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.
Subscribe to Journal
Get full journal access for 1 year
only $9.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The codes for the quantum dynamics simulations are available from the corresponding author upon request.
Bixon, M. & Jortner, J. in Electron Transfer—From Isolated Molecules to Biomolecules Ch. 3 (Wiley, 2007).
Marcus, R. A. Chemical and electrochemical electron-transfer theory. Annu. Rev. Phys. Chem. 15, 155–196 (1964).
Rafiq, S. & Scholes, G. D. From fundamental theories to quantum coherences in electron transfer. J. Am. Chem. Soc. 141, 708–722 (2019).
Scholes, G. D. et al. Utilizing coherence to enhance function in chemical and biophysical systems. Nature 543, 647–656 (2017).
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).
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).
Huang, Y. H., Rettner, C. T., Auerbach, D. J. & Wodtke, A. M. Vibrational promotion of electron transfer. Science 290, 111–114 (2000).
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).
Delor, M. et al. Toward control of electron transfer in donor–acceptor molecules by bond-specific infrared excitation. Science 346, 1492–1495 (2014).
Engel, G. S. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007).
Collini, E. et al. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644–648 (2010).
Johnson, P. J. M. et al. Local vibrational coherences drive the primary photochemistry of vision. Nat. Chem. 7, 980–986 (2015).
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).
Romero, E., Novoderezhkin, V. I. & van Grondelle, R. Quantum design of photosynthesis for bio-inspired solar-energy conversion. Nature 543, 355–365 (2017).
Romero, E. et al. Quantum coherence in photosynthesis for efficient solar-energy conversion. Nat. Phys. 10, 677–683 (2014).
Fuller, F. D. et al. Vibronic coherence in oxygenic photosynthesis. Nat. Chem. 6, 706–711 (2014).
Musser, A. J. et al. Evidence for conical intersection dynamics mediating ultrafast singlet exciton fission. Nat. Phys. 11, 352–357 (2015).
Gelinas, S. et al. Ultrafast long-range charge separation in organic semiconductor photovoltaic diodes. Science 343, 512–516 (2014).
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).
Satoshi, T. et al. Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization. Science 322, 1073–1077 (2008).
Rozzi, C. A. et al. Quantum coherence controls the charge separation in a prototypical artificial light-harvesting system. Nat. Commun. 4, 1602 (2013).
Beratan, D. N. et al. Steering electrons on moving pathways. Acc. Chem. Res. 42, 1669–1678 (2009).
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).
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).
Lin, Z. et al. Modulating unimolecular charge transfer by exciting bridge vibrations. J. Am. Chem. Soc. 131, 18060–18062 (2009).
Bakulin, A. A. et al. Mode-selective vibrational modulation of charge transport in organic electronic devices. Nat. Commun. 6, 7880 (2015).
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).
Zimmermann, C. et al. Experimental fingerprints of vibrational wave-packet motion during ultrafast heterogeneous electron transfer. J. Phys. Chem. B 105, 9245–9253 (2001).
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).
Abraham, B., Rego, L. G. C. & Gundlach, L. Electronic–vibrational coupling and electron transfer. J. Phys. Chem. C 123, 23760–23772 (2019).
Rubtsov, I. V., Shirota, H. & Yoshihara, K. Ultrafast photoinduced solute-solvent electron transfer: configuration dependence. J. Phys. Chem. A 103, 1801–1808 (1999).
Jortner, J. & Bixon, M. Intramolecular vibrational excitations accompanying solvent-controlled electron transfer reactions. J. Chem. Phys. 88, 167–170 (1988).
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).
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).
Rafiq, S. & Scholes, G. D. Slow intramolecular vibrational relaxation leads to long-lived excited-state wavepackets. J. Phys. Chem. A 120, 6792–6799 (2016).
Bixon, M. & Jortner, J. Vibrational coherence in nonadiabatic dynamics. J. Chem. Phys. 107, 1470–1482 (1997).
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).
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).
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).
Liebel, M. et al. Direct observation of the coherent nuclear response after the absorption of a photon. Phys. Rev. Lett. 112, 238301 (2014).
Jean, J. M. Vibrational coherence effects on electronic curve crossing. J. Chem. Phys. 104, 5638–5646 (1996).
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).
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).
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).
Crim, F. F. Chemical reaction dynamics. Proc. Natl Acad. Sci. USA 105, 12647–12648 (2008).
Robinson, G. W. & Frosch, R. P. Theory of electronic energy relaxation in the solid phase. J. Chem. Phys. 37, 1962 (1962).
Sumi, H. & Marcus, R. A. Dynamical effects in electron transfer reactions. J. Chem. Phys. 84, 4894–4914 (1986).
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).
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).
The authors declare no competing interests.
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.
About this article
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