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Ultrafast X-ray scattering reveals vibrational coherence following Rydberg excitation


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.

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.


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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



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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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).

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