We investigate the possibility of non-destructive electron diffraction imaging of a single molecule to determine its structure. The molecular specimen will be held on a free-standing sheet of graphene. Due to the high conductivity of graphene, electrons lost by ionization would be rapidly replaced, enabling repeated nondestructive interrogation. Limits of resolution, maximum particle size and required electron flux are assessed.
Photoelectron Angular Distributions (PADs) resulting from 800 nm and 1300 nm strong field ionization of impulsively aligned CF$_3$I molecules were analyzed using time-dependent density functional theory (TDDFT). The normalized difference between the PADs for aligned and anti-aligned molecules displays large modulations in the high-energy re-collision plateau that are assigned to the diffraction of back-scattered photoelectrons. The TDDFT calculations reveal that, in spite of their 2.6 eV energy difference, ionization from the HOMO-1 orbital contributes to the diffraction pattern on the same fo…
Ultrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments employ the classical "ball-and-stick" depictions, and the information of molecular quantum states, such as the density matrix, is missing. Here, we introduce a framework for the preparation and ultrafast coherent diffraction from rotational wave packets of molecules, and we establish a new variant of quantum state tomography for ultrafast electron diffraction to characterize the…
Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space $\left|σ(\mathbf{q})\right|^{2}$, missing its phase which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals $σ(\mathbf{q})$ itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diff…
Four-dimensional imaging of charge migration is crucial to the understanding of several ubiquitous processes in nature. The present work focuses on imaging of charge migration in an oriented epoxypropane: a chiral molecule. A linearly polarized pulse is used to induce the charge migration, which is imaged by time-resolved x-ray diffraction. It is found that the total time-resolved diffraction signals are significantly different for both enantiomers. Furthermore, a connection between time-resolved x-ray diffraction and the electronic continuity equation is discussed by analyzing the time-depend…
We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei. Several contributions to the signal are identified, representing (in decreasing strength) elastic scattering, contributions of the electronic coherences created by nonadiabatic couplings in the avoided crossing regime, and inelastic scattering. The former probes the charge density and delivers direct information on the evolving molecular geometry. The latter two contributions are weaker and carry spatial information of …
A dc electron gun, generating picosecond pulses with up to $8\times10^{6}$ electrons per pulse, was developed. Its applicability for future time-resolved-diffraction experiments on state- and conformer-selected laser-aligned or oriented gaseous samples was characterized. The focusing electrodes were arranged in a velocity-map imaging spectrometer configuration. This allowed to directly measure the spatial and velocity distributions of the electron pulses emitted from the cathode. The coherence length and pulse duration of the electron beam were characterized by these measurements combined with…
Knowledge of molecular structure is paramount in understanding, and ultimately influencing, chemical reactivity. For nearly a century, diffractive imaging has been used to identify the structures of many biologically-relevant gas-phase molecules with atomic (i.e. Angstrom, A; 1 A = 10$^{-10}$ m) spatial resolution. Unravelling the mechanisms of chemical reactions requires the capability to record multiple well-resolved snapshots of the molecular structure as it is evolving on the nuclear (i.e. femtosecond, fs; 1 fs = 10$^{-15}$ s) timescale. We present the latest, state-of-the-art ultrafast el…
Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult with increasing structural complexity, given that a global extremum must be found in a multi-dimensional solution space. Worse, pre-calculating many thousands of molecular configurations for all orientations becomes simply intractable. As a remedy, here, we propose a machine learning algorithm with a convolutional neural network which can be trained with a lim…
Free-electron laser hard X-ray light sources can provide high fluence, femtosecond pulses, enabling the time-resolved probing of structural dynamics and elementary relaxation processes in molecules. Traditional X-ray elastic scattering from crystals in the ground state consists of sharp Bragg diffraction peaks that arise from pairs of molecules and reveal the ground state charge density. Scattering of ultrashort X-ray pulses from gases, liquids, and even single molecules is more complex and involves both single- and two- molecule contributions, diffuse (non-Bragg) features, elastic and inelast…
Visualizing molecular transformations in real-time requires a structural retrieval method with Ångström spatial and femtosecond temporal atomic resolution. Imaging of hydrogen-containing molecules additionally requires an imaging method that is sensitive to the atomic positions of hydrogen nuclei, with most methods possessing relatively low sensitivity to hydrogen scattering. Laser-induced electron diffraction (LIED) is a table top technique that can image ultrafast structural changes of gas-phase polyatomic molecules with sub-Ångström and femtosecond spatiotemporal resolution together with re…
Structural information on electronically excited neutral molecules can be indirectly retrieved, largely through pump-probe and rotational spectroscopy measurements with the aid of calculations. Here, we demonstrate the direct structural retrieval of neutral carbonyl disulfide (CS$_2$) in the B$^1$B$_2$ excited electronic state using laser-induced electron diffraction (LIED). We unambiguously identify the ultrafast symmetric stretching and bending of the field-dressed neutral CS$_2$ molecule with combined picometer and attosecond resolution using intrapulse pump-probe excitation and measurement…
The structure of 1,3,5_triphenylbenzene C6H3(C6H5)3 at 473 K was investigated using the X-ray diffraction method. The measurements of scattered radiation intensity were performed in a wide range of wave vector. For the first time the theoretically predicted model of the structure 1,3,5_triphenylbenzene was experimentally confirmed. The model of short range arrangement of the molecules was proposed. The determined mean, smallest mutual distances between molecules of liquid studied are: r1=4.30 A, r2=5.30 A, r3=5.40 A. The most probable value of the packing coefficient of the molecules was found…
In this paper, we discuss the possibility of imaging molecular orbitals from photoelectron spectra obtained via Laser Induced Electron Diffraction (LIED) in linear molecules. This is an extension of our work published recently in Physical Review A \textbf{94}, 023421 (2016) to the case of the HOMO-1 orbital of the carbon dioxide molecule. We show that such an imaging technique has the potential to image molecular orbitals at different internuclear distances in a sub-femtosecond time scale and with a resolution of a fraction of an Angström.
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 ($T_\text{rot}\sim2.3~\text{K}$) molecular beams of intact dipeptide molecules, which we then spatially separate into the individual populated conformational states. This is achieved using the combination of supersonic expansion laser-desorption vaporisation with elec…
X-ray as well as electron diffraction are powerful tools for structure determination of molecules. Studies on randomly oriented molecules in the gas-phase address cases in which molecular crystals cannot be generated or the interaction-free molecular structure is to be addressed. Such studies usually yield partial geometrical information, such as interatomic distances. Here, we present a complementary approach, which allows obtaining insight to the structure, handedness and even detailed geometrical features of molecules in the gas phase. Our approach combines Coulomb explosion imaging, the in…
Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross-sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of the nuclear and corresponding electronic structure changes resulting from the dissociation dynamics in the time-dependent diffraction. Both assignments are confirmed by ab initio simulations of the phot…
Observing the motion of the nuclear wavepackets during a molecular reaction, in both space and time, is crucial for understanding and controlling the outcome of photoinduced chemical reactions. We have imaged the motion of a vibrational wavepacket in isolated iodine molecules using ultrafast electron diffraction with relativistic electrons. The time-varying interatomic distance was measured with a precision 0.07 Å and temporal resolution of 230 fs full-width at half-maximum (FWHM). The method is not only sensitive to the position but also the shape of the nuclear wavepacket.
We offer a brief overview of the solvent-based graphene production and summarize the current knowledge on the formation mechanism of graphite oxide that proceeds via graphite intercalation compounds. In addition, the results of our in situ X-ray diffraction investigation into this process are presented, discussed and contrasted to the findings by other authors, who employed the same oxidation protocol but examined the samples by ex situ X-ray diffraction. Our results suggest that, contrary to the numerous reports by other authors, no strong crystalline order, unique to graphite intercalation c…
We have investigated the structural dynamics in photoexcited 1,2-diiodotetrafluoroethane molecules (C2F4I2) in the gas phase experimentally using ultrafast electron diffraction and theoretically using FOMO-CASCI excited state dynamics simulations. The molecules are excited by an ultra-violet femtosecond laser pulse to a state characterized by a transition from the iodine 5p orbital to a mixed 5p|| hole and CF2 antibonding orbital, which results in the cleavage of one of the carbon-iodine bonds. We have observed, with sub-Angstrom resolution, the motion of the nuclear wavepacket of the dissocia…
Measurements on the strong-field ionization of carbonyl sulfide molecules by short, intense, 2~\um wavelength laser pulses are presented from experiments where angle-resolved photoelectron distributions were recorded with a high-energy velocity map imaging spectrometer, designed to reach a maximum kinetic energy of 500~eV. The laser-field-free elastic-scattering cross section of carbonyl sulfide was extracted from the measurements and is found in good agreement with previous experiments, performed using conventional electron diffraction. By comparing our measurements to the results of calculat…
X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved X-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear X-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation c…
Metal-corroles are macrocycle organic molecules with numerous practical applications. In particular, copper corroles exhibit an interesting saddled geometry, which has attracted significant attention from theoreticians and experimentalists over the years. The present work is dedicated to understand the effect of structural saddling in a copper corrole on potential probe signals via imaging ultrafast coherent electron dynamics. A linearly polarized pulse is used to trigger the electron dynamics and time-resolved x-ray diffraction is employed to image the triggered dynamics. It is found that the…
New charge transfer crystals of $π$-conjugated, aromatic molecules (phenanthrene and picene) as donors were obtained by physical vapor transport. The melting behavior, optimization of crystal growth and the crystal structure is reported for charge transfer salts with (fluorinated) tetracyanoquinodimethane (TCNQ-F$_x$, x=0, 2, 4), which was used as acceptor material. The crystal structures were determined by single-crystal X-ray diffraction. Growth conditions for different vapor pressures in closed ampules were applied and the effect of these starting conditions for crystal size and quality is …
