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Ultrafast X-ray scattering reveals vibrational coherence following Rydberg excitation

Abstract

The coherence and dephasing of vibrational motions of molecules constitute an integral part of chemical dynamics, influence material properties and underpin schemes to control chemical reactions. Considerable progress has been made in understanding vibrational coherence through spectroscopic measurements, but precise, direct measurement of the structure of a vibrating excited-state polyatomic organic molecule has remained unworkable. Here, we measure the time-evolving molecular structure of optically excited N-methylmorpholine through scattering with ultrashort X-ray pulses. The scattering signals are corrected for the differences in electron density in the excited electronic state of the molecule in comparison to the ground state. The experiment maps the evolution of the molecular geometry with femtosecond resolution, showing coherent motion that survives electronic relaxation and seems to persist for longer than previously seen using other methods.

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Fig. 1: A schematic of the experimental set-up.
Fig. 2: The calculated difference in scattering patterns caused by nuclear and electronic structure changes as a function of q.
Fig. 3: Time-dependent plots of selected structural parameters of NMM following Rydberg excitation.

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Data availability

The raw experimental data are archived on SLAC’s internal file system. The raw pools of computed structures are stored locally at Brown University. All raw data are available from the corresponding author on reasonable request.

Code availability

The calculation of elastic scattering patterns from ab initio wavefunctions has been discussed in earlier publications27,28,36. The codes used to calculate scattering patterns, process the experimental data and perform the structural determination analysis are available from the corresponding author on reasonable request.

References

  1. Heller, E. J. Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits. Phys. Rev. Lett. 53, 1515–1518 (1984).

    Article  Google Scholar 

  2. Tannor, D. J. Introduction to Quantum Mechanics: A Time-dependent Perspective (University Science Books, Sausalito, 2007).

  3. Marcus, R. A. Electron transfer reactions in chemistry: theory and experiment. Angew. Chem. Int. Ed. 32, 1111–1121 (1993).

    Article  Google Scholar 

  4. Peirce, P., Dahleh, M. A. & Rabitz, H. Optimal control of quantum-mechanical systems: existence, numerical approximation, and applications. Phys. Rev. A 37, 4950 (1988).

    Article  CAS  Google Scholar 

  5. Zewail, A. H. Femtochemistry: atomic-scale dynamics of the chemical bond using ultrafast lasers (Nobel lecture). Angew. Chem. Int. Ed. 39, 2586–2631 (2000).

    Article  CAS  Google Scholar 

  6. Lambert, W. R., Felker, P. M. & Zewail, A. H. Quantum beats and dephasing in isolated large molecules cooled by supersonic jet expansion and excited by picosecond pulses: anthracene. J. Chem. Phys. 75, 5958–5960 (1981).

    Article  CAS  Google Scholar 

  7. Minitti, M. P. et al. Imaging molecular motion: femtosecond X-ray scattering of an electrocyclic chemical reaction. Phys. Rev. Lett. 114, 255501 (2015).

    Article  CAS  Google Scholar 

  8. Glownia, J. M. et al. Self-referenced coherent diffraction X-ray movie of ångstrom- and femtosecond-scale atomic motion. Phys. Rev. Lett. 117, 153003 (2016).

    Article  CAS  Google Scholar 

  9. Küpper, J. et al. X-ray diffraction from isolated and strongly aligned gas-phase molecules with a free-electron laser. Phys. Rev. Lett. 112, 083002 (2014).

    Article  Google Scholar 

  10. Barty, A., Küpper, J. & Chapman, H. N. Molecular imaging using X-ray free-electron lasers. Annu. Rev. Phys. Chem. 64, 415–435 (2013).

    Article  CAS  Google Scholar 

  11. Harb, M. et al. Electronically driven structure changes of Si captured by femtosecond electron diffraction. Phys. Rev. Lett. 100, 155504 (2008).

    Article  Google Scholar 

  12. Ischenko, A. A., Weber, P. M. & Dwayne Miller, R. J. Capturing chemistry in action with electrons: realization of atomically resolved reaction dynamics. Chem. Rev. 117, 11066–11124 (2017).

    Article  CAS  Google Scholar 

  13. Yang, J. et al. Diffractive Imaging of coherent nuclear motion in isolated molecules. Phys. Rev. Lett. 117, 153002 (2016).

    Article  Google Scholar 

  14. Yang, J. et al. Imaging CF3I conical intersection and photodissociation dynamics with ultrafast electron diffraction. Science 361, 64–67 (2018).

    Article  CAS  Google Scholar 

  15. Zewail, A. H. 4D ultrafast electron diffraction, crystallography, and microscopy. Annu. Rev. Phys. Chem. 57, 65–103 (2006).

    Article  CAS  Google Scholar 

  16. Budarz, J. M. et al. Observation of femtosecond molecular dynamics via pump–probe gas phase x-ray scattering. J. Phys. B 49, 34001 (2016).

    Article  Google Scholar 

  17. Minitti, M. P. et al. Toward structural femtosecond chemical dynamics: imaging chemistry in space and time. Faraday Discuss. 171, 81–91 (2014).

    Article  CAS  Google Scholar 

  18. Williamson, J. C., Cao, J., Ihee, H., Frey, H. & Zewail, A. H. Clocking transient chemical changes by ultrafast electron diffraction. Nature 386, 159–162 (1997).

    Article  CAS  Google Scholar 

  19. Zhang, Y., Jónsson, H. & Weber, P. M. Coherence in nonradiative transitions: internal conversion in Rydberg-excited N-methyl and N-ethyl morpholine. Phys. Chem. Chem. Phys. 19, 26403–26411 (2017).

    Article  CAS  Google Scholar 

  20. Waters, M. D. J. et al. Symmetry controlled excited state dynamics. Phys. Chem. Chem. Phys. 21, 2283–2294 (2019).

    Article  CAS  Google Scholar 

  21. Yong, H. et al. Determining orientations of optical transition dipole moments using ultrafast X-ray scattering. J. Phys. Chem. Lett. 9, 6556–6562 (2018).

    Article  CAS  Google Scholar 

  22. Zhang, Y., Deb, S., Jónsson, H. & Weber, P. M. Observation of structural wavepacket motion: the umbrella mode in Rydberg-excited N-methyl morpholine. J. Phys. Chem. Lett. 8, 3740–3744 (2017).

    Article  CAS  Google Scholar 

  23. Dsouza, R., Cheng, X., Li, Z., Miller, R. J. D. & Kochman, A. Oscillatory photoelectron signal of N-methylmorpholine as a test case for the algebraic-diagrammatic construction method of second order. J. Phys. Chem. A 122, 9688–9700 (2018).

    Article  CAS  Google Scholar 

  24. Philipp, H. T., Hromalik, M., Tate, M., Koerner, L. & Gruner, S. M. Pixel array detector for X-ray free electron laser experiments. Nucl. Instrum. Methods Phys. Res. A 649, 67–69 (2011).

    Article  CAS  Google Scholar 

  25. Baskin, J. S. & Zewail, A. H. Ultrafast electron diffraction: oriented molecular structures in space and time. ChemPhysChem 6, 2261–2276 (2005).

    Article  CAS  Google Scholar 

  26. Lorenz, U., Møller, K. B. & Henriksen, N. E. On the interpretation of time-resolved anisotropic diffraction patterns. New J. Phys. 12, 113022 (2010).

    Article  Google Scholar 

  27. Northey, T., Zotev, N. & Kirrander, A. Ab initio calculation of molecular diffraction. J. Chem. Theory Comput. 10, 4911–4920 (2014).

    Article  CAS  Google Scholar 

  28. Northey, T., Moreno Carrascosa, A., Schäfer, S. & Kirrander, A. Elastic X-ray scattering from state-selected molecules. J. Chem. Phys. 145, 154304 (2016).

    Article  Google Scholar 

  29. Warren, B. E. X-ray Diffraction (Courier Corporation, 1969).

  30. Liang, M. et al. The coherent X-ray imaging instrument at the Linac coherent light source. J. Synchrotron Radiat. 22, 514–519 (2015).

    Article  CAS  Google Scholar 

  31. Emma, P. et al. First lasing and operation of an ångstrom-wavelength free-electron laser. Nat. Photon. 4, 641–647 (2010).

    Article  CAS  Google Scholar 

  32. Bionta, M. R. et al. Spectral encoding method for measuring the relative arrival time between X-ray/optical pulses. Rev. Sci. Instrum. 85, 083116 (2014).

    Article  CAS  Google Scholar 

  33. Ruddock, J. M. et al. Simplicity beneath complexity: counting molecular electrons reveals transients and kinetics of photodissociation reactions. Angew. Chem. Int. Ed. 58, 6371–6375 (2019).

    Article  CAS  Google Scholar 

  34. Werner, H. J. et al. MOLPRO v.2012.1 (Molpro, 2012); https://www.molpro.net

  35. Werner, H. J., Knowles, P. J., Knizia, G., Manby, F. R. & Schütz, M. Molpro: a general-purpose quantum chemistry program package. WIREs Comput. Mol. Sci. 2, 242–253 (2012).

    Article  CAS  Google Scholar 

  36. Moreno Carrascosa, A., Northey, T. & Kirrander, A. Imaging rotations and vibrations in polyatomic molecules with X-ray scattering. Phys. Chem. Chem. Phys. 19, 7853–7863 (2017).

    Article  CAS  Google Scholar 

  37. Mai, S. et al. SHARC v.2.0 (SHARC, 2018); https://sharc-md.org

  38. Mai, S., Marquetand, P. & González, L. Nonadiabatic dynamics: the SHARC approach. WIREs Comput. Mol. Sci. 8, 1370 (2018).

    Article  Google Scholar 

  39. Richter, M., Marquetand, P., González-Vázquez, J., Sola, I. & González, L. SHARC: ab initio molecular dynamics with surface hopping in the adiabatic representation including arbitrary couplings. J. Chem. Theory Comput. 7, 1253–1258 (2011).

    Article  CAS  Google Scholar 

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Acknowledgements

The authors thank G. Stewart (SLAC National Accelerator Laboratory) for his generous assistance with preparing the figures. This work was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award no. DE­SC0017995, and by the Army Research Office (grant no. W911NF-17-1-0256). Use of the LCLS, SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under contract no. DE-AC02-76SF00515.

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Authors and Affiliations

Authors

Contributions

P.M.W., A.K. and M.P.M. directed the project. M.L. and S.B. performed X-ray alignment and data collection. S.C., J.S.R. and M.P.M. performed laser alignment. T.J.L. and J.E.K. provided software support during the experiment. W.D. and Y.C. performed record keeping during the experiment. B.S., H.Y., N.Z., J.R., N.G., Y.C. and W.D. performed analyses on the experimental data. H.Y., N.Z. and D.B. performed theoretical computations and structural-determination analysis. B.S. planned the detailed experiments and implemented the data analysis. B.S. and H.Y. wrote the manuscript in consultation with the other authors.

Corresponding author

Correspondence to Peter M. Weber.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Methods, Supplementary data and analysis, Supplementary Figs. 1–6 and Supplementary Table 1.

Supplementary Table 2

All time-dependent structural parameters of NMM extracted from the structural determination analysis described in the main text. The pump–probe delay time is given in ps, all interatomic distances are given in Å and relevant angles are given in degrees.

Supplementary Video 1

The measured difference scattering signals of NMM, Pdiff(Φ,q,t). Each frame in the animation captures one pump–probe delay time point in the measurement.

Supplementary Video 2

The best-fit molecular structure of NMM across all 21 non-hydrogenic interatomic distances as a function of time.

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Stankus, B., Yong, H., Zotev, N. et al. Ultrafast X-ray scattering reveals vibrational coherence following Rydberg excitation. Nat. Chem. 11, 716–721 (2019). https://doi.org/10.1038/s41557-019-0291-0

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