Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Interplay of vibrational wavepackets during an ultrafast electron transfer reaction

Nature Chemistry volume 13, pages 70–76 (2021)Cite this article

Subjects

Abstract

Electron transfer reactions facilitate energy transduction and photoredox processes in biology and chemistry. Recent findings show that molecular vibrations can enable the dramatic acceleration of some electron transfer reactions, and control it by suppressing and enhancing reaction paths. Here, we report ultrafast spectroscopy experiments and quantum dynamics simulations that resolve how quantum vibrations participate in an electron transfer reaction. We observe ballistic electron transfer (~30 fs) along a reaction coordinate comprising high-frequency promoting vibrations. Along another vibrational coordinate, the system becomes impulsively out of equilibrium as a result of the electron transfer reaction. This leads to the generation (by the electron transfer reaction, not the laser pulse) of a new vibrational coherence along this second reaction coordinate in a mode associated with the reaction product. These results resolve a complex reaction trajectory composed of multiple vibrational coordinates that, like a sequence of ratchets, progressively diminish the recurrence of the reactant state.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Coherent dynamics during an ET reaction.
Fig. 2: Coherent vibrational dynamics reveals decoherence and the generation of new coherence.
Fig. 3: Vibrational wavepacket dynamics along the low-frequency coordinate from quantum dynamics simulations.
Fig. 4: Schematic of the wavepacket dynamics during the initial 50 fs.

Data availability

The experimental and theoretical data associated with the reported findings are available in this manuscript or the Supplementary Information. Data for the Supplementary figures are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The codes for the quantum dynamics simulations are available from the corresponding author upon request.

References

  1. Bixon, M. & Jortner, J. in Electron Transfer—From Isolated Molecules to Biomolecules Ch. 3 (Wiley, 2007).

  2. Marcus, R. A. Chemical and electrochemical electron-transfer theory. Annu. Rev. Phys. Chem. 15, 155–196 (1964).

    CAS  Google Scholar 

  3. Rafiq, S. & Scholes, G. D. From fundamental theories to quantum coherences in electron transfer. J. Am. Chem. Soc. 141, 708–722 (2019).

    CAS  PubMed  Google Scholar 

  4. Scholes, G. D. et al. Utilizing coherence to enhance function in chemical and biophysical systems. Nature 543, 647–656 (2017).

    CAS  PubMed  Google Scholar 

  5. Hoffman, D. P. & Mathies, R. A. Femtosecond stimulated Raman exposes the role of vibrational coherence in condensed-phase photoreactivity. Acc. Chem. Res. 49, 616–625 (2016).

    CAS  PubMed  Google Scholar 

  6. Lynch, M. S., Van Kuiken, B. E., Daifuku, S. L. & Khalil, M. On the role of high-frequency intramolecular vibrations in ultrafast back-electron transfer reactions. J. Phys. Chem. Lett. 2, 2252–2257 (2011).

    CAS  Google Scholar 

  7. Huang, Y. H., Rettner, C. T., Auerbach, D. J. & Wodtke, A. M. Vibrational promotion of electron transfer. Science 290, 111–114 (2000).

    CAS  PubMed  Google Scholar 

  8. Barbara, P. F., Walker, G. C. & Smith, T. P. Vibrational-modes and the dynamic solvent effect in electron and proton-transfer. Science 256, 975–981 (1992).

    CAS  PubMed  Google Scholar 

  9. Delor, M. et al. Toward control of electron transfer in donor–acceptor molecules by bond-specific infrared excitation. Science 346, 1492–1495 (2014).

    CAS  PubMed  Google Scholar 

  10. Engel, G. S. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007).

    CAS  PubMed  Google Scholar 

  11. Collini, E. et al. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644–648 (2010).

    CAS  PubMed  Google Scholar 

  12. Johnson, P. J. M. et al. Local vibrational coherences drive the primary photochemistry of vision. Nat. Chem. 7, 980–986 (2015).

    CAS  PubMed  Google Scholar 

  13. Jumper, C. C., Rafiq, S., Wang, S. & Scholes, G. D. From coherent to vibronic light harvesting in photosynthesis. Curr. Opin. Chem. Biol. 47, 39–46 (2018).

    CAS  PubMed  Google Scholar 

  14. Romero, E., Novoderezhkin, V. I. & van Grondelle, R. Quantum design of photosynthesis for bio-inspired solar-energy conversion. Nature 543, 355–365 (2017).

    CAS  PubMed  Google Scholar 

  15. Romero, E. et al. Quantum coherence in photosynthesis for efficient solar-energy conversion. Nat. Phys. 10, 677–683 (2014).

    Google Scholar 

  16. Fuller, F. D. et al. Vibronic coherence in oxygenic photosynthesis. Nat. Chem. 6, 706–711 (2014).

    CAS  PubMed  Google Scholar 

  17. Musser, A. J. et al. Evidence for conical intersection dynamics mediating ultrafast singlet exciton fission. Nat. Phys. 11, 352–357 (2015).

    CAS  Google Scholar 

  18. Gelinas, S. et al. Ultrafast long-range charge separation in organic semiconductor photovoltaic diodes. Science 343, 512–516 (2014).

    CAS  PubMed  Google Scholar 

  19. Rafiq, S., Bezdek, M. J., Chirik, P. J. & Scholes, G. D. Dinitrogen coupling to a terpyridine-molybdenum chromophore is switched on by Fermi resonance. Chem 5, 402–416 (2019).

    CAS  Google Scholar 

  20. Satoshi, T. et al. Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization. Science 322, 1073–1077 (2008).

    Google Scholar 

  21. Rozzi, C. A. et al. Quantum coherence controls the charge separation in a prototypical artificial light-harvesting system. Nat. Commun. 4, 1602 (2013).

    PubMed  Google Scholar 

  22. Beratan, D. N. et al. Steering electrons on moving pathways. Acc. Chem. Res. 42, 1669–1678 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  23. Xiao, D. Q., Skourtis, S. S., Rubtsov, I. V. & Beratan, D. N. Turning charge transfer on and off in a molecular interferometer with vibronic pathways. Nano Lett. 9, 1818–1823 (2009).

    CAS  PubMed  Google Scholar 

  24. Delor, M. et al. Directing the path of light-induced electron transfer at a molecular fork using vibrational excitation. Nat. Chem. 9, 1099–1104 (2017).

    CAS  PubMed  Google Scholar 

  25. Lin, Z. et al. Modulating unimolecular charge transfer by exciting bridge vibrations. J. Am. Chem. Soc. 131, 18060–18062 (2009).

    CAS  PubMed  Google Scholar 

  26. Bakulin, A. A. et al. Mode-selective vibrational modulation of charge transport in organic electronic devices. Nat. Commun. 6, 7880 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  27. Engleitner, S., Seel, M. & Zinth, W. Nonexponentialities in the ultrafast electron-transfer dynamics in the system oxazine 1 in N,N-dimethylaniline. J. Phys. Chem. A 103, 3013–3019 (1999).

    CAS  Google Scholar 

  28. Zimmermann, C. et al. Experimental fingerprints of vibrational wave-packet motion during ultrafast heterogeneous electron transfer. J. Phys. Chem. B 105, 9245–9253 (2001).

    CAS  Google Scholar 

  29. Rafiq, S., Dean, J. C. & Scholes, G. D. Observing vibrational wavepackets during an ultrafast electron transfer reaction. J. Phys. Chem. A 119, 11837–11846 (2015).

    CAS  PubMed  Google Scholar 

  30. Abraham, B., Rego, L. G. C. & Gundlach, L. Electronic–vibrational coupling and electron transfer. J. Phys. Chem. C 123, 23760–23772 (2019).

    CAS  Google Scholar 

  31. Rubtsov, I. V., Shirota, H. & Yoshihara, K. Ultrafast photoinduced solute-solvent electron transfer: configuration dependence. J. Phys. Chem. A 103, 1801–1808 (1999).

    CAS  Google Scholar 

  32. Jortner, J. & Bixon, M. Intramolecular vibrational excitations accompanying solvent-controlled electron transfer reactions. J. Chem. Phys. 88, 167–170 (1988).

    CAS  Google Scholar 

  33. Walker, G. C., Akesson, E., Johnson, A. E., Levinger, N. E. & Barbara, P. F. Interplay of solvent motion and vibrational–excitation in electron-transfer kinetics—experiment and theory. J. Phys. Chem. 96, 3728–3736 (1992).

    CAS  Google Scholar 

  34. Dean, J. C. & Scholes, G. D. Coherence spectroscopy in the condensed phase: insights into molecular structure, environment and interactions. Acc. Chem. Res. 50, 2746–2755 (2017).

    CAS  PubMed  Google Scholar 

  35. Rafiq, S. & Scholes, G. D. Slow intramolecular vibrational relaxation leads to long-lived excited-state wavepackets. J. Phys. Chem. A 120, 6792–6799 (2016).

    CAS  PubMed  Google Scholar 

  36. Bixon, M. & Jortner, J. Vibrational coherence in nonadiabatic dynamics. J. Chem. Phys. 107, 1470–1482 (1997).

    CAS  Google Scholar 

  37. Onuchic, J. N. & Wolynes, P. G. Classical and quantum pictures of reaction dynamics in condensed matter—resonances, dephasing and all that. J. Phys. Chem. 92, 6495–6503 (1988).

    CAS  Google Scholar 

  38. Huber, R., Dworak, L., Moser, J. E., Gratzel, M. & Wachtveitl, J. Beyond vibrationally mediated electron transfer: coherent phenomena induced by ultrafast charge separation. J. Phys. Chem. C 120, 8534–8539 (2016).

    CAS  Google Scholar 

  39. Burdett, J. J. & Bardeen, C. J. Quantum beats in crystalline tetracene delayed fluorescence due to triplet pair coherences produced by direct singlet fission. J. Am. Chem. Soc. 134, 8597–8607 (2012).

    CAS  PubMed  Google Scholar 

  40. Liebel, M. et al. Direct observation of the coherent nuclear response after the absorption of a photon. Phys. Rev. Lett. 112, 238301 (2014).

    CAS  PubMed  Google Scholar 

  41. Jean, J. M. Vibrational coherence effects on electronic curve crossing. J. Chem. Phys. 104, 5638–5646 (1996).

    CAS  Google Scholar 

  42. Egorova, D., Kuhl, A. & Domcke, W. Modeling of ultrafast electron-transfer dynamics: multi-level Redfield theory and validity of approximations. Chem. Phys. 268, 105–120 (2001).

    CAS  Google Scholar 

  43. Pisliakov, A. V., Gelin, M. F. & Domcke, W. Detection of electronic and vibrational coherence effects in electron-transfer systems by femtosecond time-resolved fluorescence spectroscopy: theoretical aspects. J. Phys. Chem. A 107, 2657–2666 (2003).

    CAS  Google Scholar 

  44. Brouwer, A. M. & Wilbrandt, R. Vibrational spectra of N,N-dimethylaniline and its radical cation. An interpretation based on quantum chemical calculations. J. Phys. Chem. 100, 9678–9688 (1996).

    CAS  Google Scholar 

  45. Crim, F. F. Chemical reaction dynamics. Proc. Natl Acad. Sci. USA 105, 12647–12648 (2008).

    CAS  PubMed  Google Scholar 

  46. Robinson, G. W. & Frosch, R. P. Theory of electronic energy relaxation in the solid phase. J. Chem. Phys. 37, 1962 (1962).

    CAS  Google Scholar 

  47. Sumi, H. & Marcus, R. A. Dynamical effects in electron transfer reactions. J. Chem. Phys. 84, 4894–4914 (1986).

    CAS  Google Scholar 

  48. Johansson, J. R., Nation, P. D. & Nori, F. QuTiP 2: a Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 184, 1234–1240 (2013).

    CAS  Google Scholar 

Download references

Acknowledgements

Financial support was provided by the Division of Chemical Sciences, Geosciences and Biosciences, Office of Basic Energy Sciences, of the US Department of Energy through grant no. DE-SC0015429. We thank the Imaging and Analysis Center in PRISM at Princeton University for providing access to the Raman facility. B.F. thanks T. Ikeda for helpful discussions. B.K. acknowledges the NSF for a Graduate Research Fellowship (DGE-1656466).

Author information

Authors and Affiliations

  1. Department of Chemistry, Princeton University, Princeton, NJ, USA

    Shahnawaz Rafiq, Bo Fu, Bryan Kudisch & Gregory D. Scholes

Authors
  1. Shahnawaz Rafiq
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bryan Kudisch
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gregory D. Scholes
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.R. and G.D.S. conceived the work and designed the experiments. S.R. performed the laboratory experiments with help from B.K. B.F. performed quantum dynamics simulations. S.R., B.F., B.K. and G.D.S analysed the data and wrote the manuscript.

Corresponding author

Correspondence to Gregory D. Scholes.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Chemistry thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Experimental and theoretical methodology, Supplementary Figs. 1–11 and Discussion.

Source data

Source Data Fig. 1

Fourier transform maps.

Source Data Fig. 2

Fourier transform data comparison.

Source Data Fig. 3

Quantum dynamics simulations data.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rafiq, S., Fu, B., Kudisch, B. et al. Interplay of vibrational wavepackets during an ultrafast electron transfer reaction. Nat. Chem. 13, 70–76 (2021). https://doi.org/10.1038/s41557-020-00607-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41557-020-00607-9

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing