1 Ultrafast Electron Diffraction from Molecules in the Gas Phase Martin Centurion University of Nebraska – Lincoln

Outline Recent progress in Gas Phase diffraction: UED from aligned molecules. Opportunities and challenges ahead: Phase retrieval algorithms. Pulse parameters 2

3 Ultrafast Gas Phase Electron Diffraction Determine the 3D structure of molecules without crystallization. Investigate photoreactions of isolated molecules. Image intermediate states with femtosecond and sub- Angstrom resolution. (groundbreaking picosecond experiments were done by the Zewail group at Caltech) Structure and Dynamics of Isolated Molecules

r ij are the interatomic distances Molecular Scattering Total Scattering Gas Electron Diffraction 4

Theory Experiment Modified scattering intensity I-I I-… F-F C-F Azimuthally averaged sM(s) Radial Distribution function Sine Transform Gas Electron Diffraction s (1/Å) Experiment Theory C2F4I2C2F4I2 5

Gas Electron Diffraction Advantages High Scattering Cross Section. Compact Setup. Limited by random orientation of molecules: 1D Information. Structure is retrieved by iteratively comparing the data with a theoretical model. Low contrast diffraction patterns. 6

Non-adiabatic (field-free) alignment Diffraction from Aligned Molecules 7 Aligned molecules: 3D structure accessible Random orientation: limited to 1D information

Fourier-Hankel Transform 1,2 Perfect alignment — = 1 α Partial alignment — = 0.50 From diffraction pattern to structure 8 z r Fourier-Hankel Transform 1,2 1 P. Ho et. al. J. Chem. Phys. 131, (2009). 2 D. Saldin, et. al. Acta Cryst. A66, 32–37 (2010).

100 µm diameter interaction region Overall resolution 850 fs (first gas phase experiment with sub-ps resolution) Experiment – Target Interaction Region Supersonic seeded gas jet (helium) electron pulse alignment laser 9 CF3ICF3I Simple molecule with 3D structure Target:

Experimental Setup Imaging Detector Turbo pump Diffusion pump 40fs, 1mJ, 800nm Magnetic Lens Gas Nozzle Cathode Anode Third Harmonic generation Electron pulses 25 keV 500 fs 2000 electrons/pulse Alignment laser pulses 800 nm 300 fs 2.2 x W/cm 2

Anisotropic Diffraction Patterns delay = -1.7 ps delay = -1.2 ps delay = -0.7 ps delay = -0.2 psdelay = 0.3 ps delay = 0.8 ps delay = 1.3 psdelay = 1.8 psdelay = 2.3 ps delay = 2.8 ps delay = 3.3 ps delay = 3.8 ps delay = 4.3 ps delay = 4.8 ps 11 5 min integration time Laser

Revivals can also be measured 12 Data collection Revival Non-zero background after initial alignment

Experimental Data 13 60° projection No laser random orientation electrons Laser polarization 90° projection

Theory – Reconstruction Diffraction with Perfect Alignment Molecular Structure Phase retrieval algorithm 14 Diffraction with Partial Alignment There is no algorithm for partial alignment Molecular Structure New path

Perfect alignment Perpendicular Partial alignment Any orientation Retrieving Perfect Alignment from Multiple Diffraction Patterns 15 Transformation requires knowledge of the degree of alignment (angular distribution), but not the structure. There is no inverse transformation. Rotation and averaging

Combine multiple diffraction patterns to build the pattern corresponding to perfect alignment Partial alignment 90° Retrieving Perfect Alignment from Multiple Diffraction Patterns 16 60° Random orientation

partial aligned uniform guess Difference with data defines error error locally minimized? no reconstruct object Genetic Algorithm for Retrieving Perfect Alignment small change yes error reduced? no yes retain change discard change Rotation and averaging 17

Retrieval Result from Data k iterations 2 hours The algorithm also optimizes for the degree of alignment.

Reconstruction of CF 3 I Structure from experimental data ExperimentLiterature r CI 2.19±0.07Å2.14 Å r FI 2.92±0.09Å2.89 Å I-C-F Angle 120± C. J. Hensley, J. Yang and M. Centurion, Phys. Rev. Lett. 109, (2012) 19 r (Å) z (Å) The image is retrieved form the data without any previous knowledge of the structure

Outline Recent progress in Gas Phase diffraction: 3D structure determination with aligned molecules. Opportunities and challenges ahead: Phase retrieval algorithms. Pulse parameters 20

Work in progress: Modified iterative phase retrieval algorithm for molecules of unknown symmetry Simulated pattern in cylindrical coordinates 2D object Inputs: Diffraction Pattern Constraints applied on object plane. Algorithm: Fienup Hybrid Input-Output + Flip-Charge 21 3D objects 1 D. Starodub, J. Spence, D. Saldin, Proc. SPIE Conf., 7800, 7800 (2010). 2 D. Saldin, et. al. Acta Cryst. A66, 32–37 (2010). Benzotrifluoride (C 7 H 5 F 3 )

Temporal Resolution Ideal parameters: Pulse duration: ~ 20 fs Charge: as high as possible With RF Gun: 100 fs, 1 million e Group velocity mismatch Laser with a tilted pulse front System was purchased from AccTec in Eindhoven 22

Summary 3D imaging of molecules possible with laser-aligned molecules. Molecular dynamics can be probed in a field free environment. We are working to apply this method to larger molecules. RF gun will greatly improve the experimental conditions. 23

24 Acknowledgements Funding Department of Energy, Basic Energy Sciences Air Force Office of Scientific Research Group Members Chris Hensley (postdoc) Jie Yang (grad student) Ping Zhang (postdoc) Omid Zandi (grad student) Walter Bircher (undergrad) Former members Cory Baumgarten (undergrad) James Ferguson (undergrad)