Impact of ultrafast electronic damage in single-particle x-ray imaging experiments

Millijoule Femtosecond X-Ray Pulses from an Efficient Fresh-Slice Multistage Free-Electron Laser

We present the generation of x-ray pulses with average pulse energies up to one millijoule and rms pulse durations down to the femtosecond level. We have produced these intense and short pulses by employing the fresh-slice multistage amplification scheme with a transversely tilted electron beam in a free-electron laser. In this scheme, a short pulse is produced in the first stage and later amplified by fresh parts of the electron bunch in up to a total of four stages of amplification. Our implementation is efficient, since practically the full electron beam contributes to produce the x-ray pulse. Our implementation is also compact, utilizing only 32 m of undulator. The demonstration was done at Athos, the soft x-ray beamline of SwissFEL, which was designed with high flexibility to take full advantage of the multistage amplification scheme. It opens the door for scientific opportunities following ultrafast dynamics using nonlinear x-ray spectroscopy techniques or avoiding electronic damage when capturing structures with a single intense pulse via single-particle imaging.

Sequential mechanism in H3+ formation dynamics on the ethanol dication

Two- and three-body Coulomb explosion dynamics of isolated ethanol dications are studied via single-photon double-ionization with ultrafast extreme-ultraviolet pulses. The measured 3-body momentum correlations obtained via 3D coincidence imaging of the ionic products provide evidence for several concerted and sequential mechanisms: (1) a concerted 3-body breakup mechanism, with dominating channels such as CH₃⁺ + COH⁺ + H₂; (2) sequential dissociation in which the ejection of a low-kinetic-energy neutral OH precedes the Coulomb explosion of C₂H₅²⁺ → CH₃⁺ + CH₂⁺; and (3) a sequential 3-body breakup mechanism that dominates H₃⁺ formation from the ethanol dication via a mechanism that is different from the well-studied H₃⁺ formation in the 2-body Coulomb explosion of the methanol dication. Furthermore, we report surprising branching ratios of the competing C-O bond dissociation channels, resulting in H₃O⁺, H₂O⁺ and OH⁺ formation.

Fluorescence intensity correlation imaging with high spatial resolution and elemental contrast using intense x-ray pulses

We theoretically investigate the fluorescence intensity correlation (FIC) of Ar clusters and Mo-doped iron oxide nanoparticles subjected to intense, femtosecond, and sub-femtosecond x-ray free-electron laser pulses for high-resolution and elemental contrast imaging. We present the FIC of K α and K α h emission in Ar clusters and discuss the impact of sample damage on retrieving high-resolution structural information and compare the obtained structural information with those from the coherent diffractive imaging (CDI) approach. We found that, while sub-femtosecond pulses will substantially benefit the CDI approach, few-femtosecond pulses may be sufficient for achieving high-resolution information with the FIC. Furthermore, we show that the fluorescence intensity correlation computed from the fluorescence of the Mo atoms in Mo-doped iron oxide nanoparticles can be used to image dopant distributions in the nonresonant regime.

Ultraintense, ultrashort pulse X-ray scattering in small molecules

We examine X-ray scattering from an isolated organic molecule from the linear to nonlinear absorptive regime. In the nonlinear regime, we explore the importance of both the coherent and incoherent channels and observe the onset of nonlinear behavior as a function of pulse duration and energy. In the linear regime, we test the sensitivity of the scattering signal to molecular bonding and electronic correlation via calculations using the independent atom model (IAM), Hartree-Fock (HF) and density functional theory (DFT). Finally, we describe how coherent X-ray scattering can be used to directly visualize femtosecond charge transfer and dissociation within a single molecule undergoing X-ray multiphoton absorption.

Multiple Sequential Ionization of Valence n = 4 Shell of Krypton by Intense Femtosecond XUV Pulses

Sequential photoionization of krypton by intense extreme ultraviolet femtosecond pulses is studied theoretically for the photon energies below the 3d excitation threshold. This regime with energetically forbidden Auger decay is characterized by special features, such as time scaling of the level population. The model is based on the solution of rate equations with photoionization cross sections of krypton in different charge and multiplet states determined using R-matrix calculations. Predictions of the ion yields and photoelectron spectra for various photon fluence are presented and discussed.

An advanced workflow for single-particle imaging with the limited data at an X-ray free-electron laser

An improved analysis for single-particle imaging (SPI) experiments, using the limited data, is presented here. Results are based on a study of bacteriophage PR772 performed at the Atomic, Molecular and Optical Science instrument at the Linac Coherent Light Source as part of the SPI initiative. Existing methods were modified to cope with the shortcomings of the experimental data: inaccessibility of information from half of the detector and a small fraction of single hits. The general SPI analysis workflow was upgraded with the expectation-maximization based classification of diffraction patterns and mode decomposition on the final virus-structure determination step. The presented processing pipeline allowed us to determine the 3D structure of bacteriophage PR772 without symmetry constraints with a spatial resolution of 6.9 nm. The obtained resolution was limited by the scattering intensity during the experiment and the relatively small number of single hits.

Effect of radiation damage and illumination variability on signal-to-noise ratio in X-ray free-electron laser single-particle imaging

The deterioration of both the signal-to-noise ratio and the spatial resolution in the electron-density distribution reconstructed from diffraction intensities collected at different orientations of a sample is analysed theoretically with respect to the radiation damage to the sample and the variations in the X-ray intensities illuminating different copies of the sample. The simple analytical expressions and numerical estimates obtained for models of radiation damage and incident X-ray pulses may be helpful in planning X-ray free-electron laser (XFEL) imaging experiments and in analysis of experimental data. This approach to the analysis of partially coherent X-ray imaging configurations can potentially be used for analysis of other forms of imaging where the temporal behaviour of the sample and the incident intensity during exposure may affect the inverse problem of sample reconstruction.

Recovery of undamaged electron-density maps in the presence of damage-induced partial coherence in single-particle imaging

Resolving the electronic structure of single biological molecules in their native state was among the primary motivations behind X-ray free-electron lasers. The ultra-short pulses they produce can outrun the atomic motion induced by radiation damage, but the electronic structure of the sample is still significantly modified from its original state. This paper explores the decoherence of the scattered signal induced by temporal evolution of the electronic structure in the sample molecule. It is shown that the undamaged electron density of a single-molecule sample can often be retrieved using only the two most occupied modes from the coherent mode decomposition of the partially coherent diffraction fluence.

A Perspective on Molecular Structure and Bond-Breaking in Radiation Damage in Serial Femtosecond Crystallography

X-ray free-electron lasers (XFELs) have a unique capability for time-resolved studies of protein dynamics and conformational changes on femto- and pico-second time scales. The extreme intensity of X-ray pulses can potentially cause significant modifications to the sample structure during exposure. Successful time-resolved XFEL crystallography depends on the unambiguous interpretation of the protein dynamics of interest from the effects of radiation damage. Proteins containing relatively heavy elements, such as sulfur or metals, have a higher risk for radiation damage. In metaloenzymes, for example, the dynamics of interest usually occur at the metal centers, which are also hotspots for damage due to the higher atomic number of the elements they contain. An ongoing challenge with such local damage is to understand the residual bonding in these locally ionized systems and bond-breaking dynamics. Here, we present a perspective on radiation damage in XFEL experiments with a particular focus on the impacts for time-resolved protein crystallography. We discuss recent experimental and modelling results of bond-breaking and ion motion at disulfide bonding sites in protein crystals.

The role of transient resonances for ultra-fast imaging of single sucrose nanoclusters

Intense x-ray free-electron laser (XFEL) pulses hold great promise for imaging function in nanoscale and biological systems with atomic resolution. So far, however, the spatial resolution obtained from single shot experiments lags averaging static experiments. Here we report on a combined computational and experimental study about ultrafast diffractive imaging of sucrose clusters which are benchmark organic samples. Our theoretical model matches the experimental data from the water window to the keV x-ray regime. The large-scale dynamic scattering calculations reveal that transient phenomena driven by non-linear x-ray interaction are decisive for ultrafast imaging applications. Our study illuminates the complex interplay of the imaging process with the rapidly changing transient electronic structures in XFEL experiments and shows how computational models allow optimization of the parameters for ultrafast imaging experiments.

X-ray free electron lasers provide high photon flux to explore single particle diffraction imaging of biological samples. Here the authors present dynamic electronic structure calculations and benchmark them to single-particle XFEL diffraction data of sucrose clusters to predict optimal single-shot imaging conditions.

Single-particle imaging without symmetry constraints at an X-ray free-electron laser

The analysis of a single-particle imaging (SPI) experiment performed at the AMO beamline at LCLS as part of the SPI initiative is presented here. A workflow for the three-dimensional virus reconstruction of the PR772 bacteriophage from measured single-particle data is developed. It consists of several well defined steps including single-hit diffraction data classification, refined filtering of the classified data, reconstruction of three-dimensional scattered intensity from the experimental diffraction patterns by orientation determination and a final three-dimensional reconstruction of the virus electron density without symmetry constraints. The analysis developed here revealed and quantified nanoscale features of the PR772 virus measured in this experiment, with the obtained resolution better than 10 nm, with a clear indication that the structure was compressed in one direction and, as such, deviates from ideal icosahedral symmetry.

Incorporating particle symmetry into orientation determination in single-particle imaging

In coherent-diffraction-imaging experiments X-ray diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. If the particle has symmetry, finding the orientation of a pattern can be ambiguous. With some modifications, the correlation-maximization method can find the relative orientations of the diffraction patterns for the case of symmetric particles as well. After convergence, the correlation maps show the symmetry of the particle and can be used to determine the symmetry elements and their orientations. The C factor, slightly modified for the symmetric case, can indicate the consistency of the assembled three-dimensional intensity distribution.

Correlations in Scattered X-Ray Laser Pulses Reveal Nanoscale Structural Features of Viruses

We use extremely bright and ultrashort pulses from an x-ray free-electron laser (XFEL) to measure correlations in x rays scattered from individual bioparticles. This allows us to go beyond the traditional crystallography and single-particle imaging approaches for structure investigations. We employ angular correlations to recover the three-dimensional (3D) structure of nanoscale viruses from x-ray diffraction data measured at the Linac Coherent Light Source. Correlations provide us with a comprehensive structural fingerprint of a 3D virus, which we use both for model-based and ab initio structure recovery. The analyses reveal a clear indication that the structure of the viruses deviates from the expected perfect icosahedral symmetry. Our results anticipate exciting opportunities for XFEL studies of the structure and dynamics of nanoscale objects by means of angular correlations.

Start-to-end simulation of single-particle imaging using ultra-short pulses at the European X-ray Free-Electron Laser

Single-particle imaging with X-ray free-electron lasers (XFELs) has the potential to provide structural information at atomic resolution for non-crystalline biomolecules. This potential exists because ultra-short intense pulses can produce interpretable diffraction data notwithstanding radiation damage. This paper explores the impact of pulse duration on the interpretability of diffraction data using comprehensive and realistic simulations of an imaging experiment at the European X-ray Free-Electron Laser. It is found that the optimal pulse duration for molecules with a few thousand atoms at 5 keV lies between 3 and 9 fs.

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

The precise details of the interaction of intense X-ray pulses with matter are a topic of intense interest to researchers attempting to interpret the results of femtosecond X-ray free electron laser (XFEL) experiments. An increasing number of experimental observations have shown that although nuclear motion can be negligible, given a short enough incident pulse duration, electronic motion cannot be ignored. The current and widely accepted models assume that although electrons undergo dynamics driven by interaction with the pulse, their motion could largely be considered 'random'. This would then allow the supposedly incoherent contribution from the electronic motion to be treated as a continuous background signal and thus ignored. The original aim of our experiment was to precisely measure the change in intensity of individual Bragg peaks, due to X-ray induced electronic damage in a model system, crystalline C60. Contrary to this expectation, we observed that at the highest X-ray intensities, the electron dynamics in C60 were in fact highly correlated, and over sufficiently long distances that the positions of the Bragg reflections are significantly altered. This paper describes in detail the methods and protocols used for these experiments, which were conducted both at the Linac Coherent Light Source (LCLS) and the Australian Synchrotron (AS) as well as the crystallographic approaches used to analyse the data.

X-ray holography with an atomic scatterer

X-ray holography scheme with reference scatterer consisting of heavy atom as reference center and its link to an object consisting of several light atoms and using controlled variation of the alignment is represented. The scheme can reproduce an object in three dimensions with atomic resolution. The distorting factors of reconstruction are considered.

Observation of femtosecond X-ray interactions with matter using an X-ray-X-ray pump-probe scheme

Resolution in the X-ray structure determination of noncrystalline samples has been limited to several tens of nanometers, because deep X-ray irradiation required for enhanced resolution causes radiation damage to samples. However, theoretical studies predict that the femtosecond (fs) durations of X-ray free-electron laser (XFEL) pulses make it possible to record scattering signals before the initiation of X-ray damage processes; thus, an ultraintense X-ray beam can be used beyond the conventional limit of radiation dose. Here, we verify this scenario by directly observing femtosecond X-ray damage processes in diamond irradiated with extraordinarily intense (∼10(19) W/cm(2)) XFEL pulses. An X-ray pump-probe diffraction scheme was developed in this study; tightly focused double-5-fs XFEL pulses with time separations ranging from sub-fs to 80 fs were used to excite (i.e., pump) the diamond and characterize (i.e., probe) the temporal changes of the crystalline structures through Bragg reflection. It was found that the pump and probe diffraction intensities remain almost constant for shorter time separations of the double pulse, whereas the probe diffraction intensities decreased after 20 fs following pump pulse irradiation due to the X-ray-induced atomic displacement. This result indicates that sub-10-fs XFEL pulses enable conductions of damageless structural determinations and supports the validity of the theoretical predictions of ultraintense X-ray-matter interactions. The X-ray pump-probe scheme demonstrated here would be effective for understanding ultraintense X-ray-matter interactions, which will greatly stimulate advanced XFEL applications, such as atomic structure determination of a single molecule and generation of exotic matters with high energy densities.

Sorting algorithms for single-particle imaging experiments at X-ray free-electron lasers

Modern X-ray free-electron lasers (XFELs) operating at high repetition rates produce a tremendous amount of data. It is a great challenge to classify this information and reduce the initial data set to a manageable size for further analysis. Here an approach for classification of diffraction patterns measured in prototypical diffract-and-destroy single-particle imaging experiments at XFELs is presented. It is proposed that the data are classified on the basis of a set of parameters that take into account the underlying diffraction physics and specific relations between the real-space structure of a particle and its reciprocal-space intensity distribution. The approach is demonstrated by applying principal component analysis and support vector machine algorithms to the simulated and measured X-ray data sets.

Single-molecule imaging with longer X-ray laser pulses

During the last five years, serial femtosecond crystallography using X-ray laser pulses has been developed into a powerful technique for determining the atomic structures of protein molecules from micrometre- and sub-micrometre-sized crystals. One of the key reasons for this success is the 'self-gating' pulse effect, whereby the X-ray laser pulses do not need to outrun all radiation damage processes. Instead, X-ray-induced damage terminates the Bragg diffraction prior to the pulse completing its passage through the sample, as if the Bragg diffraction were generated by a shorter pulse of equal intensity. As a result, serial femtosecond crystallography does not need to be performed with pulses as short as 5-10 fs, but can succeed for pulses 50-100 fs in duration. It is shown here that a similar gating effect applies to single-molecule diffraction with respect to spatially uncorrelated damage processes like ionization and ion diffusion. The effect is clearly seen in calculations of the diffraction contrast, by calculating the diffraction of the average structure separately to the diffraction from statistical fluctuations of the structure due to damage ('damage noise'). The results suggest that sub-nanometre single-molecule imaging with 30-50 fs pulses, like those produced at currently operating facilities, should not yet be ruled out. The theory presented opens up new experimental avenues to measure the impact of damage on single-particle diffraction, which is needed to test damage models and to identify optimal imaging conditions.

The linac coherent light source single particle imaging road map

Intense femtosecond x-ray pulses from free-electron laser sources allow the imaging of individual particles in a single shot. Early experiments at the Linac Coherent Light Source (LCLS) have led to rapid progress in the field and, so far, coherent diffractive images have been recorded from biological specimens, aerosols, and quantum systems with a few-tens-of-nanometers resolution. In March 2014, LCLS held a workshop to discuss the scientific and technical challenges for reaching the ultimate goal of atomic resolution with single-shot coherent diffractive imaging. This paper summarizes the workshop findings and presents the roadmap toward reaching atomic resolution, 3D imaging at free-electron laser sources.

Perspectives for imaging single protein molecules with the present design of the European XFEL

The Single Particles, Clusters and Biomolecules & Serial Femtosecond Crystallography (SPB/SFX) instrument at the European XFEL is located behind the SASE1 undulator and aims to support imaging and structure determination of biological specimen between about 0.1 μm and 1 μm size. The instrument is designed to work at photon energies from 3 keV up to 16 keV. Here, we propose a cost-effective proof-of-principle experiment, aiming to demonstrate the actual feasibility of a single molecule diffraction experiment at the European XFEL. To this end, we assume self-seeding capabilities at SASE1 and we suggest to make use of the baseline European XFEL accelerator complex-with the addition of a slotted-foil setup-and of the SPB/SFX instrument. As a first step towards the realization of an actual experiment, we developed a complete package of computational tools for start-to-end simulations predicting its performance. Single biomolecule imaging capabilities at the European XFEL can be reached by exploiting special modes of operation of the accelerator complex and of the SASE1 undulator. The output peak power can be increased up to more than 1.5 TW, which allows to relax the requirements on the focusing efficiency of the optics and to reach the required fluence without changing the present design of the SPB/SFX instrument. Explicit simulations are presented using the 15-nm size RNA Polymerase II molecule as a case study. Noisy diffraction patterns were generated and they were processed to generate the 3D intensity distribution. We discuss requirements to the signal-to-background ratio needed to obtain a correct pattern orientation. When these are fulfilled, our results indicate that one can achieve diffraction without destruction with about 0.1 photons per Shannon pixel per shot at 4 Å resolution with 10(13) photons in a 4 fs pulse at 4 keV photon energy and in a 0.3 μm focus, corresponding to a fluence of 10(14) photons/μm(2). We assume negligible structured background. At this signal level, one needs only about 30 000 diffraction patterns to recover full 3D information. At the highest repetition rate manageable by detectors at European XFEL, one will be able to accumulate these data within a fraction of an hour, even assuming a relatively low hit probability of about a percent.

Toward atomic resolution diffractive imaging of isolated molecules with X-ray free-electron lasers

We give a detailed account of the theoretical analysis and the experimental results of an X-ray-diffraction experiment on quantum-state selected and strongly laser-aligned gas-phase ensembles of the prototypical large asymmetric rotor molecule 2,5-diiodobenzonitrile, performed at the Linac Coherent Light Source [Phys. Rev. Lett.112, 083002 (2014)]. This experiment is the first step toward coherent diffractive imaging of structures and structural dynamics of isolated molecules at atomic resolution, i.e., picometers and femtoseconds, using X-ray free-electron lasers.

Theoretical study of electronic damage in single-particle imaging experiments at x-ray free-electron lasers for pulse durations from 0.1 to 10 fs

X-ray free-electron lasers (XFELs) may allow us to employ the single-particle imaging (SPI) method to determine the structure of macromolecules that do not form stable crystals. Ultrashort pulses of 10 fs and less allow us to outrun complete disintegration by Coulomb explosion and minimize radiation damage due to nuclear motion, but electronic damage is still present. The major contribution to the electronic damage comes from the plasma generated in the sample that is strongly dependent on the amount of Auger ionization. Since the Auger process has a characteristic time scale on the order of femtoseconds, one may expect that its contribution will be significantly reduced for attosecond pulses. Here we study the effect of electronic damage on the SPI at pulse durations from 0.1 to 10 fs and in a large range of XFEL fluences to determine optimal conditions for imaging of biological samples. We analyzed the contribution of different electronic excitation processes and found that at fluences higher than 10(13)-10(15) photons/μm(2) (depending on the photon energy and pulse duration) the diffracted signal saturates and does not increase further. A significant gain in the signal is obtained by reducing the pulse duration from 10 to 1 fs. Pulses below a duration of 1 fs do not give a significant gain in the scattering signal in comparison with 1-fs pulses. We also study the limits imposed on SPI by Compton scattering.

Efficient calculation of diffracted intensities in the case of nonstationary scattering by biological macromolecules under XFEL pulses

The calculation of diffracted intensities from an atomic model is a routine step in the course of structure solution, and its efficiency may be crucial for the feasibility of the study. An intense X-ray free-electron laser (XFEL) pulse can change the electron configurations of atoms during its action. This results in time-dependence of the diffracted intensities and complicates their calculation. An algorithm is suggested that enables this calculation with a computational cost comparable to that for the time-independent case. The intensity is calculated as a sum of the `effective' intensity and a finite series of `correcting' intensities. These intensities are calculated in the conventional way but with modified atomic scattering factors that are specially derived for a particular XFEL experiment. The total number of members of the series does not exceed the number of chemically different elements present in the object under study. This number is small for biological molecules; in addition, the correcting terms are negligible within the parameter range and accuracy acceptable in biological crystallography. The time-dependent atomic scattering factors were estimated for different pulse fluence levels by solving the system of rate equations. The simulation showed that the changes in a diffraction pattern caused by the time-dependence of scattering factors are negligible if the pulse fluence does not exceed the limit that is currently achieved in experiments with biological macromolecular crystals (10(4) photons Å(-2) per pulse) but become significant with an increase in the fluence to 10(6) or 10(8) photons Å(-2) per pulse.

Time dependence of X-ray polarizability of a crystal induced by an intense femtosecond X-ray pulse

The time evolution of the electron density and the resulting time dependence of Fourier components of the X-ray polarizability of a crystal irradiated by highly intense femtosecond pulses of an X-ray free-electron laser (XFEL) is investigated theoretically on the basis of rate equations for bound electrons and the Boltzmann equation for the kinetics of the unbound electron gas. The photoionization, Auger process, electron-impact ionization, electron-electron scattering and three-body recombination have been implemented in the system of rate equations. An algorithm for the numerical solution of the rate equations was simplified by incorporating analytical expressions for the cross sections of all the electron configurations in ions within the framework of the effective charge model. Using this approach, the time dependence of the inner shell populations during the time of XFEL pulse propagation through the crystal was evaluated for photon energies between 4 and 12 keV and a pulse width of 40 fs considering a flux of 10(12) photons pulse(-1) (focusing on a spot size of ∼1 µm). This flux corresponds to a fluence ranging between 0.8 and 2.4 mJ µm(-2). The time evolution of the X-ray polarizability caused by the change of the atomic scattering factor during the pulse propagation is numerically analyzed for the case of a silicon crystal. The time-integrated polarizability drops dramatically if the fluence of the X-ray pulse exceeds 1.6 mJ µm(-2).

Selection and orientation of different particles in single particle imaging

The short pulses of X-ray free electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. The particles are injected into the beam in random orientations and they should be identical. However, in real experimental conditions it is not always possible to have identical particles. In this paper we show that the correlation maximization method, developed earlier, is able to select identical particles from a mixture and find their orientations simultaneously.

Double core-hole creation by sequential attosecond photoionization

X-ray fluorescence spectroscopy demonstrates that a single core-hole krypton with a 170-as lifetime can be photoionized again to a double core-hole state by an intense x-ray pulse. The observation indicates that unconventional interaction between intense x rays and atoms is no more negligible in applications with x-ray free-electron lasers. Quantitative analysis of the double core-hole creation including effects of a pulsed and spiky temporal structure enables estimation of the x-ray pulse duration in the sub-10-fs range.