Diffractive imaging of coherent nuclear motion in isolated molecules
Abstract
Observing the motion of the nuclear wave packets during a molecular reaction, in both space and time, is crucial for understanding and controlling the outcome of photoinduced chemical reactions. We have imaged the motion of a vibrational wave packet in isolated iodine molecules using ultrafast electron diffraction with relativistic electrons. The time-varying interatomic distance was measured with a precision 0.07 Å and temporal resolution of 230 fs full width at half maximum. As a result, the method is not only sensitive to the position but also the shape of the nuclear wave packet.
- Authors:
-
- Univ. of Nebraska-Lincoln, Lincoln, NE (United States)
- SLAC National Accelerator Lab., Menlo Park, CA (United States); Potsdam Univ., Potsdam (Germany)
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1331204
- Alternate Identifier(s):
- OSTI ID: 1328470; OSTI ID: 1348858
- Report Number(s):
- SLAC-PUB-16860
Journal ID: ISSN 0031-9007; PRLTAO; TRN: US1601861
- Grant/Contract Number:
- AC02-76SF00515; SC0014170; IIA-1430519
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 117; Journal Issue: 15; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Yang, Jie, Guehr, Markus, Shen, Xiaozhe, Li, Renkai, Vecchione, Theodore, Coffee, Ryan, Corbett, Jeff, Fry, Alan, Hartmann, Nick, Hast, Carsten, Hegazy, Kareem, Jobe, Keith, Makasyuk, Igor, Robinson, Joseph, Robinson, Matthew S., Vetter, Sharon, Weathersby, Stephen, Yoneda, Charles, Wang, Xijie, and Centurion, Martin. Diffractive imaging of coherent nuclear motion in isolated molecules. United States: N. p., 2016.
Web. doi:10.1103/PhysRevLett.117.153002.
Yang, Jie, Guehr, Markus, Shen, Xiaozhe, Li, Renkai, Vecchione, Theodore, Coffee, Ryan, Corbett, Jeff, Fry, Alan, Hartmann, Nick, Hast, Carsten, Hegazy, Kareem, Jobe, Keith, Makasyuk, Igor, Robinson, Joseph, Robinson, Matthew S., Vetter, Sharon, Weathersby, Stephen, Yoneda, Charles, Wang, Xijie, & Centurion, Martin. Diffractive imaging of coherent nuclear motion in isolated molecules. United States. https://doi.org/10.1103/PhysRevLett.117.153002
Yang, Jie, Guehr, Markus, Shen, Xiaozhe, Li, Renkai, Vecchione, Theodore, Coffee, Ryan, Corbett, Jeff, Fry, Alan, Hartmann, Nick, Hast, Carsten, Hegazy, Kareem, Jobe, Keith, Makasyuk, Igor, Robinson, Joseph, Robinson, Matthew S., Vetter, Sharon, Weathersby, Stephen, Yoneda, Charles, Wang, Xijie, and Centurion, Martin. 2016.
"Diffractive imaging of coherent nuclear motion in isolated molecules". United States. https://doi.org/10.1103/PhysRevLett.117.153002. https://www.osti.gov/servlets/purl/1331204.
@article{osti_1331204,
title = {Diffractive imaging of coherent nuclear motion in isolated molecules},
author = {Yang, Jie and Guehr, Markus and Shen, Xiaozhe and Li, Renkai and Vecchione, Theodore and Coffee, Ryan and Corbett, Jeff and Fry, Alan and Hartmann, Nick and Hast, Carsten and Hegazy, Kareem and Jobe, Keith and Makasyuk, Igor and Robinson, Joseph and Robinson, Matthew S. and Vetter, Sharon and Weathersby, Stephen and Yoneda, Charles and Wang, Xijie and Centurion, Martin},
abstractNote = {Observing the motion of the nuclear wave packets during a molecular reaction, in both space and time, is crucial for understanding and controlling the outcome of photoinduced chemical reactions. We have imaged the motion of a vibrational wave packet in isolated iodine molecules using ultrafast electron diffraction with relativistic electrons. The time-varying interatomic distance was measured with a precision 0.07 Å and temporal resolution of 230 fs full width at half maximum. As a result, the method is not only sensitive to the position but also the shape of the nuclear wave packet.},
doi = {10.1103/PhysRevLett.117.153002},
url = {https://www.osti.gov/biblio/1331204},
journal = {Physical Review Letters},
issn = {0031-9007},
number = 15,
volume = 117,
place = {United States},
year = {Mon Oct 03 00:00:00 EDT 2016},
month = {Mon Oct 03 00:00:00 EDT 2016}
}
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Works referenced in this record:
Imaging Molecular Motion: Femtosecond X-Ray Scattering of an Electrocyclic Chemical Reaction
journal, June 2015
- Minitti, M. P.; Budarz, J. M.; Kirrander, A.
- Physical Review Letters, Vol. 114, Issue 25
Dark Structures in Molecular Radiationless Transitions Determined by Ultrafast Diffraction
journal, January 2005
- Srinivasan, R.
- Science, Vol. 307, Issue 5709
Reinvestigation of the Molecular Structure of 1,3,5,7‐Cyclooctatetraene by Electron Diffraction
journal, December 1957
- Bastiansen, O.; Hedberg, Lise; Hedberg, Kenneth
- The Journal of Chemical Physics, Vol. 27, Issue 6
The Ultrafast Pathway of Photon-Induced Electrocyclic Ring-Opening Reactions: The Case of 1,3-Cyclohexadiene
journal, May 2011
- Deb, Sanghamitra; Weber, Peter M.
- Annual Review of Physical Chemistry, Vol. 62, Issue 1
elsepa—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules
journal, January 2005
- Salvat, Francesc; Jablonski, Aleksander; Powell, Cedric J.
- Computer Physics Communications, Vol. 165, Issue 2
Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium
journal, June 2001
- Ruan, C. -Y.; Lobastov, V. A.; Srinivasan, R.
- Proceedings of the National Academy of Sciences, Vol. 98, Issue 13
Direct observation of collective modes coupled to molecular orbital-driven charge transfer
journal, December 2015
- Ishikawa, T.; Hayes, S. A.; Keskin, S.
- Science, Vol. 350, Issue 6267
Mapping molecular motions leading to charge delocalization with ultrabright electrons
journal, April 2013
- Gao, Meng; Lu, Cheng; Jean-Ruel, Hubert
- Nature, Vol. 496, Issue 7445
Imaging of Isolated Molecules with Ultrafast Electron Pulses
journal, September 2012
- Hensley, Christopher J.; Yang, Jie; Centurion, Martin
- Physical Review Letters, Vol. 109, Issue 13
Ultrafast time-resolved electron diffraction with megavolt electron beams
journal, October 2006
- Hastings, J. B.; Rudakov, F. M.; Dowell, D. H.
- Applied Physics Letters, Vol. 89, Issue 18
Erratum : Reinvestigation of the Molecular Structure of 1,3,5,7‐Cyclooctatetraene
journal, March 1958
- Bastiansen, O.; Hedberg, Lise; Hedberg, Kenneth
- The Journal of Chemical Physics, Vol. 28, Issue 3
Imaging of alignment and structural changes of carbon disulfide molecules using ultrafast electron diffraction
journal, September 2015
- Yang, Jie; Beck, Joshua; Uiterwaal, Cornelis J.
- Nature Communications, Vol. 6, Issue 1
Time-Resolved Molecular Frame Dynamics of Fixed-in-Space CS2 Molecules
journal, March 2009
- Bisgaard, C. Z.; Clarkin, O. J.; Wu, G.
- Science, Vol. 323, Issue 5920
Time-Resolved Electron Diffraction from Selectively Aligned Molecules
journal, May 2009
- Reckenthaeler, Peter; Centurion, Martin; Fuß, Werner
- Physical Review Letters, Vol. 102, Issue 21
Imaging an aligned polyatomic molecule with laser-induced electron diffraction
journal, June 2015
- Pullen, Michael G.; Wolter, Benjamin; Le, Anh-Thu
- Nature Communications, Vol. 6, Issue 1
Mega-electron-volt ultrafast electron diffraction at SLAC National Accelerator Laboratory
journal, July 2015
- Weathersby, S. P.; Brown, G.; Centurion, M.
- Review of Scientific Instruments, Vol. 86, Issue 7
Single shot time stamping of ultrabright radio frequency compressed electron pulses
journal, July 2013
- Gao, M.; Jiang, Y.; Kassier, G. H.
- Applied Physics Letters, Vol. 103, Issue 3
Mechanism and Dynamics of Azobenzene Photoisomerization
journal, July 2003
- Schultz, Thomas; Quenneville, Jason; Levine, Benjamin
- Journal of the American Chemical Society, Vol. 125, Issue 27
Reconstruction of three-dimensional molecular structure from diffraction of laser-aligned molecules
journal, July 2014
- Yang, Jie; Makhija, Varun; Kumarappan, Vinod
- Structural Dynamics, Vol. 1, Issue 4
Mapping atomic motions with ultrabright electrons: towards fundamental limits in space-time resolution
journal, January 2015
- Manz, Stephanie; Casandruc, Albert; Zhang, Dongfang
- Faraday Discussions, Vol. 177
Imaging ultrafast molecular dynamics with laser-induced electron diffraction
journal, March 2012
- Blaga, Cosmin I.; Xu, Junliang; DiChiara, Anthony D.
- Nature, Vol. 483, Issue 7388
Diffractive imaging of a rotational wavepacket in nitrogen molecules with femtosecond megaelectronvolt electron pulses
journal, April 2016
- Yang, Jie; Guehr, Markus; Vecchione, Theodore
- Nature Communications, Vol. 7, Issue 1
Time-Resolved Photoelectron Spectra of : Dynamics at Conical Intersections
journal, March 2014
- Wang, Kwanghsi; McKoy, Vincent; Hockett, Paul
- Physical Review Letters, Vol. 112, Issue 11
Experimental observation of high-brightness microbunching in a photocathode rf electron gun
journal, October 1996
- Wang, X. J.; Qiu, X.; Ben-Zvi, I.
- Physical Review E, Vol. 54, Issue 4
The Validity of the "Diradical" Hypothesis: Direct Femtoscond Studies of the Transition-State Structures
journal, November 1994
- Pedersen, S.; Herek, J. L.; Zewail, A. H.
- Science, Vol. 266, Issue 5189
Compression of Subrelativistic Space-Charge-Dominated Electron Bunches for Single-Shot Femtosecond Electron Diffraction
journal, December 2010
- van Oudheusden, T.; Pasmans, P. L. E. M.; van der Geer, S. B.
- Physical Review Letters, Vol. 105, Issue 26
Direct Imaging of Transient Molecular Structures with Ultrafast Diffraction
journal, January 2001
- Ihee, H.
- Science, Vol. 291, Issue 5503
Self-Referenced Coherent Diffraction X-Ray Movie of Ångstrom- and Femtosecond-Scale Atomic Motion
journal, October 2016
- Glownia, J. M.; Natan, A.; Cryan, J. P.
- Physical Review Letters, Vol. 117, Issue 15
Pump–probe diffraction imaging of vibrational wave functions
journal, May 1998
- Geiser, Joseph D.; Weber, Peter M.
- The Journal of Chemical Physics, Vol. 108, Issue 19
Imaging single electrons to enable the generation of ultrashort beams for single-shot femtosecond relativistic electron diffraction
journal, October 2011
- Li, R. K.; Musumeci, P.; Bender, H. A.
- Journal of Applied Physics, Vol. 110, Issue 7
Direct observation of the femtosecond excited-state cis-trans isomerization in bacteriorhodopsin
journal, May 1988
- Mathies, R.; Brito Cruz, C.; Pollard, W.
- Science, Vol. 240, Issue 4853
Time-resolved imaging of purely valence-electron dynamics during a chemical reaction
journal, April 2011
- Hockett, Paul; Bisgaard, Christer Z.; Clarkin, Owen J.
- Nature Physics, Vol. 7, Issue 8
Ultrafast Electron Diffraction (UED): A New Development for the 4D Determination of Transient Molecular Structures
journal, June 2003
- Srinivasan, Ramesh; Lobastov, Vladimir A.; Ruan, Chong-Yu
- Helvetica Chimica Acta, Vol. 86, Issue 6
Molecular Spectra and Molecular Structure
journal, November 1929
- Garner, W. E.; Lennard-Jones, J. E.
- Nature, Vol. 124, Issue 3133
Molecular Spectra and Molecular Structure
journal, October 1929
- Garner, W. E.; Lennard-Jones, J. E.
- Nature, Vol. 124, Issue 3128
Ultrafast Electron Diffraction (UED). A New Development for the 4D Determination of Transient Molecular Structures
journal, October 2003
- Srinivasan, Ramesh; Lobastov, Vladimir A.; Ruan, Chong-Yu
- ChemInform, Vol. 34, Issue 40
Compression of sub-relativistic space-charge-dominated electron bunches for single-shot femtosecond electron diffraction
text, January 2010
- van Oudheusden, T.; Pasmans, P. L. E. M.; van der Geer, S. B.
- arXiv
Imaging an aligned polyatomic molecule with laser-induced electron diffraction
text, January 2015
- Pullen, Michael; Wolter, Benjamin; Le, Anh-Thu
- arXiv
Works referencing / citing this record:
Räumliche Trennung der Konformere eines Dipeptids
journal, September 2018
- Teschmit, Nicole; Horke, Daniel A.; Küpper, Jochen
- Angewandte Chemie, Vol. 130, Issue 42
Spatially Separating the Conformers of a Dipeptide
journal, October 2018
- Teschmit, Nicole; Horke, Daniel A.; Küpper, Jochen
- Angewandte Chemie International Edition, Vol. 57, Issue 42
Different flavors of nonadiabatic molecular dynamics
journal, April 2019
- Agostini, Federica; Curchod, Basile F. E.
- Wiley Interdisciplinary Reviews: Computational Molecular Science
Conical-intersection dynamics and ground-state chemistry probed by extreme-ultraviolet time-resolved photoelectron spectroscopy
journal, August 2018
- von Conta, A.; Tehlar, A.; Schletter, A.
- Nature Communications, Vol. 9, Issue 1
All-optical field-free three-dimensional orientation of asymmetric-top molecules
journal, December 2018
- Lin, Kang; Tutunnikov, Ilia; Qiang, Junjie
- Nature Communications, Vol. 9, Issue 1
Long-lasting field-free alignment of large molecules inside helium nanodroplets
journal, January 2019
- Chatterley, Adam S.; Schouder, Constant; Christiansen, Lars
- Nature Communications, Vol. 10, Issue 1
The photochemical ring-opening of 1,3-cyclohexadiene imaged by ultrafast electron diffraction
journal, April 2019
- Wolf, T. J. A.; Sanchez, D. M.; Yang, J.
- Nature Chemistry, Vol. 11, Issue 6
Ultrafast X-ray scattering reveals vibrational coherence following Rydberg excitation
journal, July 2019
- Stankus, Brian; Yong, Haiwang; Zotev, Nikola
- Nature Chemistry, Vol. 11, Issue 8
A direct electron detector for time-resolved MeV electron microscopy
journal, March 2017
- Vecchione, T.; Denes, P.; Jobe, R. K.
- Review of Scientific Instruments, Vol. 88, Issue 3
High current table-top setup for femtosecond gas electron diffraction
journal, July 2017
- Zandi, Omid; Wilkin, Kyle J.; Xiong, Yanwei
- Structural Dynamics, Vol. 4, Issue 4
Theoretical study of ultrafast x-ray photoelectron diffraction from molecules undergoing photodissociation
journal, March 2018
- Tsuru, Shota; Fujikawa, Takashi; Stener, Mauro
- The Journal of Chemical Physics, Vol. 148, Issue 12
Communication: Strong laser alignment of solvent-solute aggregates in the gas-phase
journal, March 2018
- Trippel, Sebastian; Wiese, Joss; Mullins, Terry
- The Journal of Chemical Physics, Vol. 148, Issue 10
Atomic-resolution imaging of carbonyl sulfide by laser-induced electron diffraction
journal, June 2019
- Karamatskos, Evangelos T.; Goldsztejn, Gildas; Raabe, Sebastian
- The Journal of Chemical Physics, Vol. 150, Issue 24
Scattering off molecules far from equilibrium
journal, August 2019
- Yong, Haiwang; Ruddock, Jennifer M.; Stankus, Brian
- The Journal of Chemical Physics, Vol. 151, Issue 8
Femtosecond gas-phase mega-electron-volt ultrafast electron diffraction
journal, September 2019
- Shen, X.; Nunes, J. P. F.; Yang, J.
- Structural Dynamics, Vol. 6, Issue 5
Excited-state dynamics of molecules with classically driven trajectories and Gaussians
journal, September 2019
- Ibele, Lea M.; Nicolson, Angus; Curchod, Basile F. E.
- Molecular Physics, Vol. 118, Issue 8
Roadmap of ultrafast x-ray atomic and molecular physics
journal, January 2018
- Young, Linda; Ueda, Kiyoshi; Gühr, Markus
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 51, Issue 3
Attomicroscopy: from femtosecond to attosecond electron microscopy
journal, January 2018
- Hassan, Mohammed Th
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 51, Issue 3
Roadmap on photonic, electronic and atomic collision physics: II. Electron and antimatter interactions
journal, August 2019
- Schippers, Stefan; Sokell, Emma; Aumayr, Friedrich
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 52, Issue 17
Time-resolved photoelectron angular distributions from nonadiabatically aligned CO 2 molecules with SX-FEL at SACLA
journal, November 2018
- Minemoto, Shinichirou; Shimada, Hiroyuki; Komatsu, Kazma
- Journal of Physics Communications, Vol. 2, Issue 11
On the limits of observing motion in time-resolved X-ray scattering
journal, April 2019
- Ware, Matthew R.; Glownia, James M.; Natan, Adi
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2145
Energy-resolved coherent diffraction from laser-driven electronic motion in atoms
journal, October 2017
- Shao, Hua-Chieh; Starace, Anthony F.
- Physical Review A, Vol. 96, Issue 4
Multiple-orbital effects in laser-induced electron diffraction of aligned molecules
journal, October 2018
- Krečinić, Faruk; Wopperer, Philipp; Frusteri, Biagio
- Physical Review A, Vol. 98, Issue 4
Strong-field- versus weak-field-ionization pump-probe spectroscopy
journal, November 2018
- Horton, Spencer L.; Liu, Yusong; Chakraborty, Pratip
- Physical Review A, Vol. 98, Issue 5
Violation of centrosymmetry in time-resolved coherent x-ray diffraction from rovibrational states of diatomic molecules
journal, March 2019
- Shao, Hua-Chieh; Starace, Anthony F.
- Physical Review A, Vol. 99, Issue 3
Real-Time Observation of Internal Motion within Ultrafast Dissipative Optical Soliton Molecules
journal, June 2017
- Krupa, Katarzyna; Nithyanandan, K.; Andral, Ugo
- Physical Review Letters, Vol. 118, Issue 24
Imaging CF 3 I conical intersection and photodissociation dynamics with ultrafast electron diffraction
journal, July 2018
- Yang, Jie; Zhu, Xiaolei; Wolf, Thomas J. A.
- Science, Vol. 361, Issue 6397
Ultrafast isomerization in acetylene dication after carbon K-shell ionization
text, January 2017
- Li, Zheng; Inhester, Ludger; Liekhus-Schmaltz, Chelsea
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Laser-induced alignment of weakly bound molecular aggregates
text, January 2018
- Thesing, Linda Vanessa; Yachmenev, Andrey; González-Férez, Rosario
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Molecular movie of ultrafast coherent rotational dynamics of OCS
text, January 2019
- Karamatskos, Evangelos Thomas; Raabe, Sebastian; Mullins, Terence
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Ultrashort Free-Electron Laser X-ray Pulses
journal, September 2017
- Helml, Wolfram; Grguraš, Ivanka; Juranić, Pavle
- Applied Sciences, Vol. 7, Issue 9
Recent Advances in Ultrafast Structural Techniques
journal, April 2019
- Sciaini, Germán
- Applied Sciences, Vol. 9, Issue 7
Ultrafast isomerization in acetylene dication after carbon K-shell ionization
journal, September 2017
- Li, Zheng; Inhester, Ludger; Liekhus-Schmaltz, Chelsea
- Nature Communications, Vol. 8, Issue 1
Laser-induced alignment of weakly bound molecular aggregates
journal, November 2018
- Thesing, Linda V.; Yachmenev, Andrey; González-Férez, Rosario
- Physical Review A, Vol. 98, Issue 5
Roadmap of ultrafast x-ray atomic and molecular physics
text, January 2019
- Young, Linda; Ueda, Kiyoshi; Gühr, Markus
- Universität Potsdam
Ultrashort Free-Electron Laser X-ray Pulses
text, January 2017
- Helml, Wolfram; Grguraš, Ivanka; Juranic, Pavle
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Communication: Strong laser alignment of solvent-solute aggregates in the gas-phase
text, January 2018
- Trippel, Sebastian; Wiese, Joss; Mullins, Terence
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Conical-intersection dynamics and ground-state chemistry probed by extreme-ultraviolet time-resolved photoelectron spectroscopy
text, January 2018
- Aaron, von Conta,; Andres, Tehlar,; Albert, Schletter,
- ETH Zurich
Time-resolved inner-shell photoelectron spectroscopy: From a bound molecule to an isolated atom
text, January 2018
- Brauße, Felix; Goldsztejn, Gildas; Amini, Kasra
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Atomic-resolution imaging of carbonyl sulfide by laser-induced electron diffraction
text, January 2019
- Karamatskos, Evangelos T.; Goldsztejn, Gildas; Raabe, Sebastian
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Excited-state dynamics of molecules with classically driven trajectories and Gaussians
text, January 2019
- Ibele, Lea M.; Nicolson, Angus; Curchod, Basile F. E.
- Taylor & Francis
Molecular movie of ultrafast coherent rotational dynamics of OCS
journal, July 2019
- Karamatskos, Evangelos T.; Raabe, Sebastian; Mullins, Terry
- Nature Communications, Vol. 10, Issue 1
Spatially Separating the Conformers of a Dipeptide
text, January 2018
- Teschmit, Nicole; Horke, Daniel A.; Küpper, Jochen
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Excited-state dynamics of molecules with classically driven trajectories and Gaussians
text, January 2019
- Ibele, Lea M.; Nicolson, Angus; Curchod, Basile F. E.
- Taylor & Francis
Roadmap of ultrafast x-ray atomic and molecular physics
text, January 2018
- Young, Linda; Ueda, Kiyoshi; Gühr, Markus
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Attomicroscopy: from Femtosecond to Attosecond Electron Microscopy
text, January 2018
- Hassan, Mohammed Th.
- arXiv
Terahertz streaking of few-femtosecond relativistic electron beams
text, January 2018
- Zhao, Lingrong; Wang, Zhe; Lu, Chao
- arXiv