2010

  7. [6]

    P.; Schrieffer, J

    Su, W. P.; Schrieffer, J. R.; Heeger, A. J. Solitons in Polyacetylene. Phys. Rev. Lett. 1979, 42, 1698--1701

    work page 1979

  8. [7]

    H.; Gole z z , D.; Berkelbach, T

    Fetherolf, J. H.; Gole z z , D.; Berkelbach, T. C. A Unification of the Holstein Polaron and Dynamic Disorder Pictures of Charge Transport in Organic Crystals. Phys. Rev. X 2020, 10, 021062

    work page 2020

Show all 46 references
  1. [8]

    A Stochastic Schr \"o dinger Equation and Matrix Product State Approach to Carrier Transport in Organic Semiconductors with Nonlocal Electron--Phonon Interaction

    Zhou, L.; Gao, X.; Shuai, Z. A Stochastic Schr \"o dinger Equation and Matrix Product State Approach to Carrier Transport in Organic Semiconductors with Nonlocal Electron--Phonon Interaction. J. Chem. Phys. 2024, 161, 084118

    2024

  2. [9]

    B.; Michl, J

    Smith, M. B.; Michl, J. Singlet Fission. Chem. Rev. 2010, 110, 6891--6936

    2010

  3. [10]

    Singlet fission photovoltaic cells as dual-wavelength laser power converters compatible with highly efficient solar cells

    Takeda, Y. Singlet fission photovoltaic cells as dual-wavelength laser power converters compatible with highly efficient solar cells. J. Appl. Phys. 2024, 136, 043106

    2024

  4. [11]

    F.; Li, A.; Lee, Y.; Zhong, X.; Lee, S.; Weisburn, L

    Nagaya, N.; Lee, K.; Perkinson, C. F.; Li, A.; Lee, Y.; Zhong, X.; Lee, S.; Weisburn, L. P.; Wang, J. Z.; Baikie, T. K. et al. Exciton fission enhanced silicon solar cell. Joule 2025, 101965

    2025

  5. [12]

    C.; Hybertsen, M

    Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Microscopic Theory of Singlet Exciton Fission. I. General Formulation. J. Chem. Phys. 2013, 138, 114102

    2013

  6. [14]

    K.; Zhu, X.-L.; Li, Z.; Martinez, T

    Duan, H.-G.; Jha, A.; Li, X.; Tiwari, V.; Ye, H.; Nayak, P. K.; Zhu, X.-L.; Li, Z.; Martinez, T. J.; Thorwart, M. et al. Intermolecular Vibrations Mediate Ultrafast Singlet Fission. Sci. Adv. 2020, 6, eabb0052

    2020

  7. [15]

    A.; Huo, P

    Castellanos, M. A.; Huo, P. Enhancing Singlet Fission Dynamics by Suppressing Destructive Interference between Charge-Transfer Pathways. J. Phys. Chem. Lett. 2017, 8, 2480--2488

    2017

  8. [16]

    Tempelaar, R.; Reichman, D. R. Vibronic Exciton Theory of Singlet Fission. III. How Vibronic Coupling and Thermodynamics Promote Rapid Triplet Generation in Pentacene Crystals . J. Chem. Phys. 2018, 148, 244701

    2018

  9. [17]

    Coherent Singlet Fission Activated by Symmetry Breaking

    Miyata, K.; Kurashige, Y.; Watanabe, K.; Sugimoto, T.; Takahashi, S.; Tanaka, S.; Takeya, J.; Yanai, T.; Matsumoto, Y. Coherent Singlet Fission Activated by Symmetry Breaking. Nat. Chem. 2017, 9, 983--989

    2017

  10. [18]

    M.; Lukman, S.; Hele, T

    Alvertis, A. M.; Lukman, S.; Hele, T. J. H.; Fuemmeler, E. G.; Feng, J.; Wu, J.; Greenham, N. C.; Chin, A. W.; Musser, A. J. Switching between Coherent and Incoherent Singlet Fission via Solvent-Induced Symmetry Breaking. J. Am. Chem. Soc. 2019, 141, 17558--17570

    2019

  11. [19]

    First-Principles Quantum Dynamics of Singlet Fission: Coherent versus Thermally Activated Mechanisms Governed by Molecular Stacking

    Tamura, H.; Huix-Rotllant, M.; Burghardt, I.; Olivier, Y.; Beljonne, D. First-Principles Quantum Dynamics of Singlet Fission: Coherent versus Thermally Activated Mechanisms Governed by Molecular Stacking. Phys. Rev. Lett. 2015, 115, 107401

    2015

  12. [20]

    C.; Subotnik, J

    Alguire, E. C.; Subotnik, J. E.; Damrauer, N. H. Exploring Non-Condon Effects in a Covalent Tetracene Dimer: How Important Are Vibrations in Determining the Electronic Coupling for Singlet Fission? J. Phys. Chem. A 2015, 119, 299--311

    2015

  13. [21]

    Charge and Energy Transfer Dynamics in Molecular Systems; Wiley-VCH, 2011

    May, V.; Kühn, O. Charge and Energy Transfer Dynamics in Molecular Systems; Wiley-VCH, 2011

    2011

  14. [22]

    The Theory of a General Quantum System Interacting with a Linear Dissipative System

    Feynman, R.; Vernon, F. The Theory of a General Quantum System Interacting with a Linear Dissipative System. Ann. Phys. (N. Y.) 1963, 24, 118--173

    1963

  15. [23]

    Suess, D.; Eisfeld, A.; Strunz, W. T. Hierarchy of Stochastic Pure States for Open Quantum System Dynamics. Phys. Rev. Lett. 2014, 113, 150403

    2014

  16. [24]

    Diósi, L.; Strunz, W. T. The Non-Markovian Stochastic Schrödinger Equation for Open Systems. Phys. Lett. A 1997, 235, 569--573

    1997

  17. [25]

    Hartmann, R.; Strunz, W. T. Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS). J. Chem. Theory Comput. 2017, 13, 5834--5845

    2017

  18. [26]

    Müller, K.; Strunz, W. T. nuHOPS: A Quantum Trajectory Method for Highly Excited Environments in Non-Markovian Open Quantum Dynamics. 2025; https://arxiv.org/abs/2503.03368

    2025

  19. [27]

    Non- Markovian Stochastic Schrödinger Equation: Matrix-Product-State Approach to the Hierarchy of Pure States

    Gao, X.; Ren, J.; Eisfeld, A.; Shuai, Z. Non- Markovian Stochastic Schrödinger Equation: Matrix-Product-State Approach to the Hierarchy of Pure States. Phys. Rev. A 2022, 105, L030202

    2022

  20. [28]

    Boettcher, V.; Hartmann, R.; Beyer, K.; Strunz, W. T. Dynamics of a Strongly Coupled Quantum Heat Engine—Computing Bath Observables from the Hierarchy of Pure States. J. Chem. Phys. 2024, 160, 094108

    2024

  21. [29]

    Chen, L.; Bennett, D. I. G.; Eisfeld, A. Calculating Nonlinear Response Functions for Multidimensional Electronic Spectroscopy Using Dyadic Non-Markovian Quantum State Diffusion. J. Chem. Phys. 2022, 157, 114104

    2022

  22. [30]

    K.; Bennett, D

    Varvelo, L.; Lynd, J. K.; Bennett, D. I. G. Formally exact Simulations of Mesoscale Exciton Dynamics in Molecular Materials. Chem. Sci. 2021, 12, 9704--9711

    2021

  23. [31]

    K.; Citty, B.; Kühn, O.; Raccah, D

    Varvelo, L.; Lynd, J. K.; Citty, B.; Kühn, O.; Raccah, D. I. G. B. Formally Exact Simulations of Mesoscale Exciton Diffusion in a Light-Harvesting 2 Antenna Nanoarray. J. Chem. Phys. Lett. 2023, 14, 3077--3083

    2023

  24. [32]

    R.; Taffet, E

    Gera, T.; Chen, L.; Eisfeld, A.; Reimers, J. R.; Taffet, E. J.; Raccah, D. I. G. B. Simulating Optical Linear Absorption for Mesoscale Molecular Aggregates: An Adaptive Hierarchy of Pure States Approach. J. Chem. Phys. 2023, 158, 174103

    2023

  25. [33]

    K.; Gera, T.; Varvelo, L.; Raccah, D

    Citty, B.; Lynd, J. K.; Gera, T.; Varvelo, L.; Raccah, D. I. G. B. MesoHOPS: Size-Invariant Scaling Calculations of Multi-Excitation Open Quantum Systems . J. Chem. Phys. 2024, 160, 144118

    2024

  26. [34]

    Gera, T.; Hartzell, A.; Chen, L.; Eisfeld, A.; Raccah, D. I. G. B. Formally Exact Fluorescence Spectroscopy Simulations for Mesoscale Molecular Aggregates with N^0 Scaling. 2025; https://arxiv.org/abs/2503.00584

    2025 arXiv

  27. [35]

    All CPU times were measured by running each trajectory on a single thread of an AMD EPYC 9534 64-Core Processor

  28. [36]

    K.; Bender, J

    Le, A. K.; Bender, J. A.; Arias, D. H.; Cotton, D. E.; Johnson, J. C.; Roberts, S. T. Singlet Fission Involves an Interplay between Energetic Driving Force and Electronic Coupling in Perylenediimide Films. J. Am. Chem. Soc. 2018, 140, 814--826

    2018

  29. [37]

    C.; Hybertsen, M

    Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Microscopic Theory of Singlet Exciton Fission. III. Crystalline Pentacene. J. Chem. Phys. 2014, 141, 074705

    2014

  30. [38]

    For the CT state indexing, C_n indicates a cationic hole in the HOMO of molecule n and A_m indicates an anionic electron in the LUMO of molecule m

  31. [39]

    Quantum Interference in Singlet Fission: J- and H-Aggregate Behavior

    Zang, H.; Zhao, Y.; Liang, W. Quantum Interference in Singlet Fission: J- and H-Aggregate Behavior. J. Phys. Chem. Lett. 2017, 8, 5105--5112

    2017

  32. [40]

    We note here that, given these vibrational relaxation effects, an equivalent material in an H-aggregate structure with a positive effective nearest-neighbor coupling V_ NN >0 would have J_1 as the singlet exciton ground state and the anti-symmetry V_ HL =-V_ LH would promote, ...

  33. [41]

    S.; Verkamp, M

    Volek, T. S.; Verkamp, M. A.; Ruiz, G. N.; Staat, A. J.; Li, B. C.; Rose, M. J.; Eaves, J. D.; Roberts, S. T. Slowed Singlet Exciton Fission Enhances Triplet Exciton Transport in Select Perylenediimide Crystals. J. Am. Chem. Soc. 2024, 146, 29575--29587

    2024

  34. [42]

    Exciton transport in singlet fission materials: A new hare and tortoise story

    Zhu, T.; Huang, L. Exciton transport in singlet fission materials: A new hare and tortoise story. J. Phys. Chem. Lett. 2018, 9, 6502--6510

    2018

  35. [43]

    Vibronic Coupling Density Analysis and Quantum Dynamics Simulation for Singlet Fission in Pentacene and its Halogenated Derivatives

    Nagami, T.; Tonami, T.; Okada, K.; Yoshida, W.; Miyamoto, H.; Nakano, M. Vibronic Coupling Density Analysis and Quantum Dynamics Simulation for Singlet Fission in Pentacene and its Halogenated Derivatives. J. Chem. Phys. 2020, 153, 134302

    2020

  36. [44]

    Locally Broken Crystal Symmetry Facilitates Singlet Exciton Fission

    Petelenz, P.; Snamina, M. Locally Broken Crystal Symmetry Facilitates Singlet Exciton Fission. J. Phys. Chem. Lett. 2016, 7, 1913--1916

    2016

  37. [45]

    The Energy Barrier in Singlet Fission can be Overcome Through Coherent Coupling and Entropic Gain

    Chan, W.-L.; Ligges, M.; Zhu, X.-Y. The Energy Barrier in Singlet Fission can be Overcome Through Coherent Coupling and Entropic Gain. Nat. Chem. 2012, 4, 840--845

    2012

  38. [46]

    Characterizing the Role of Peierls Vibrations in Singlet Fission with the Adaptive Hierarchy of Pure States

    Lynd, J. K.; Raccah, D. I. G. B. Figure, Input, and Analysis Scripts for "Characterizing the Role of Peierls Vibrations in Singlet Fission with the Adaptive Hierarchy of Pure States". 2025; https://doi.org/10.5281/zenodo.15337336 mcitethebibliography Main_Text.tex0000664000000...

    2025 doi

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.