Femtosecond response of polyatomic molecules to ultra-intense hard X-rays


X-ray free-electron lasers enable the investigation of the structure and dynamics of diverse systems, including atoms, molecules, nanocrystals and single bioparticles, under extreme conditions1,2,3,4,5,6,7. Many imaging applications that target biological systems and complex materials use hard X-ray pulses with extremely high peak intensities (exceeding 1020 watts per square centimetre)3,5. However, fundamental investigations have focused mainly on the individual response of atoms and small molecules using soft X-rays with much lower intensities8,9,10,11,12,13,14,15,16,17. Studies with intense X-ray pulses have shown that irradiated atoms reach a very high degree of ionization, owing to multiphoton absorption8,12,13,18, which in a heteronuclear molecular system occurs predominantly locally on a heavy atom (provided that the absorption cross-section of the heavy atom is considerably larger than those of its neighbours) and is followed by efficient redistribution of the induced charge14,15,16,17,19,20. In serial femtosecond crystallography of biological objects—an application of X-ray free-electron lasers that greatly enhances our ability to determine protein structure2,3—the ionization of heavy atoms increases the local radiation damage that is seen in the diffraction patterns of these objects21,22 and has been suggested as a way of phasing the diffraction data23,24. On the basis of experiments using either soft or less-intense hard X-rays14,15,16,17,18,19,25, it is thought that the induced charge and associated radiation damage of atoms in polyatomic molecules can be inferred from the charge that is induced in an isolated atom under otherwise comparable irradiation conditions. Here we show that the femtosecond response of small polyatomic molecules that contain one heavy atom to ultra-intense (with intensities approaching 1020 watts per square centimetre), hard (with photon energies of 8.3 kiloelectronvolts) X-ray pulses is qualitatively different: our experimental and modelling results establish that, under these conditions, the ionization of a molecule is considerably enhanced compared to that of an individual heavy atom with the same absorption cross-section. This enhancement is driven by ultrafast charge transfer within the molecule, which refills the core holes that are created in the heavy atom, providing further targets for inner-shell ionization and resulting in the emission of more than 50 electrons during the X-ray pulse. Our results demonstrate that efficient modelling of X-ray-driven processes in complex systems at ultrahigh intensities is feasible.

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Figure 1: Experimental charge-state distributions.
Figure 2: Enhanced ionization of the molecule.
Figure 3: Kinetic energies of the iodine ions.
Figure 4: Simulated evolution of molecular geometry and charge distribution.


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This work is supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, who supported the Kansas group under contract no. DE-FG02-86ER13491 and the Argonne group under contract no. DE-AC02-06CH11357, and by the excellence cluster ‘The Hamburg Centre for Ultrafast Imaging: Structure, Dynamics, and Control of Matter at the Atomic Scale’ of the Deutsche Forschungsgemeinschaft. Use of the Linac Coherent Light Source (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. A.R. acknowledges support from the National Science Foundation EPSCoR Track II Award No. IIA-1430493. T.G. acknowledges the Peter–Ewald Fellowship from the Volkswagen foundation. D.R. acknowledges support from the Helmholtz Gemeinschaft through the Helmholtz Young Investigator Program. K.U. acknowledges the XFEL strategy programme of MEXT, the five stars alliance and the TAGEN project for support. We are grateful to the SLAC staff for their support and hospitality during the beamtime.

Author information

A.R., B.R. and D.R. conceived the experiment, which was coordinated by A.R. and D.R. and carried out by A.R., B.E., R.B., C.Bom., E.S., B.R., L.F., S.H.S., C.S.L., B.K., T.M., M.S., K.U., K.R.F., M.B., T.G., S.C., R.A.-M., J.E.K., J.C., G.J.W., S.B., L.Y., C.Bos. and D.R. The ion spectrometer with the delay-line detector was assembled and operated mainly by A.R., B.E., R.B., C.Bom., E.S., B.R. and D.R. K.R.F., T.G., M.B. and C.Bos. were responsible for molecular beam alignment and operation. The LCLS CXI beamline and related LCLS equipment was mainly operated by R.A.-M., J.E.K., G.J.W. and S.B. Data acquisition was coordinated by L.F. and S.C. X.L. and S.J.R. analysed the data with help from B.E., R.B. and L.F. under guidance from A.R. and D.R. L.I., K.H., Y.H., O.V., S.-K.S. and R.S. developed the XMOLECULE toolkit and carried out the calculations. K.T. conducted the calibration of the pulse parameters with the atomic argon data. A.R., L.I., S.-K.S., R.S. and D.R. interpreted the results and wrote the manuscript with input from all authors.

Correspondence to A. Rudenko or S.-K. Son.

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Extended data figures and tables

Extended Data Figure 1 Experimental temporal profile of the X-ray pulse.

Averaged experimental X-ray pulse shape (blue), obtained by averaging 369 single-pulse measurements using the X-band transverse deflecting cavity (XTCAV), compared to a Gaussian-shaped model pulse (red). The error bars reflect the standard deviations.

Extended Data Figure 2 Experimental ion yield of CH3I after photoionization with ultra-intense LCLS pulses at a photon energy of 8.3 keV.

a, Ion yield (colour scale) plotted as a function of the measured TOF and hit (X) position on the detector. In addition to the mass-to-charge ratio, this spectrum also shows the scaled momentum distribution of each fragment projected onto the xz plane, which can be seen as the spread in the measured TOF and position peak for each ion species. The LCLS pulse parameters are the same as for Fig. 1a. The experimental data are accumulated over 287,400 LCLS shots. b, Same as a, but zoomed into the region of short TOFs, that is, high charge states.

Extended Data Figure 3 Effect of nuclear dynamics on the total molecular charge.

Calculated average total molecular charge of the CH3I molecule obtained from the full calculation (solid red line), for fixed nuclear positions (dashed red line), and within the independent atom model (solid black line), each as a function of the X-ray fluence.

Extended Data Figure 4 Sketch of the experimental set-up.

The linearly polarized, focused X-ray beam intersects a cold molecular beam inside an ion spectrometer that measures all three components of the ion momentum vectors. Ions are extracted by a constant electric field onto a position- and time-sensitive charged particle detector. From the TOF and hit position of each ion, its three-dimensional momentum vector can be calculated. The size and shape of the X-ray focus was determined from a calibration measurement of the charge-state yield of argon, as described in Methods.

Extended Data Figure 5 Charge-state distribution of argon.

The purple and green lines show the experimental and theoretical charge-state distributions, respectively, of argon atoms at a photon energy of 8.3 keV (‘Ar@8.3 keV’) and a pulse energy of 3.5 mJ measured at the gas monitor detector (upstream from beamline optics). The experimental data are accumulated over 52,200 LCLS shots. The calculations assume a beamline transmission of 32% and were averaged over a focal spot size of 0.35 μm × 0.3 μm assuming a double-Gaussian spatial distribution. The ratio of peak fluences and widths of the two Gaussians were chosen to be 0.16 and 2.5, respectively, to best fit the experimental data.

Extended Data Figure 6 Fluence distribution function obtained from the argon calibration.

The peak fluence is 4.13 × 1012 photons per μm2. The vertical axis shows how often each fluence value occurs in the interaction volume.

Extended Data Figure 7 Comparison of the measured and calculated KEDs for a CH3I molecule.

Means and standard deviations (STDs) of the experimental KEDs of the iodine fragments compared to their calculated values. The LCLS pulse parameters are the same as for Fig. 1a. The experimental data are accumulated over 287,400 LCLS shots. For the calculation, the experimentally determined X-ray pulse shape shown in Extended Data Fig. 1 was assumed. Note that the vertical bars depict the measured (black) or calculated (red) standard deviations (that is, the width) of the KEDs, not the standard error of the mean as in Fig. 3. The blue line depicts the energies that are expected for instantaneous ionization.

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Rudenko, A., Inhester, L., Hanasaki, K. et al. Femtosecond response of polyatomic molecules to ultra-intense hard X-rays. Nature 546, 129–132 (2017). https://doi.org/10.1038/nature22373

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