Molecular imaging using X-ray free-electron lasers

Preparation of Tautomer-Pure Molecular Beams by Electrostatic Deflection

Tautomers are ubiquitous throughout chemistry and typically considered inseparable in solution. Yet (bio)chemical activity is highly tautomer-specific, with common examples being the amino and nucleic acids. While tautomers exist in an equilibrium in solution, in the cold environment of a molecular beam the barrier to tautomerization is typically much too high for interconversion, and tautomers can be considered separate species. Here we demonstrate the first separation of tautomers within a molecular beam and the production of tautomerically pure gas-phase samples. We show this for the 2-pyridone/2-hydroxypyridine system, an important structural motif in both uracil and cytosine. Spatial separation of the tautomers is achieved via electrostatic deflection in strong inhomogeneous fields. We furthermore collect tautomer-resolved photoelectron spectra using femtosecond multiphoton ionization. This paves the way for studying the structure-function-dynamic relationship on the level of individual tautomers, using approaches that typically lack the resolution to do so, such as ultrafast dynamics experiments.

Unraveling the ultrafast dynamics of thermal-energy chemical reactions

In this perspective, we discuss how one can initiate, image, and disentangle the ultrafast elementary steps of thermal-energy chemical dynamics, building upon advances in technology and scientific insight. We propose that combinations of ultrashort mid-infrared laser pulses, controlled molecular species in the gas phase, and forefront imaging techniques allow to unravel the elementary steps of general-chemistry reaction processes in real time. We detail, for prototypical first reaction systems, experimental methods enabling these investigations, how to sufficiently prepare and promote gas-phase samples to thermal-energy reactive states with contemporary ultrashort mid-infrared laser systems, and how to image the initiated ultrafast chemical dynamics. The results of such experiments will clearly further our understanding of general-chemistry reaction dynamics.

Temporal structured illumination and vision-transformer enables large field-of-view binary snapshot ptychography

Ptychography, a widely used computational imaging method, generates images by processing coherent interference patterns scattered from an object of interest. In order to capture scenes with large field-of-view (FoV) and high spatial resolution simultaneously in a single shot, we propose a temporal-compressive structured-light Ptychography system. A novel three-step reconstruction algorithm composed of multi-frame spectra reconstruction, phase retrieval, and multi-frame image stitching is developed, where we employ the emerging Transformer-based network in the first step. Experimental results demonstrate that our system can expand the FoV by 20× without losing spatial resolution. Our results offer huge potential for enabling lensless imaging of molecules with large FoV as well as high spatial-temporal resolutions. We also notice that due to the loss of low-intensity information caused by the compressed sensing process, our method so far is only applicable to binary targets.

High-Throughput UV Photoionization and Fragmentation of Neutral Biomolecules as a Structural Fingerprint

We present UV photofragmentation studies of the structural isomers paracetamol, 3-Pyridinepropionic acid (3-PPIA) and (R)-(-)-2-Phenylglycine. In particular, we utilized a new laser-based thermal desorption source in combination with femtosecond multiphoton ionization at 343 nm and 257 nm. The continuous nature of our molecule source, combined with the 50 kHz repetition rate of the laser, allowed us to perform these experiments at high throughput. In particular, we present detailed laser intensity dependence studies at both wavelengths, producing 2D mass spectra with highly differential information about the underlying fragmentation processes. We show that UV photofragmentation produces highly isomer-specific mass spectra, and assign all major fragmentation pathways observed. The intensity-dependence measurements, furthermore, allowed us to evaluate the appearance intensities for each fragmentation channel, which helped to distinguish competing from consecutive fragmentation pathways.

Vaporization of Intact Neutral Biomolecules Using Laser-Based Thermal Desorption

The production of a clean neutral molecular sample is a crucial step in many gas-phase spectroscopy and reaction dynamics experiments investigating neutral species. Unfortunately, conventional methods based on heating cannot be used with most nonvolatile biomolecules due to their thermal instability. In this paper, we demonstrate the application of laser-based thermal desorption (LBTD) to produce neutral molecular plumes of biomolecules such as dipeptides and lipids. Specifically, we report mass spectra of glycylglycine, glycyl-l-alanine, and cholesterol obtained using LBTD vaporization, followed by soft femtosecond multiphoton ionization (fs-MPI) at 400 nm. For all molecules, the signal from the intact precursor ion was observed, highlighting the softness and applicability of the LBTD and fs-MPI approach. In more detail, cholesterol underwent hardly any fragmentation. Both dipeptides fragmented significantly, although mostly through only a single channel, which we attribute to the fs-MPI process.

Filming enhanced ionization in an ultrafast triatomic slingshot

Filming atomic motion within molecules is an active pursuit of molecular physics and quantum chemistry. A promising method is laser-induced Coulomb Explosion Imaging (CEI) where a laser pulse rapidly ionizes many electrons from a molecule, causing the remaining ions to undergo Coulomb repulsion. The ion momenta are used to reconstruct the molecular geometry which is tracked over time (i.e., filmed) by ionizing at an adjustable delay with respect to the start of interatomic motion. Results are distorted, however, by ultrafast motion during the ionizing pulse. We studied this effect in water and filmed the rapid "slingshot" motion that enhances ionization and distorts CEI results. Our investigation uncovered both the geometry and mechanism of the enhancement which may inform CEI experiments in many other polyatomic molecules.

Novel Ultrafast Molecular Imaging Based on the Combination of X-ray and Electron Diffraction

Recent development of X-ray free-electron lasers and megaelectronvolt radio-frequency electron guns have made ultrafast X-ray and electron diffraction measurements possible, thereby capturing chemical dynamics with atomic-spatial and femtosecond-temporal resolutions. We present a unified formulation of standard homodyne-detected and heterodyne-detected signals for both techniques. Noting that X-rays scatter from molecular electrons while electrons scatter from both molecular electrons and nuclei, we show how the two diffraction signals can be combined to reveal novel chemical information that is unavailable by solely using each technique alone. By subtracting the homodyne-detected X-ray and electron diffraction signals, a mixed electronic-nuclear interference in electron diffraction can be identified with a self-heterodyne nature for the direct imaging of attosecond electron dynamics where the scattering off molecular nuclei serves as a local oscillator for the scattering off molecular electrons. By subtracting heterodyne-detected X-ray and electron diffraction, the purely nuclear charge density can be singled out.

Ultrafast light-induced dynamics in the microsolvated biomolecular indole chromophore with water

Interactions between proteins and their solvent environment can be studied in a bottom-up approach using hydrogen-bonded chromophore-solvent clusters. The ultrafast dynamics following UV-light-induced electronic excitation of the chromophores, potential radiation damage, and their dependence on solvation are important open questions. The microsolvation effect is challenging to study due to the inherent mix of the produced gas-phase aggregates. We use the electrostatic deflector to spatially separate different molecular species in combination with pump-probe velocity-map-imaging experiments. We demonstrate that this powerful experimental approach reveals intimate details of the UV-induced dynamics in the near-UV-absorbing prototypical biomolecular indole-water system. We determine the time-dependent appearance of the different reaction products and disentangle the occurring ultrafast processes. This approach ensures that the reactants are well-known and that detailed characteristics of the specific reaction products are accessible - paving the way for the complete chemical-reactivity experiment.

Time-resolved X-ray and XUV based spectroscopic methods for nonadiabatic processes in photochemistry

The photochemistry of numerous molecular systems is influenced by conical intersections (CIs). These omnipresent nonadiabatic phenomena provide ultra-fast radiationless relaxation channels by creating degeneracies between electronic states and decide over the final photoproducts. In their presence, the Born-Oppenheimer approximation breaks down, and the timescales of the electron and nuclear dynamics become comparable. Due to the ultra-fast dynamics and the complex interplay between nuclear and electronic degrees of freedom, the direct experimental observation of nonadiabatic processes close to CIs remains challenging. In this article, we give a theoretical perspective on novel spectroscopic techniques capable of observing clear signatures of CIs. We discuss methods that are based on ultra-short laser pulses in the extreme ultraviolet and X-ray regime, as their spectral and temporal resolution allow for resolving the ultra-fast dynamics near CIs.

The Scatman: an approximate method for fast wide-angle scattering simulations

Single-shot coherent diffraction imaging (CDI) is a powerful approach to characterize the structure and dynamics of isolated nanoscale objects such as single viruses, aerosols, nanocrystals and droplets. Using X-ray wavelengths, the diffraction images in CDI experiments usually cover only small scattering angles of a few degrees. These small-angle patterns represent the magnitude of the Fourier transform of the 2D projection of the sample's electron density, which can be reconstructed efficiently but lacks any depth information. In cases where the diffracted signal can be measured up to scattering angles exceeding ∼10°, i.e. in the wide-angle regime, some 3D morphological information of the target is contained in a single-shot diffraction pattern. However, the extraction of the 3D structural information is no longer straightforward and defines the key challenge in wide-angle CDI. So far, the most convenient approach relies on iterative forward fitting of the scattering pattern using scattering simulations. Here the Scatman is presented, an approximate and fast numerical tool for the simulation and iterative fitting of wide-angle scattering images of isolated samples. Furthermore, the open-source software implementation of the Scatman algorithm, PyScatman, is published and described in detail. The Scatman approach, which has already been applied in previous work for forward-fitting-based shape retrieval, adopts the multi-slice Fourier transform method. The effects of optical properties are partially included, yielding quantitative results for small, isolated and weakly interacting samples. PyScatman is capable of computing wide-angle scattering patterns in a few milliseconds even on consumer-level computing hardware, potentially enabling new data analysis schemes for wide-angle coherent diffraction experiments.

Performance enhancement of coherent modulation imaging in the presence of missing data

Coherent diffraction imaging (CDI) has become a powerful imaging modality in synchrotron x-ray imaging and electron microscopy communities. In the far-field geometry, image quality of CDI depends strongly on the performance of detector; specifically, the dynamic range, pixel size, and the absence of missing data. Coherent modulation imaging (CMI), an innovative variant of CDI, improves the algorithmic convergence by inserting a modulator upstream of the detector. Here, we explore the potential of CMI in eliminating nonideal effects of detector by modifying the modulus constraint to extrapolate the missing part of diffraction pattern. Nine folds of extrapolation in area of diffraction pattern have been shown feasible in experiment; while sixteen folds in simulation. For image quality measured by Structural Similarity (SSIM), our method shows a maximum of 32% improvement over the traditional method. Our method provides a way to alleviate the effects of beamstop, gaps between modules, limited dynamic range, and limited detector size for CMI.

Chemical effects on the dynamics of organic molecules irradiated with high intensity x rays

The interaction of a high intensity x-ray pulse with matter causes ionization of the constituent atoms through various atomic processes, and the system eventually goes through a complex structural dynamics. Understanding this whole process is important from the perspective of structure determination of molecules using single particle imaging. XMDYN, which is a classical molecular dynamics-Monte Carlo based hybrid approach, has been successful in simulating the dynamical evolution of various systems under intense irradiation over the past years. The present study aims for extending the XMDYN toolkit to treat chemical bonds using the reactive force field. In order to study its impact, a highly intense x-ray pulse was made to interact with the simplest amino acid, glycine. Different model variants were used to highlight the consequences of charge rearrangement and chemical bonds on the time evolution. The charge-rearrangement-enhanced x-ray ionization of molecules effect is also discussed to address the capability of a classical MD based approach, i.e., XMDYN, to capture such a molecular phenomenon.

Perspectives of Gas Phase Ion Chemistry: Spectroscopy and Modeling

The study of ions in the gas phase has a long history and has involved both chemists and physicists. The interplay of their competences with the use of very sophisticated commercial and/or homemade instrumentations and theoretical models has improved the knowledge of thermodynamics and kinetics of many chemical reactions, even if still many stages of these processes need to be fully understood. The new technologies and the novel free-electron laser facilities based on plasma acceleration open new opportunities to investigate the chemical reactions in some unrevealed fundamental aspects. The synchrotron light source can be put beside the FELs, and by mass spectrometric techniques and spectroscopies coupled with versatile ion sources it is possible to really change the state of the art of the ion chemistry in different areas such as atmospheric and astro chemistry, plasma chemistry, biophysics, and interstellar medium (ISM). In this manuscript we review the works performed by a joint combination of the experimental studies of ion–molecule reactions with synchrotron radiation and theoretical models adapted and developed to the experimental evidence. The review concludes with the perspectives of ion–molecule reactions by using FEL instrumentations as well as pump probe measurements and the initial attempt in the development of more realistic theoretical models for the prospective improvement of our predictive capability.

Picosecond pulse-shaping for strong three-dimensional field-free alignment of generic asymmetric-top molecules

Fixing molecules in space is a crucial step for the imaging of molecular structure and dynamics. Here, we demonstrate three-dimensional (3D) field-free alignment of the prototypical asymmetric top molecule indole using elliptically polarized, shaped, off-resonant laser pulses. A truncated laser pulse is produced using a combination of extreme linear chirping and controlled phase and amplitude shaping using a spatial-light-modulator (SLM) based pulse shaper of a broadband laser pulse. The angular confinement is detected through velocity-map imaging of H+ and C2+ fragments resulting from strong-field ionization and Coulomb explosion of the aligned molecules by intense femtosecond laser pulses. The achieved three-dimensional alignment is characterized by comparing the result of ion-velocity-map measurements for different alignment directions and for different times during and after the alignment laser pulse to accurate computational results. The achieved strong three-dimensional field-free alignment of [Formula: see text] demonstrates the feasibility of both, strong three-dimensional alignment of generic complex molecules and its quantitative characterization.

Ultrafast Imaging of Molecular Dynamics Using Ultrafast Low-Frequency Lasers, X-ray Free Electron Lasers, and Electron Pulses

The requirement of high space-time resolution and brightness is a great challenge for imaging atomic motion and making molecular movies. Important breakthroughs in ultrabright tabletop laser, X-ray, and electron sources have enabled the direct imaging of evolving molecular structures in chemical processes, and recent experimental advances in preparing ultrafast laser and electron pulses resulted in molecular imaging with femtosecond time resolution. This Perspective presents an overview of the versatile imaging methods of molecular dynamics. High-order harmonic generation imaging and photoelectron diffraction imaging are based on laser-induced ionization and rescattering processes. Coulomb explosion imaging retrieves molecular structural information by detecting the momentum vectors of fragmented ions. Diffraction imaging encodes molecular structural and electronic information in reciprocal space. We also present various applications of these ultrafast imaging methods in resolving laser-induced nuclear and electronic dynamics.

Energetics and J-coupling constants for Ala, Gly, and Val peptides demonstrated using ABEEM polarizable force field in vacuo and an aqueous solution

The development of an atom-bond electronegativity equalisation method at the σπ-level (ABEEM) polarisable force field (PFF) for peptides is presented. ABEEM PFF utilises a fluctuating charge model to explicitly describe...

Coherent modulation imaging using unknown modulators

Coherent modulation imaging (CMI) is an effective lensless diffraction imaging method with fast algorithmic convergence and high robustness to data defects. In the reported algorithms for CMI, one important requirement is that the modulator function need to be known a priori; and an additional step for the modulator characterization is required to be carried out in advance by other methods, such as ptychography, which could be cumbersome in practice. Here, we propose an improved algorithm that allows for the transmission function of a completely unknown modulator to be recovered during the same iterative process of image reconstruction. We have verified the method in both simulations and optical experiments. This improvement would turn CMI into a more practical and standalone technique for broader applications in biology and materials science.

Time-resolving the UV-initiated photodissociation dynamics of OCS

We present a time-resolved study of the photodissociation dynamics of OCS after UV-photoexcitation at λ = 237 nm. OCS molecules (X1Σ+) were primarily excited to the 11A'' and the 21A' Renner-Teller components of the 1Σ- and 1Δ states. Dissociation into CO and S fragments was observed through time-delayed strong-field ionisation and imaging of the kinetic energy of the resulting CO+ and S+ fragments by intense 790 nm laser pulses. Surprisingly, fast oscillations with a period of ∼100 fs were observed in the S+ channel of the UV dissociation. Based on wavepacket-dynamics simulations coupled with a simple electrostatic-interaction model, these oscillations do not correspond to the known highly-excited rotational motion of the leaving CO(X1Σ+, J ≫ 0) fragments, which has a timescale of ∼140 fs. Instead, we suggest to assign the observed oscillations to the excitation of vibrational wavepackets in the 23A'' or 21A'' states of the molecule that predissociate to form S(3PJ) photoproducts.

Imaging of electron transition and bond breaking in the photodissociation of H2+ via ultrafast X-ray photoelectron diffraction

We theoretically investigate the photodissociation dynamics of H2+ using the methodology of ultrafast X-ray photoelectron diffraction (UXPD). We use a femtosecond infrared pulse to prompt a coherent excitation from the molecular vibrational state (v = 9) of the electronic ground state (1sσ_g) and then adopt another time-delayed attosecond X-ray pulse to probe the dynamical properties. We have calculated photoionization momentum distributions by solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). We unambiguously identify the phenomena associated with the g - u symmetry breakdown in the time-resolved photoelectron diffraction spectra. Using the two-center interference model, we can determine the variation in nuclear spacing with high accuracy. In addition, we use a strong field approximation (SFA) model to interpret the UXPD profile, and the SFA simulations can reproduce the TDSE results in a quantitative way.

Artificial Neural Networks for Noise Removal in Data-Sparse Charged Particle Imaging Experiments

We present the first demonstration of artificial neural networks (ANNs) for the removal of Poissonian noise in charged particle imaging measurements with very low overall counts. The approach is successfully applied to both simulated and real experimental image data relating to the detection of photoions/photoelectrons in unimolecular photochemical dynamics studies. Specific examples consider the multiphoton ionization of pyrrole and (S)-camphor. Our results reveal an extremely high level of performance, with the ANNs transforming images that are unusable for any form of quantitative analysis into statistically reliable data with an impressive similarity to benchmark references. Given the widespread use of charged particle imaging methods within the chemical dynamics community, we anticipate that the use of ANNs has significant potential impact - particularly, for example, when working in the limit of very low absorption/photoionization cross-sections, or when attempting to reliably extract subtle image features originating from phenomena such as photofragment vector correlations or photoelectron circular dichroism.

Controlled beams of shock-frozen, isolated, biological and artificial nanoparticles

X-ray free-electron lasers promise diffractive imaging of single molecules and nanoparticles with atomic spatial resolution. This relies on the averaging of millions of diffraction patterns of identical particles, which should ideally be isolated in the gas phase and preserved in their native structure. Here, we demonstrated that polystyrene nanospheres and Cydia pomonella granulovirus can be transferred into the gas phase, isolated, and very quickly shock-frozen, i.e., cooled to 4 K within microseconds in a helium-buffer-gas cell, much faster than state-of-the-art approaches. Nanoparticle beams emerging from the cell were characterized using particle-localization microscopy with light-sheet illumination, which allowed for the full reconstruction of the particle beams, focused to < 100   μ m , as well as for the determination of particle flux and number density. The experimental results were quantitatively reproduced and rationalized through particle-trajectory simulations. We propose an optimized setup with cooling rates for particles of few-nanometers on nanosecond timescales. The produced beams of shock-frozen isolated nanoparticles provide a breakthrough in sample delivery, e.g., for diffractive imaging and microscopy or low-temperature nanoscience.

Recoil-Induced Asymmetry of Nondipole Molecular Frame Photoelectron Angular Distributions in the Hard X-ray Regime

We investigate angular emission distributions of the 1s photoelectrons of N_{2} ionized by linearly polarized synchrotron radiation at hν=40  keV. As expected, nondipole contributions cause a very strong forward-backward asymmetry in the measured emission distributions. In addition, we observe an unexpected asymmetry with respect to the polarization direction, which depends on the direction of the molecular fragmentation. In particular, photoelectrons are predominantly emitted in the direction of the forward nitrogen atom. This observation cannot be explained via asymmetries introduced by the initial bound and final continuum electronic states of the oriented molecule. The present simulations assign this asymmetry to a novel nontrivial effect of the recoil imposed to the nuclei by the fast photoelectrons and high-energy photons, which results in a propensity for the ions to break up along the axis of the recoil momentum. The results are of particular importance for the interpretation of future experiments at x-ray free electron lasers operating in the few tens of keV regime, where such nondipole and recoil effects will be essential.

Light-sheet imaging for the recording of transverse absolute density distributions of gas-phase particle-beams from nanoparticle injectors

Imaging biological molecules in the gas-phase requires novel sample delivery methods, which generally have to be characterized and optimized to produce high-density particle beams. A non-destructive characterization method of the transverse particle beam profile is presented. It enables the characterization of the particle beam in parallel to the collection of, for instance, x-ray-diffraction patterns. As a rather simple experimental method, it requires the generation of a small laser-light sheet using a cylindrical telescope and a microscope. The working principle of this technique was demonstrated for the characterization of the fluid-dynamic-focusing behavior of 220 nm polystyrene beads as prototypical nanoparticles. The particle flux was determined and the velocity distribution was calibrated using Mie-scattering calculations.

Molecular movie of ultrafast coherent rotational dynamics of OCS

Recording molecular movies on ultrafast timescales has been a longstanding goal for unravelling detailed information about molecular dynamics. Here we present the direct experimental recording of very-high-resolution and -fidelity molecular movies over more than one-and-a-half periods of the laser-induced rotational dynamics of carbonylsulfide (OCS) molecules. Utilising the combination of single quantum-state selection and an optimised two-pulse sequence to create a tailored rotational wavepacket, an unprecedented degree of field-free alignment, 〈cos2θ2D〉 = 0.96 (〈cos2θ〉 = 0.94) is achieved, exceeding the theoretical limit for single-pulse alignment. The very rich experimentally observed quantum dynamics is fully recovered by the angular probability distribution obtained from solutions of the time-dependent Schrödinger equation with parameters refined against the experiment. The populations and phases of rotational states in the retrieved time-dependent three-dimensional wavepacket rationalises the observed very high degree of alignment.

Ultrafast X-ray scattering reveals vibrational coherence following Rydberg excitation

The coherence and dephasing of vibrational motions of molecules constitute an integral part of chemical dynamics, influence material properties and underpin schemes to control chemical reactions. Considerable progress has been made in understanding vibrational coherence through spectroscopic measurements, but precise, direct measurement of the structure of a vibrating excited-state polyatomic organic molecule has remained unworkable. Here, we measure the time-evolving molecular structure of optically excited N-methylmorpholine through scattering with ultrashort X-ray pulses. The scattering signals are corrected for the differences in electron density in the excited electronic state of the molecule in comparison to the ground state. The experiment maps the evolution of the molecular geometry with femtosecond resolution, showing coherent motion that survives electronic relaxation and seems to persist for longer than previously seen using other methods.

Microfluidic sample delivery for serial crystallography using XFELs

Serial femtosecond crystallography (SFX) with X-ray free electron lasers (XFELs) is an emerging field for structural biology. One of its major impacts lies in the ability to reveal the structure of complex proteins previously inaccessible with synchrotron-based crystallography techniques and allowing time-resolved studies from femtoseconds to seconds. The nature of this serial technique requires new approaches for crystallization, data analysis, and sample delivery. With continued advancements in microfabrication techniques, various developments have been reported in the past decade for innovative and efficient microfluidic sample delivery for crystallography experiments using XFELs. This article summarizes the recent developments in microfluidic sample delivery with liquid injection and fixed-target approaches, which allow exciting new research with XFELs. Graphical abstract.

Imaging Quantum Vortices in Superfluid Helium Droplets

Free superfluid helium droplets constitute a versatile medium for a diverse range of experiments in physics and chemistry that extend from studies of the fundamental laws of superfluid motion to the synthesis of novel nanomaterials. In particular, the emergence of quantum vortices in rotating helium droplets is one of the most dramatic hallmarks of superfluidity and gives detailed access to the wave function describing the quantum liquid. This review provides an introduction to quantum vorticity in helium droplets, followed by a historical account of experiments on vortex visualization in bulk superfluid helium and a more detailed discussion of recent advances in the study of the rotational motion of isolated, nano- to micrometer-scale superfluid helium droplets. Ultrafast X-ray and extreme ultraviolet scattering techniques enabled by X-ray free-electron lasers and high-order harmonic generation in particular have facilitated the in situ detection of droplet shapes and the imaging of vortex structures inside individual, isolated droplets. New applications of helium droplets ranging from studies of quantum phase separations to mechanisms of low-temperature aggregation are discussed.

Robust and Accurate Computational Estimation of the Polarizability Tensors of Macromolecules

Alignment of molecules through electric fields minimizes the averaging over orientations, e.g., in single-particle-imaging experiments. The response of molecules to external ac electric fields is governed by their polarizability tensor, which is usually calculated using quantum chemistry methods. These methods are not feasible for large molecules. Here, we calculate the polarizability tensor of proteins using a regression model that correlates the polarizabilities of the 20 amino acids with perfect conductors of the same shape. The dielectric constant of the molecules could be estimated from the slope of the regression line based on the Clausius-Mossotti equation. We benchmark our predictions against the quantum chemistry results for the Trp cagemini protein and the measured dielectric constants of larger proteins. Our method has applications in computing laser alignment of macromolecules, for instance, benefiting single-particle imaging, as well as for estimation of the optical and electrostatic characteristics of proteins and other macromolecules.

Ab Initio Calculation of Total X-ray Scattering from Molecules

We present a method to calculate total X-ray scattering cross sections directly from ab initio electronic wave functions in atoms and molecules. The approach can be used in conjunction with multiconfigurational wave functions and exploits analytical integrals of Gaussian-type functions over the scattering operator, which leads to accurate and efficient calculations. The results are validated by comparison to experimental results and previous theory for the molecules H₂ and CO₂. Importantly, we find that the inelastic component of the total scattering varies strongly with molecular geometry. The method is appropriate for use in conjunction with quantum molecular dynamics simulations for the analysis of new ultrafast X-ray scattering experiments and to interpret accurate gas-phase scattering experiments.

Simplicity Beneath Complexity: Counting Molecular Electrons Reveals Transients and Kinetics of Photodissociation Reactions

Time-resolved pump-probe gas-phase X-ray scattering signals, extrapolated to zero momentum transfer, provide a measure of the number of electrons in a system, an effect that arises from the coherent addition of elastic scattering from the electrons. This allows to identify reactive transients and determine the chemical reaction kinetics without the need for extensive scattering simulations or complicated inversion of scattering data. We examine the photodissociation reaction of trimethylamine and identify two reaction paths upon excitation to the 3p state at 200 nm: a fast dissociation path out of the 3p state to the dimethyl amine radical (16.6±1.2 %) and a slower dissociation via internal conversion to the 3s state (83.4±1.2 %). The time constants for the two reactions are 640±130 fs and 74±6 ps, respectively. Additionally, it is found that the transient dimethyl amine radical has a N-C bond length of 1.45±0.02 Å and a C-N-C bond angle of 118°±4°.

Inner-shell X-ray absorption spectra of the cationic series NHy+ (y = 0–3)

Determination of the electronic structure of mass-selected transient molecular ions which can be considered as building blocks of biomolecules.

Dynamics of soft nanoparticle suspensions at hard X-ray FEL sources below the radiation-damage threshold

The application of X-ray photon correlation spectroscopy (XPCS) at free-electron laser (FEL) facilities enables, for the first time, the study of dynamics on a (sub-)nanometre scale in an unreached time range between femtoseconds and seconds. For soft-matter materials, radiation damage is a major limitation when going beyond single-shot applications. Here, an XPCS study is presented at a hard X-ray FEL on radiation-sensitive polymeric poly(N-isopropylacrylamide) (PNIPAM) nanoparticles. The dynamics of aqueous suspensions of densely packed silica-PNIPAM core-shell particles and a PNIPAM nanogel below the radiation-damage threshold are determined. The XPCS data indicate non-diffusive behaviour, suggesting ballistic and stress-dominated heterogeneous particle motions. These results demonstrate the feasibility of XPCS experiments on radiation-sensitive soft-matter materials at FEL sources and pave the way for future applications at MHz repetition rates as well as ultrafast modes using split-pulse devices.

Conformer Selection by Matter-Wave Interference

We establish that matter-wave diffraction at near-resonant ultraviolet optical gratings can be used to spatially separate individual conformers of complex molecules. Our calculations show that the conformational purity of the prepared beam can be close to 100% and that all molecules remain in their electronic ground state. The proposed technique is independent of the dipole moment and the spin of the molecule and thus paves the way for structure-sensitive experiments with hydrocarbons and biomolecules, such as neurotransmitters and hormones, which have evaded conformer-pure isolation so far.

Spatially Separating the Conformers of a Dipeptide

Atomic-resolution-imaging approaches for single molecules, such as coherent X-ray diffraction at free-electron lasers, require the delivery of high-density beams of identical molecules. However, even very cold beams of biomolecules typically have multiple conformational states populated. We demonstrate the production of very cold (T_rot ≈2.3 K) molecular beams of intact dipeptide molecules, which were then spatially separated into the individual populated conformational states. This is achieved using the combination of supersonic expansion laser-desorption vaporization with electrostatic deflection in strong inhomogeneous fields. This represents the first demonstration of a conformer-separated and rotationally cold molecular beam of a peptide, which enables the investigation of conformer-specific chemistry using inherently non-conformer-specific techniques. It furthermore represents a milestone toward the direct structural imaging of individual biological molecules with atomic resolution by ultrafast diffractive-imaging methods.

Applications of Powder X-Ray Diffraction in Small Molecule Pharmaceuticals: Achievements and Aspirations

Since the discovery of X-ray diffraction and its potential to elucidate crystal symmetry, powder X-ray diffraction has found diverse applications in the field of pharmaceutical sciences. This review summarizes significant achievements of the technique during various stages of dosage form development. Improved understanding of the principle involved and development of automated hardware and reliable software have led to increased instrumental sensitivity and improved data analysis. These advances continue to expand the applications of powder X-ray diffraction to emerging research fields such as amorphous systems, mechanistic understanding of phase transformations, and "Quality by Design" in formulation development.

Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction

Ultrafast time-resolved X-ray scattering, made possible by free-electron laser sources, provides a wealth of information about electronic and nuclear dynamical processes in molecules. The technique provides stroboscopic snapshots of the time-dependent electronic charge density traditionally used in structure determination and reflects the interplay of elastic and inelastic processes, nonadiabatic dynamics, and electronic populations and coherences. The various contributions to ultrafast off-resonant diffraction from populations and coherences of molecules in crystals, in the gas phase, or from single molecules are surveyed for core-resonant and off-resonant diffraction. Single-molecule [Formula: see text] scaling and two-molecule [Formula: see text] scaling contributions, where N is the number of active molecules, are compared. Simulations are presented for the excited-state nonadiabatic dynamics of the electron harpooning at the avoided crossing in NaF. We show how a class of multiple diffraction signals from a single molecule can reveal charge-density fluctuations through multidimensional correlation functions of the charge density.

Structure determination from single molecule X-ray scattering with three photons per image

Scattering experiments with femtosecond high-intensity free-electron laser pulses provide a new route to macromolecular structure determination. While currently limited to nano-crystals or virus particles, the ultimate goal is scattering on single biomolecules. The main challenges in these experiments are the extremely low signal-to-noise ratio due to the very low expected photon count per scattering image, often well below 100, as well as the random orientation of the molecule in each shot. Here we present a de novo correlation-based approach and show that three coherently scattered photons per image suffice for structure determination. Using synthetic scattering data of a small protein, we demonstrate near-atomic resolution of  3.3 Å using 3.3 × 10¹⁰ coherently scattered photons from 3.3 × 10⁹ images, which is within experimental reach. Further, our three-photon correlation approach is robust to additional noise from incoherent scattering; the number of disordered solvent molecules attached to the macromolecular surface should be kept small.

Existing methods to extract structural information from single-molecule scattering measurements require large number of photons per image. Here the authors discuss a method to reconstruct the structure of a molecule from X-ray scattering data by using only three photons per image.

Time-dependent analysis of the mixed-field orientation of molecules without rotational symmetry

We present a theoretical study of the mixed-field orientation of molecules without rotational symmetry. The time-dependent one-dimensional and three-dimensional orientation of a thermal ensemble of 6-chloropyridazine-3-carbonitrile molecules in combined linearly or elliptically polarized laser fields and tilted dc electric fields is computed. The results are in good agreement with recent experimental results of one-dimensional orientation for weak dc electric fields [J. L. Hansen, J. Chem. Phys. 139, 234313 (2013)]. Moreover, they predict that using elliptically polarized laser fields or strong dc fields, three-dimensional orientation is obtained. The field-dressed dynamics of excited rotational states is characterized by highly non-adiabatic effects. We analyze the sources of these non-adiabatic effects and investigate their impact on the mixed-field orientation for different field configurations in mixed-field-orientation experiments.

Femtosecond X-ray diffraction from an aerosolized beam of protein nanocrystals

High-resolution Bragg diffraction from aerosolized single granulovirus nanocrystals using an X-ray free-electron laser is demonstrated. The outer dimensions of the in-vacuum aerosol injector components are identical to conventional liquid-microjet nozzles used in serial diffraction experiments, which allows the injector to be utilized with standard mountings. As compared with liquid-jet injection, the X-ray scattering background is reduced by several orders of magnitude by the use of helium carrier gas rather than liquid. Such reduction is required for diffraction measurements of small macromolecular nanocrystals and single particles. High particle speeds are achieved, making the approach suitable for use at upcoming high-repetition-rate facilities.

Photophysics of indole upon X-ray absorption

A photofragmentation study of gas-phase indole (C₈H₇N) upon single-photon ionization at a photon energy of 420 eV is presented.