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Ultrafast Electron Diffraction from Molecules in the Gas Phase

Martin Centurion

University of Nebraska – Lincoln

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Outline

Recent progress in Gas Phase diffraction:• UED from aligned molecules.

Opportunities and challenges ahead:• Phase retrieval algorithms.• Pulse parameters

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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

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( ) ( ) ( ) tot at molI s I s I s

4 sin( / 2)s

sin( )( ) ij

mol ij i jij

s rI s F f f

s r

rij are the interatomic distances

Molecular Scattering

Total Scattering

Gas Electron Diffraction

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( ) mol

at

s IsM sI

Theory

Experiment

Modified scattering intensity

I-I

I-…

F-FC-F

Azimuthally averaged sM(s)

Radial Distribution function

Sine Transform

Gas Electron Diffraction

6 4 2 0 2 4 6

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4

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s (1/Å)

s (1

/Å)

Experiment

Theory

C2F4I2

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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.

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Non-adiabatic (field-free) alignment

Diffraction from Aligned Molecules

Aligned molecules:3D structure accessible

Random orientation:limited to 1D information

Fourier-Hankel Transform1,2

Perfect alignment — <cos2α> = 1

α

Partial alignment — <cos2α> = 0.50

From diffraction pattern to structure

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z

r

Fourier-Hankel Transform1,2

1P. Ho et. al. J. Chem. Phys. 131, 131101 (2009). 2D. Saldin, et. al. Acta Cryst. A66, 32–37 (2010).

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100 µm diameter interaction regionOverall resolution 850 fs(first gas phase experiment with sub-ps resolution)

Experiment – Target Interaction Region

Supersonic seeded gas jet (helium)

electron pulse

alignment laser

CF3I

Simple molecule with 3D structure

Target:

Experimental Setup

Imaging Detector

Turbo pump

Diffusion pump

40fs, 1mJ, 800nm

Magnetic Lens Gas NozzleCathodeA

nodeThird Harmonic generation

Electron pulses• 25 keV• 500 fs • 2000 electrons/pulse

Alignment laser pulses• 800 nm• 300 fs• 2.2 x 1013 W/cm2

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-0.2

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Anisotropic Diffraction Patterns

delay = -1.7 ps

p3500

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delay = -1.2 ps

p3490

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delay = -0.7 ps

p3480

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delay = -0.2 ps

p3475

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delay = 0.3 ps

p3470

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delay = 0.8 ps

p3460

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delay = 1.3 ps

p3455

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delay = 1.8 ps

p34451refNO0x2E3

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delay = 2.3 ps

p3440

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p3430

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delay = 3.3 ps

p34201refNO0x2E5

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p34151refNO0x2E5

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delay = 4.3 ps

p3405

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p3400

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Δ 𝑠𝑀 (𝑡 )=𝑠𝑀 (𝑡 ) −𝑠𝑀𝐺𝑟𝑜𝑢𝑛𝑑

5 min integration timeLaser

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Revivals can also be measured

Data collection Revival

Non-zero background after initial alignment

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Experimental Data

Δ 𝑠𝑀

60° projection

𝑠𝑀

No laser

random orientation

Δ 𝑠𝑀

electrons

Laser polarization

90° projection

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Theory – Reconstruction

Diffraction with Perfect Alignment

Molecular StructurePhase retrieval algorithm

Diffraction with Partial Alignment

There is no algorithm for partial alignment

Molecular Structure

New path

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Perfect alignment Perpendicular

Partial alignment Any orientation

Retrieving Perfect Alignment from Multiple Diffraction Patterns

• Transformation requires knowledge of the degree of alignment (angular distribution), but not the structure.

• There is no inverse transformation.

Rotation and averaging

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Combine multiple diffraction patterns to build the pattern corresponding to perfect alignment

Partial alignment 90°

Retrieving Perfect Alignment from Multiple Diffraction Patterns

60° Random orientation

partial aligned

uniformguess

Difference with data

defines error

error locally minimized?

no

reconstruct object

Genetic Algorithm for Retrieving Perfect Alignment

smallchange

yes

error reduced?no

yes

retain change

discard change

Rotation and averaging

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Retrieval Result from Data

100k iterations2 hours

The algorithm also optimizes for the degree of alignment.

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Reconstruction of CF3I

Structure from experimental data

Experiment Literature

rCI 2.19±0.07Å 2.14 ÅrFI 2.92±0.09Å 2.89 ÅI-C-F Angle 120±90 1110

C. J. Hensley, J. Yang and M. Centurion, Phys. Rev. Lett. 109, 133202(2012)

r (Å)

z (Å)

The image is retrieved form the data without any previous knowledge of the structure

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Outline

Recent progress in Gas Phase diffraction:• 3D structure determination with aligned

molecules.

Opportunities and challenges ahead:• Phase retrieval algorithms.• Pulse parameters

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Work in progress: Modified iterative phase retrieval algorithm for molecules of unknown symmetry

Simulated pattern in cylindrical coordinates

2D object

Inputs: Diffraction PatternConstraints applied on object plane.Algorithm: Fienup Hybrid Input-Output + Flip-Charge

3D objects

1D. Starodub, J. Spence, D. Saldin, Proc. SPIE Conf., 7800, 7800 (2010).2D. Saldin, et. al. Acta Cryst. A66, 32–37 (2010).

Benzotrifluoride (C7H5F3)

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Temporal Resolution

Ideal parameters:Pulse duration: ~ 20 fsCharge: as high as possible

With RF Gun: 100 fs, 1 million e

Group velocity mismatchLaser with a tilted pulse front

System was purchased from AccTec in Eindhoven

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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.

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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)