pith. sign in

arxiv: 2606.31905 · v1 · pith:WC53LU5Onew · submitted 2026-06-30 · ⚛️ physics.chem-ph

Conical Intersections Enable Ultrafast Molecular Spin Control in a Chromium Complex

Pith reviewed 2026-07-01 02:20 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords conical intersectionsintersystem crossingchromium complexultrafast spectroscopyspin dynamicsvibronic couplingspin-vibronic dynamicsmolecular spintronics
0
0 comments X

The pith

Conical intersections from ligand vibrations enable ultrafast spin flips in a chromium complex despite weak spin-orbit coupling.

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

The paper examines spin-state dynamics in the chromium complex [Cr(acac)3] with ultrafast transient grating and two-dimensional electronic spectroscopy at 10-fs resolution. It identifies coherent vibrational modes that mediate the 4T2 to 2E intersystem crossing. Theoretical modeling demonstrates that vibronic coupling combined with spin-orbit interactions creates multiple conical intersections. These intersections use metal-ligand bending and stretching modes as tuning and coupling coordinates. The result supplies a route to rapid spin control even when spin-orbit coupling is weak in 3d metals.

Core claim

Vibronic coupling and spin-orbit interactions promote the formation of multiple conical intersections that provide ultrafast channels for spin-flip dynamics in [Cr(acac)3], with metal-ligand bending and stretching modes serving as tuning and coupling coordinates to enable the 4T2 to 2E intersystem crossing despite weak spin-orbit coupling.

What carries the argument

Conical intersections between spin states, promoted by vibronic coupling with metal-ligand bending and stretching modes acting as tuning and coupling coordinates.

If this is right

  • Provides a design framework for achieving ultrafast molecular spin switching in transition metal complexes.
  • Enables intersystem crossing in 3d metals through vibrational channels even when spin-orbit coupling is weak.
  • Reveals specific bending and stretching modes that mediate nonadiabatic spin transitions.
  • Advances the development of optically addressable spin centres for spintronic and quantum technologies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same vibrational-coordinate strategy could be tested in other chromium or 3d-metal complexes by changing ligand sets to shift the mode frequencies.
  • If the intersections prove general, ligand design rules might be derived to position conical intersections at desired energies.
  • Room-temperature operation of such spin centres would follow if the observed coherence survives in solid matrices.

Load-bearing premise

The modeling assumes that the observed coherent vibrational modes directly correspond to the tuning and coupling coordinates at the conical intersections without independent experimental confirmation of the intersection geometries or dynamics.

What would settle it

Femtosecond time-resolved structural measurements that locate or fail to locate the predicted conical intersection geometries during the spin transition would test the claim.

Figures

Figures reproduced from arXiv: 2606.31905 by Ajay Jha, Fulu Zheng, Hong-Guang Duan, Junhua Zhou, Mengyuan Cui, Michael Penny, R. J. Dwayne Miller, Sara Mosca, Tianrui Chen, Vandana Tiwari, Zihui Liu.

Figure 1
Figure 1. Figure 1: Photoinduced spin-state dynamics in [Cr(acac) [PITH_FULL_IMAGE:figures/full_fig_p032_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Two-dimensional electronic spectroscopy reveals ultrafast excited-state dynamics in [PITH_FULL_IMAGE:figures/full_fig_p033_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Vibronic coherences and time-frequency-resolved dynamics in [Cr(acac) [PITH_FULL_IMAGE:figures/full_fig_p034_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Conical intersection mediated by vibrational coordinates in [Cr(acac) [PITH_FULL_IMAGE:figures/full_fig_p035_4.png] view at source ↗
read the original abstract

Molecular spintronics seeks to control spin states in single molecules for ultrafast switching and efficient information processing. Transition metal complexes are promising candidates for such applications due to their modular ligand fields, diverse spin configurations, and potential for spin-vibronic coupling that facilitates rapid spin dynamics. Chromium(III) complexes, in particular, offer long-lived emissive doublet states and chemical robustness, making them attractive for room-temperature spin control. Here we investigate the spin-state dynamics of tris(2,4-pentanedionato)chromium(III), [Cr(acac)3], a photochemically stable d3 complex with minimal vibrational congestion. Using ultrafast transient grating and two dimensional electronic spectroscopy with ~10 fs resolution, we directly probe vibrational and electronic dynamics associated with the 4T2 -> 2E intersystem crossing (ISC). These measurements reveal coherent vibrational modes implicated in mediating nonadiabatic spin transitions. Complementary theoretical modelling shows that vibronic coupling and spin orbit interactions promote the formation of multiple conical intersections, providing ultrafast channels for spin-flip dynamics. Metal-ligand bending and stretching modes serve as tuning and coupling coordinates, enabling ISC despite weak spin-orbit coupling in 3d transition metal. Our study provides mechanistic insight into spin-vibronic dynamics in Cr(III) complexes and establishes a design framework for achieving ultrafast molecular spin switching, advancing the development of optically addressable spin centres for future spintronic and quantum technologies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports ~10 fs resolution transient grating and 2D electronic spectroscopy on [Cr(acac)3] that detects coherent vibrational modes during the 4T2 → 2E intersystem crossing. Complementary theoretical modeling is presented as showing that vibronic coupling and spin-orbit interactions create multiple conical intersections between these states, with metal-ligand bending and stretching modes acting as tuning and coupling coordinates that enable ultrafast spin-flip dynamics despite weak SOC in this 3d complex.

Significance. If the mapping from observed coherences to the specific conical-intersection coordinates is rigorously demonstrated, the work supplies mechanistic insight into spin-vibronic coupling in Cr(III) complexes and a concrete design motif for ultrafast molecular spin switching relevant to spintronics and quantum technologies.

major comments (2)
  1. [Theoretical modelling] Theoretical modelling section: no optimized 4T2/2E conical-intersection geometries, nonadiabatic coupling vectors, or time-dependent wave-packet propagations are reported that would quantitatively link the experimentally observed vibrational frequencies and phases to the proposed metal-ligand bending/stretching tuning and coupling modes.
  2. [Results] Experimental results (2D ES and transient-grating data): the central claim that the detected coherent modes mediate the ISC rests on an interpretive assignment whose support cannot be evaluated because quantitative fitting details, error bars on mode amplitudes/phases, and controls excluding alternative origins of the coherences are not provided.
minor comments (2)
  1. [Theoretical modelling] The level of theory (e.g., CASPT2, TDDFT functional, active space) and basis sets used for the conical-intersection search should be stated explicitly.
  2. Figure captions for the spectroscopic data should include the precise pump/probe wavelengths, pulse durations, and solvent conditions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their detailed and thoughtful report. Their comments highlight areas where additional information can improve the manuscript. We address each point below and indicate the changes we will implement.

read point-by-point responses
  1. Referee: [Theoretical modelling] Theoretical modelling section: no optimized 4T2/2E conical-intersection geometries, nonadiabatic coupling vectors, or time-dependent wave-packet propagations are reported that would quantitatively link the experimentally observed vibrational frequencies and phases to the proposed metal-ligand bending/stretching tuning and coupling modes.

    Authors: The theoretical section of the manuscript presents calculations demonstrating the formation of conical intersections due to vibronic coupling and spin-orbit interactions. However, we recognize that optimized geometries at the CIs, nonadiabatic coupling vectors, and wave-packet dynamics are not explicitly reported. We will revise the manuscript to include optimized 4T2/2E conical intersection geometries and nonadiabatic coupling vectors. These will be used to confirm the role of the metal-ligand modes. Time-dependent wave-packet propagations are not feasible within the current computational framework but we will provide a more detailed analysis of the CI seams and their implications for the dynamics. Thus, this will be a partial revision. revision: partial

  2. Referee: [Results] Experimental results (2D ES and transient-grating data): the central claim that the detected coherent modes mediate the ISC rests on an interpretive assignment whose support cannot be evaluated because quantitative fitting details, error bars on mode amplitudes/phases, and controls excluding alternative origins of the coherences are not provided.

    Authors: We agree that the experimental section would benefit from more quantitative details on the data analysis. In the revised version, we will provide the quantitative fitting details for the coherent oscillations, including error bars on mode amplitudes and phases. Additionally, we will include controls and arguments to exclude alternative origins of the coherences, such as by comparing with off-resonant excitation or ground state spectra. This will strengthen the support for our assignment that the modes mediate the ISC. revision: yes

Circularity Check

0 steps flagged

No significant circularity; modeling presented as complementary to independent experimental data.

full rationale

The paper's central claim rests on ultrafast spectroscopy data (transient grating and 2D ES) revealing coherent vibrational modes, with complementary theoretical modelling invoked to link those modes to conical intersections via vibronic coupling and SOC. No equations, parameters, or results are shown to be fitted to the same dataset and then re-presented as predictions; the modelling is explicitly described as complementary rather than derived from the observed frequencies. No self-citations, uniqueness theorems, or ansatzes are load-bearing in the provided text. The derivation chain remains self-contained against external benchmarks because the experimental coherences stand as independent observations and the theory is not required to reproduce its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; conical intersections are a standard concept in nonadiabatic photochemistry and not introduced as new here.

pith-pipeline@v0.9.1-grok · 5826 in / 1204 out tokens · 57691 ms · 2026-07-01T02:20:08.980447+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

67 extracted references · 55 canonical work pages

  1. [1]

    + 1 2 ℏΩc(α† cαc + 1

  2. [2]

    Here, it denotes the S 1 and S2 (4T2 and 2E), respectively

    +κ iQt, (1) where,|e i⟩is the electronic singlet or triplet states. Here, it denotes the S 1 and S2 (4T2 and 2E), respectively. Thus, N = 2 in this work. Vij andλ ij are the parameters of the SOC and the vibronic coupling of the coupling mode, which tune the couplings between two electronic states. Moreover, κi is the parameter determining vibronic coupli...

  3. [3]

    & Das Sarma, S

    ˇZuti´c, I., Fabian, J. & Das Sarma, S. Spintronics: Fundamentals and applications. Reviews of Modern Physics76, 323-410 (2004).https://doi.org/10.1103/RevModPhys. 76.323

  4. [4]

    Molecular spintronics

    Sanvito, S. Molecular spintronics. Chemical Society Reviews40, 3336-3355 (2011).https: //doi.org/10.1039/C1CS15047B

  5. [5]

    Gu, X. et al. Challenges and Prospects of Molecular Spintronics. Precision Chemistry2, 1-13 (2024).https://doi.org/10.1021/prechem.3c00071

  6. [6]

    & Powell, B

    Nadeem, M., Cruddas, J., Ruzzi, G. & Powell, B. J. Toward High-Temperature Light-Induced Spin-State Trapping in Spin-Crossover Materials: The Interplay of Collective and Molecular 20 Effects. Journal of the American Chemical Society144, 9138-9148 (2022).https://doi. org/10.1021/jacs.2c03202

  7. [7]

    Sutcliffe, E., Kazmierczak, N. P. & Hadt, R. G. Ultrafast all-optical coherence of molecular electron spins in room-temperature water solution. Science386, 888-892 (2024).https: //doi.org/doi:10.1126/science.ads0512

  8. [8]

    Nakaya, M., Ohtani, R., Lindoy, L. F. & Hayami, S. Light-induced excited spin state trapping in iron(iii) complexes. Inorganic Chemistry Frontiers8, 484-498 (2021).https://doi. org/10.1039/D0QI01188F

  9. [9]

    Liedy, F. et al. Vibrational coherences in manganese single-molecule magnets after ultrafast photoexcitation. Nature Chemistry12, 452-458 (2020).https://doi.org/10.1038/ s41557-020-0431-6

  10. [10]

    Johansson, J. O. et al. Directly probing spin dynamics in a molecular magnet with femtosecond time-resolution. Chemical science7, 7061-7067 (2016).https://doi.org/10.1039/ C6SC01105E

  11. [11]

    V ., Ovcharenko, V

    Dong, X., Lorenc, M., Tretyakov, E. V ., Ovcharenko, V . I. & Fedin, M. V . Light-induced spin state switching in copper (ii)-nitroxide-based molecular magnet at room temperature. The Journal of Physical Chemistry Letters8, 5587-5592 (2017).https://doi.org/10. 1021/acs.jpclett.7b02497 21

  12. [12]

    Monat, J. E. & McCusker, J. K. Femtosecond excited-state dynamics of an iron (II) polypyridyl solar cell sensitizer model. Journal of the American Chemical Society122, 4092-4097 (2000). https://doi.org/10.1021/ja992436o

  13. [13]

    & Chergui, M

    Aub ¨ock, G. & Chergui, M. Sub-50-fs photoinduced spin crossover in [Fe (bpy) 3] 2+. Nature chemistry7, 629-633 (2015).https://doi.org/10.1038/nchem.2305

  14. [14]

    Lemke, H. T. et al. Coherent structural trapping through wave packet dispersion during pho- toinduced spin state switching. Nature Communications8, 15342 (2017).https://doi. org/10.1038/ncomms15342

  15. [15]

    Zerdane, S. et al. Comparison of structural dynamics and coherence of d–d and MLCT light- induced spin state trapping. Chemical science8, 4978-4986 (2017).https://doi.org/ 10.1039/C6SC05624E

  16. [16]

    Consani, C. et al. Vibrational Coherences and Relaxation in the High-Spin State of Aqueous [FeII (bpy) 3] 2+. Angewandte Chemie International Edition48, 7184-7187 (2009).https: //doi.org/10.1002/anie.200902728

  17. [17]

    Phelps, R., Agapaki, E., Brechin, E. K. & Johansson, J. O. Tracking the conical intersection dynamics for the photoinduced Jahn–Teller switch of a Mn(iii) complex. Chemical Science 15, 11956-11964 (2024).https://doi.org/10.1039/D4SC00145A

  18. [18]

    L ¨upke, A., Carrella, L. M. & Rentschler, E. Filling the Gap in the Metallacrown Family: The 9-MC-3 Chromium Metallacrown. Chemistry – A European Journal27, 4283-4286 (2021). https://doi.org/https://doi.org/10.1002/chem.202004947 22

  19. [19]

    Barlow, K. et al. Capturing Ultrafast Spin Dynamics in Single-Molecule Magnets Using Femtosecond X-ray Emission Spectroscopy. J. Phys. Chem. Lett.16, 4148–4154 (2025). https://doi.org/10.1021/acs.jpclett.5c00383

  20. [20]

    J., Johansson, J

    Penfold, T. J., Johansson, J. O. & Eng, J. Towards Understanding and Controlling Ultrafast Dynamics in Molecular Photomagnets. Coordination Chemistry Reviews494215346 (2023). https://doi.org/10.1016/j.ccr.2023.215346

  21. [21]

    Ye, Y . et al. Modulating the spin–flip rates and emission energies through ligand design in chromium(iii) molecular rubies. Chemical Science16, 5205-5213 (2025).https://doi. org/10.1039/D4SC08021A

  22. [22]

    Paulus, B. C. & McCusker, J. K. On the use of vibronic coherence to identify reaction coor- dinates for ultrafast excited-state dynamics of transition metal-based chromophores. Faraday Discussions237, 274-299 (2022).https://doi.org/10.1039/D2FD00106C

  23. [23]

    Ultrafast Photophysics of Transition Metal Complexes

    Chergui, M. Ultrafast Photophysics of Transition Metal Complexes. Accounts of Chemical Research48, 801-808 (2015).https://doi.org/10.1021/ar500358q

  24. [24]

    Photochemistry and photophysics of transition metal complexes: Quantum chemistry

    Daniel, C. Photochemistry and photophysics of transition metal complexes: Quantum chemistry. Coordination Chemistry Reviews282-283, 19-32 (2015).https://doi.org/ https://doi.org/10.1016/j.ccr.2014.05.023

  25. [25]

    & Tahara, T

    Iwamura, M., Takeuchi, S. & Tahara, T. Ultrafast Excited-State Dynamics of Copper(I) Com- plexes. Accounts of Chemical Research48, 782-791 (2015).https://doi.org/10. 1021/ar500353h 23

  26. [27]

    Gaffney, K. J. Capturing photochemical and photophysical transformations in iron complexes with ultrafast X-ray spectroscopy and scattering. Chemical Science12, 8010-8025 (2021). https://doi.org/https://doi.org/10.1016/j.ccr.2014.06.013

  27. [28]

    Jiang, Y . et al. Direct observation of photoinduced sequential spin transition in a halogen- bonded hybrid system by complementary ultrafast optical and electron probes. Nature Com- munications15, 4604 (2024).https://doi.org/10.1038/s41467-024-48529-1

  28. [29]

    Tiwari, V . et al. Crystal Lattice-Induced Stress modulates Photoinduced Jahn–Teller Distor- tion Dynamics. ACS Physical Chemistry Au4, 660-668 (2024).https://doi.org/10. 1021/acsphyschemau.4c00047

  29. [30]

    Ultrafast processes: coordination chemistry and quantum theory

    Daniel, C. Ultrafast processes: coordination chemistry and quantum theory. Physical Chem- istry Chemical Physics23, 43-58 (2021).https://doi.org/10.1039/D0CP05116K

  30. [31]

    J., Gindensperger, E., Daniel, C

    Penfold, T. J., Gindensperger, E., Daniel, C. & Marian, C. M. Spin-Vibronic Mechanism for Intersystem Crossing. Chemical Reviews118, 6975-7025 (2018).https://doi.org/ 10.1021/acs.chemrev.7b00617 24

  31. [32]

    Marian, C. M. Understanding and Controlling Intersystem Crossing in Molecules. Annu. Rev. Phys. Chem.72, 617–640 (2021).https://doi.org/10.1146/ annurev-physchem-061020-053433

  32. [33]

    R., Weingartz, N

    Rather, S. R., Weingartz, N. P., Kromer, S., Castellano, F. N. Chen, L. X. Spin–Vibronic Coherence Drives Singlet–Triplet Conversion. Nature620, 776–781 (2023).https://doi. org/10.1038/s41586-023-06233-y

  33. [34]

    Liao, C. et al. Spin–Vibronic Coupling Enhanced Intersystem Crossing beyond El-Sayed Re- strictions. Journal of the American Chemical Society147, 22176–22184 (2025).https: //doi.org/10.1021/jacs.5c06949

  34. [35]

    A., Sazanovich, I

    Delor, M., Keane, T., Scattergood, P. A., Sazanovich, I. V ., Greetham, G. M., Towrie, M., Meijer, A. J. H. M., Weinstein, J. A. On the Mechanism of Vibrational Control of Light- Induced Charge Transfer in Donor–Bridge–Acceptor Assemblies. Nat. Chem.7, 689–695 (2015).https://doi.org/10.1038/nchem.2327

  35. [36]

    Spin-vibronic mechanism at work in a luminescent square-planar cy- clometalated tridentate Pt(ii) complex: absorption and ultrafast photophysics

    Mandal, S., Daniel, C. Spin-vibronic mechanism at work in a luminescent square-planar cy- clometalated tridentate Pt(ii) complex: absorption and ultrafast photophysics. Phys. Chem. Chem. Phys.25, 18720– 18727 (2023).https://doi.org/10.1039/D3CP01890C

  36. [37]

    Excited-state dynamics of [Mn(im)(CO)3(phen)]+: PhotoCORM, catalyst, luminescent probe?

    Fumanal, M., Daniel, C., Gindensperger, E. Excited-state dynamics of [Mn(im)(CO)3(phen)]+: PhotoCORM, catalyst, luminescent probe?. J. Chem. Phys. 154, 154102 (2021).https://doi.org/10.1063/5.0044108 25

  37. [38]

    & Sugano, S

    Tanabe, Y . & Sugano, S. On the Absorption Spectra of Complex Ions. I. Journal of the Physical Society of Japan9, 753-766 (1954).https://doi.org/10.1143/JPSJ.9.753

  38. [39]

    Yang, J. et al. Mapping Vibronic Dynamics of Ultrafast Intersystem Crossing in an Earth- Abundant Ligand-Field Excited Complex. Journal of the American Chemical Society148, 1977-1988 (2026).https://doi.org/10.1021/jacs.5c20395

  39. [40]

    Gao, J. et al. Vibronic and Spin–Orbit Interplay Governs Ultrafast Spin Crossover in an Iron(II) Carbene Complex. ChemPhysChem e202500768 (2026).https://doi.org/10.1002/ cphc.202500768

  40. [41]

    N., Dillman, K

    Schrauben, J. N., Dillman, K. L., Beck, W. F. & McCusker, J. K. Vibrational coherence in the excited state dynamics of Cr(acac)3: probing the reaction coordinate for ultrafast inter- system crossing. Chemical Science1, 405-410 (2010).https://doi.org/10.1039/ C0SC00262C

  41. [42]

    A., Smeigh, A

    Juban, E. A., Smeigh, A. L., Monat, J. E. & McCusker, J. K. Ultrafast dynamics of ligand-field excited states. Coordination Chemistry Reviews250, 1783-1791 (2006).https://doi. org/https://doi.org/10.1016/j.ccr.2006.02.010

  42. [43]

    & Sheridan, P

    Zinato, E., Riccieri, P. & Sheridan, P. S. Photochemical and thermal reactions of tris(acetylacetonato)chromium(III) in water-ethanol solution. Inorganic Chemistry18, 720- 724 (1979).https://doi.org/10.1021/ic50193a038 26

  43. [44]

    Foszcz, E. D. Understanding the Interplay Between Geometry and Ultrafast Dynamics in Lig- and Field Excited States of Inorganic Chromophores PhD thesis, Michigan State University, (2015).https://doi.org/doi:10.25335/3a6t-ja13

  44. [45]

    Juban, E. A. & McCusker, J. K. Ultrafast Dynamics of 2E State Formation in Cr(acac)3. Journal of the American Chemical Society127, 6857-6865 (2005).https://doi.org/ 10.1021/ja042153i

  45. [46]

    Mac ¸ˆoas, E. M. S., Kananavicius, R., Myllyperki¨o, P., Pettersson, M. & Kunttu, H. Relaxation Dynamics of Cr(acac)3 Probed by Ultrafast Infrared Spectroscopy. Journal of the American Chemical Society129, 8934-8935 (2007).https://doi.org/10.1021/ja071859k

  46. [47]

    Mac ¸ˆoas, E. M. S., Mustalahti, S., Myllyperki¨o, P., Kunttu, H. & Pettersson, M. Role of Vibra- tional Dynamics in Electronic Relaxation of Cr(acac)3. The Journal of Physical Chemistry A 119, 2727-2734 (2015).https://doi.org/10.1021/jp509905q

  47. [48]

    Duan, H.-G. et al. Intermolecular vibrations mediate ultrafast singlet fission. Science Advances 6, eabb0052 (2020).https://doi.org/doi:10.1126/sciadv.abb0052

  48. [49]

    Duan, H.-G. et al. Photoinduced Vibrations Drive Ultrafast Structural Distortion in Lead Halide Perovskite. Journal of the American Chemical Society142, 16569-16578 (2020). https://doi.org/10.1021/jacs.0c03970

  49. [50]

    Fuller, F. D. & Ogilvie, J. P. Experimental Implementations of Two-Dimensional Fourier Transform Electronic Spectroscopy. Annual Review of Physical Chem- 27 istry66, 667-690 (2015).https://doi.org/https://doi.org/10.1146/ annurev-physchem-040513-103623

  50. [51]

    & Scholes, G

    Biswas, S., Kim, J., Zhang, X. & Scholes, G. D. Coherent Two-Dimensional and Broad- band Electronic Spectroscopies. Chemical Reviews122, 4257-4321 (2022).https://doi. org/10.1021/acs.chemrev.1c00623

  51. [52]

    Jha, A. et al. Quantum coherent dynamics in photosynthetic protein complexes. Chemical Society Reviews55, 1089-1130 (2026).https://doi.org/10.1039/D5CS00948K

  52. [53]

    Fresch, E. et al. Two-dimensional electronic spectroscopy. Nature Reviews Methods Primers 3, 84 (2023).https://doi.org/10.1038/s43586-023-00267-2

  53. [54]

    Duan, H.-G. et al. Quantum coherent energy transport in the Fenna–Matthews–Olson complex at low temperature. Proceedings of the National Academy of Sciences119, e2212630119 (2022).https://doi.org/doi:10.1073/pnas.2212630119

  54. [55]

    Jha, A. et al. Unraveling quantum coherences mediating primary charge transfer processes in photosystem II reaction center. Science Advances10, eadk1312 (2024).https://doi. org/doi:10.1126/sciadv.adk1312

  55. [56]

    Jha, A. et al. Origin of poor doping efficiency in solution processed organic semiconductors. Chemical Science9, 4468-4476 (2018).https://doi.org/10.1039/C8SC00758F

  56. [57]

    Mitra,et al.Elucidating the Transition Kernel and Anharmonic Coupling in the Spin- crossover Process of a [Fe III (qsal)2] CH3OSO3 Complex

    S. Mitra,et al.Elucidating the Transition Kernel and Anharmonic Coupling in the Spin- crossover Process of a [Fe III (qsal)2] CH3OSO3 Complex. Angewandte Chemie International Edition, e1079807 (2026).https://doi.org/10.1002/anie.1079807 28

  57. [58]

    & Tufts, D

    Kumaresan, R. & Tufts, D. W. Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise. IEEE Transactions on Acoustics, Speech, and Signal Pro- cessing30, 833-840 (1982).https://doi.org/10.1109/TASSP.1982.1163974

  58. [59]

    Software update: the ORCA program system – Version 5.0

    Neese, F. Software update: the ORCA program system – Version 5.0. Wiley Interdisciplinary Reviews: Computational Molecular Science12, e1606 (2022).https://doi.org/10. 1002/wcms.1606

  59. [60]

    Density-Functional, D

    Becke, A. Density-Functional, D. Thermochemistry .3. The Role of Exact Exchange. The Journal of Chemical Physics98, 5648-5652 (1993).https://doi.org/10.1063/1. 464913

  60. [61]

    & Ahlrichs, R

    Weigend, F. & Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadru- ple zeta valence quality for H to Rn: Design and assessment of accuracy. Physical Chemistry Chemical Physics7, 3297-3305 (2005).https://doi.org/10.1039/b508541a

  61. [62]

    Why do many resource-rich countries have negative genuine saving? Anticipation of better times or rapacious rent seeking.Resource and Energy Economics, 32(1):28–44, 2010

    H. Ando,et al.Theoretical study on ultrafast intersystem crossing of chromium(III) acety- lacetonate. Chemical Physics Letters535, 177 (2012).https://doi.org/10.1016/j. cplett.2012.03.043

  62. [64]

    & Tanimura, Y

    Ishizaki, A. & Tanimura, Y . Quantum Dynamics of System Strongly Coupled to Low- Temperature Colored Noise Bath: Reduced Hierarchy Equations Approach. Journal of the Physical Society of Japan74, 3131-3134 (2005).https://doi.org/10.1143/JPSJ. 74.3131

  63. [65]

    Faraday Discussions194, 61 (2016).https://doi.org/ 10.1039/C6FD00088F

    Chen, L.et al.Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method. Faraday Discussions194, 61 (2016).https://doi.org/ 10.1039/C6FD00088F

  64. [66]

    Cheng, R.-R

    Chen, L.et al.Mapping of Wave Packet Dynamics at Conical Intersections by Time- and Frequency-Resolved Fluorescence Spectroscopy: A Computational Study. The Journal of Physical Chemistry Letters10, 5873 (2019).https://doi.org/10.1021/acs. jpclett.9b02208

  65. [67]

    Journal of the American Chemical Society147, 43858–43869 (2025).https: //doi.org/10.1021/jacs.5c15799

    Tiwari, V .et al.Unraveling Exciton-Carrier Correlations in Orthorhombic Lead Halide Per- ovskite. Journal of the American Chemical Society147, 43858–43869 (2025).https: //doi.org/10.1021/jacs.5c15799

  66. [68]

    Communications Physics8, 71 (2025).https: //doi.org/10.1038/s42005-025-01995-5

    Zhang, X.et al.Ultrafast exciton-phonon coupling and energy transfer dynamics in quasi- 2D layered Ruddlesden-Popper perovskites. Communications Physics8, 71 (2025).https: //doi.org/10.1038/s42005-025-01995-5

  67. [69]

    D., Ferro, A

    Hybl, J. D., Ferro, A. A. & Jonas, D. M. Two-dimensional Fourier transform electronic spec- troscopy. The Journal of Chemical Physics115, 6606–6622 (2001).https://doi.org/ 10.1063/1.1398579 30 AcknowledgementsThis work was supported by the National Key Research and Development Program of China (Grant No. 2024YFA1409800), NSFC Grants with No. 12274247 and ...