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.
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 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.
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.
Heller, E. J. Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits. Phys. Rev. Lett. 53, 1515–1518 (1984).
Tannor, D. J. Introduction to Quantum Mechanics: A Time-dependent Perspective (University Science Books, Sausalito, 2007).
Marcus, R. A. Electron transfer reactions in chemistry: theory and experiment. Angew. Chem. Int. Ed. 32, 1111–1121 (1993).
Peirce, P., Dahleh, M. A. & Rabitz, H. Optimal control of quantum-mechanical systems: existence, numerical approximation, and applications. Phys. Rev. A 37, 4950 (1988).
Zewail, A. H. Femtochemistry: atomic-scale dynamics of the chemical bond using ultrafast lasers (Nobel lecture). Angew. Chem. Int. Ed. 39, 2586–2631 (2000).
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).
Minitti, M. P. et al. Imaging molecular motion: femtosecond X-ray scattering of an electrocyclic chemical reaction. Phys. Rev. Lett. 114, 255501 (2015).
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).
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).
Barty, A., Küpper, J. & Chapman, H. N. Molecular imaging using X-ray free-electron lasers. Annu. Rev. Phys. Chem. 64, 415–435 (2013).
Harb, M. et al. Electronically driven structure changes of Si captured by femtosecond electron diffraction. Phys. Rev. Lett. 100, 155504 (2008).
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).
Yang, J. et al. Diffractive Imaging of coherent nuclear motion in isolated molecules. Phys. Rev. Lett. 117, 153002 (2016).
Yang, J. et al. Imaging CF3I conical intersection and photodissociation dynamics with ultrafast electron diffraction. Science 361, 64–67 (2018).
Zewail, A. H. 4D ultrafast electron diffraction, crystallography, and microscopy. Annu. Rev. Phys. Chem. 57, 65–103 (2006).
Budarz, J. M. et al. Observation of femtosecond molecular dynamics via pump–probe gas phase x-ray scattering. J. Phys. B 49, 34001 (2016).
Minitti, M. P. et al. Toward structural femtosecond chemical dynamics: imaging chemistry in space and time. Faraday Discuss. 171, 81–91 (2014).
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).
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).
Waters, M. D. J. et al. Symmetry controlled excited state dynamics. Phys. Chem. Chem. Phys. 21, 2283–2294 (2019).
Yong, H. et al. Determining orientations of optical transition dipole moments using ultrafast X-ray scattering. J. Phys. Chem. Lett. 9, 6556–6562 (2018).
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).
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).
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).
Baskin, J. S. & Zewail, A. H. Ultrafast electron diffraction: oriented molecular structures in space and time. ChemPhysChem 6, 2261–2276 (2005).
Lorenz, U., Møller, K. B. & Henriksen, N. E. On the interpretation of time-resolved anisotropic diffraction patterns. New J. Phys. 12, 113022 (2010).
Northey, T., Zotev, N. & Kirrander, A. Ab initio calculation of molecular diffraction. J. Chem. Theory Comput. 10, 4911–4920 (2014).
Northey, T., Moreno Carrascosa, A., Schäfer, S. & Kirrander, A. Elastic X-ray scattering from state-selected molecules. J. Chem. Phys. 145, 154304 (2016).
Warren, B. E. X-ray Diffraction (Courier Corporation, 1969).
Liang, M. et al. The coherent X-ray imaging instrument at the Linac coherent light source. J. Synchrotron Radiat. 22, 514–519 (2015).
Emma, P. et al. First lasing and operation of an ångstrom-wavelength free-electron laser. Nat. Photon. 4, 641–647 (2010).
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).
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).
Werner, H. J. et al. MOLPRO v.2012.1 (Molpro, 2012); https://www.molpro.net
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).
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).
Mai, S. et al. SHARC v.2.0 (SHARC, 2018); https://sharc-md.org
Mai, S., Marquetand, P. & González, L. Nonadiabatic dynamics: the SHARC approach. WIREs Comput. Mol. Sci. 8, 1370 (2018).
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).
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.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Methods, Supplementary data and analysis, Supplementary Figs. 1–6 and Supplementary Table 1.
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.
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.
The best-fit molecular structure of NMM across all 21 non-hydrogenic interatomic distances as a function of time.
About this article
Cite this article
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
Nature Communications (2020)
Tracking the ultraviolet-induced photochemistry of thiophenone during and after ultrafast ring opening
Nature Chemistry (2020)