State- and conformer-selected beams of aligned and oriented molecules for ultrafast diffraction studies

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.

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.

Trends in angle-resolved molecular photoelectron spectroscopy

In this perspective article, main trends of angle-resolved molecular photoelectron spectroscopy in the laboratory up to the molecular frame, in different regimes of light-matter interactions, are highlighted with emphasis on foundations and most recent applications.

Conformer-specific photochemistry imaged in real space and time

[Figure: see text].

The Effect of Nuclear-Quadrupole Coupling in the Laser-Induced Alignment of Molecules

We present a theoretical study of the time-dependent laser alignment of molecules taking into account the hyperfine coupling due to nuclear-quadrupole interactions. The coupling of nuclear spins to the overall angular momentum of molecules significantly influences their rotational dynamics. Here, we systematically analyze the impact of the nuclear-quadrupole coupling on the rotational dynamics of the linear and the asymmetric-top diiodobenzene molecule induced by external laser fields. We explore different regimes of pulse shapes and laser-pulse intensities and detail under which conditions the quadrupole coupling cannot be neglected in the description of the laser alignment of molecules.

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.

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.

Long-lasting field-free alignment of large molecules inside helium nanodroplets

Molecules with their axes sharply confined in space, available through laser-induced alignment methods, are essential for many current experiments, including ultrafast molecular imaging. For these applications the aligning laser field should ideally be turned-off, to avoid undesired perturbations, and the strong alignment should last long enough that reactions and dynamics can be mapped out. Presently, this is only possible for small, linear molecules and for times less than 1 picosecond. Here, we demonstrate strong, field-free alignment of large molecules inside helium nanodroplets, lasting >10 picoseconds. One-dimensional or three-dimensional alignment is created by a slowly switched-on laser pulse, made field-free through rapid pulse truncation, and retained thanks to the impeding effect of the helium environment on molecular rotation. The opportunities field-free aligned molecules open are illustrated by measuring the alignment-dependent strong-field ionization yield of dibromothiophene oligomers. Our technique will enable molecular frame experiments, including ultrafast excited state dynamics, on a variety of large molecules and complexes.

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.

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.

Accessing the molecular frame through strong-field alignment of distributions of gas phase molecules

A rationale for creating highly aligned distributions of molecules is that it enables vector properties referenced to molecule-fixed axes (the molecular frame) to be determined. In the present work, the degree of alignment that is necessary for this to be achieved in practice is explored. Alignment is commonly parametrized in experiments by a single parameter, [Formula: see text], which is insufficient to enable predictive calculations to be performed. Here, it is shown that, if the full distribution of molecular axes takes a Gaussian form, this single parameter can be used to determine the complete set of alignment moments needed to characterize the distribution. In order to demonstrate the degree of alignment that is required to approach the molecular frame, the alignment moments corresponding to a few chosen values of [Formula: see text] are used to project a model molecular frame photoelectron angular distribution into the laboratory frame. These calculations show that [Formula: see text] needs to approach 0.9 in order to avoid significant blurring to be caused by averaging.This article is part of the theme issue 'Modern theoretical chemistry'.

Electron diffraction of CBr4 in superfluid helium droplets: A step towards single molecule diffraction

We demonstrate the practicality of electron diffraction of single molecules inside superfluid helium droplets using CBr4 as a testing case. By reducing the background from pure undoped droplets via multiple doping, with small corrections for dimers and trimers, clearly resolved diffraction rings of CBr4 similar to those of gas phase molecules can be observed. The experimental data from CBr4 doped droplets are in agreement with both theoretical calculations and with experimental results of gaseous species. The abundance of monomers and clusters in the droplet beam also qualitatively agrees with the Poisson statistics. Possible extensions of this approach to macromolecular ions will also be discussed. This result marks the first step in building a molecular goniometer using superfluid helium droplet cooling and field induced orientation. The superior cooling effect of helium droplets is ideal for field induced orientation, but the diffraction background from helium is a concern. This work addresses this background issue and identifies a possible solution. Accumulation of diffraction images only becomes meaningful when all images are produced from molecules oriented in the same direction, and hence a molecular goniometer is a crucial technology for serial diffraction of single molecules.

Enhancing scattering images for orientation recovery with diffusion map

We explore the possibility for orientation recovery in single-molecule coherent diffractive imaging with diffusion map. This algorithm approximates the Laplace-Beltrami operator, which we diagonalize with a metric that corresponds to the mapping of Euler angles onto scattering images. While suitable for images of objects with specific properties we show why this approach fails for realistic molecules. We introduce a modification of the form factor in the scattering images which facilitates the orientation recovery and should be suitable for all recovery algorithms based on the distance of individual images.

High-intracavity-power thin-disk laser for the alignment of molecules

We propose a novel approach for strong alignment of gas-phase molecules for experiments at arbitrary repetition rates. A high-intracavity-power continuous-wave laser will provide the necessary ac electric field of 10(10)-10(11) W/cm(2). We demonstrate thin-disk lasers based on Yb:YAG and Yb:Lu(2)O(3) in a linear high-finesse resonator providing intracavity power levels in excess of 100 kW at pump power levels on the order of 50 W. The multi-longitudinal-mode operation of this laser avoids spatial-hole burning even in a linear standing-wave resonator. The system will be scaled up as in-vacuum system to allow for the generation of fields of 10(11) W/cm(2). This system will be directly applicable for experiments at modern X-ray light sources, such as synchrotrons or free-electron lasers, which operate at various very high repetition rates. This would allow to record molecular movies through temporally resolved diffractive imaging of fixed-in-space molecules, as well as the spectroscopic investigation of combined X-ray-NIR strong-field effects of atomic and molecular systems.

Photoelectron diffraction from laser-aligned molecules with X-ray free-electron laser pulses

We report on the measurement of deep inner-shell 2p X-ray photoelectron diffraction (XPD) patterns from laser-aligned I₂ molecules using X-ray free-electron laser (XFEL) pulses. The XPD patterns of the I₂ molecules, aligned parallel to the polarization vector of the XFEL, were well matched with our theoretical calculations. Further, we propose a criterion for applying our molecular-structure-determination methodology to the experimental XPD data. In turn, we have demonstrated that this approach is a significant step toward the time-resolved imaging of molecular structures.

Velocity map imaging with non-uniform detection: Quantitative molecular axis alignment measurements via Coulomb explosion imaging

We present a method for inverting charged particle velocity map images which incorporates a non-uniform detection function. This method is applied to the specific case of extracting molecular axis alignment from Coulomb explosion imaging probes in which the probe itself has a dependence on molecular orientation which often removes cylindrical symmetry from the experiment and prevents the use of standard inversion techniques for the recovery of the molecular axis distribution. By incorporating the known detection function, it is possible to remove the angular bias of the Coulomb explosion probe process and invert the image to allow quantitative measurement of the degree of molecular axis alignment.

Conformation-Selective Resonant Photoelectron Spectroscopy via Dipole-Bound States of Cold Anions

Molecular conformation is important in chemistry and biochemistry. Conformers connected by low energy barriers can only be observed at low temperatures and are difficult to be separated. Here we report a new method to obtain conformation-selective spectroscopic information about dipolar molecular radicals via dipole-bound excited states of the corresponding anions cooled in a cryogenic ion trap. We observed two conformers of cold 3-hydroxyphenoxide anions [m-HO(C6H4)O(-)] in high-resolution photoelectron spectroscopy and measured different electron affinities, 18,850(8) and 18,917(5) cm(-1), for the syn and anti 3-hydroxyphenoxy radicals, respectively. We also observed dipole-bound excited states for m-HO(C6H4)O(-) with different binding energies for the two conformers due to the different dipole moments of the corresponding 3-hydroxyphenoxy radicals. Excitations to selected vibrational levels of the dipole-bound states result in conformation-selective photoelectron spectra. This method should be applicable to conformation-selective spectroscopic studies of any anions with dipolar neutral cores.

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.

Cold and Controlled Molecular Beams: Production and Applications

The field of cold molecules has become an important source of new insight in fundamental chemistry and molecular physics. High-resolution spectroscopy benefits from translationally and internally cold molecules by increased interaction times and reduced spectral congestion. Completely new effects in scattering dynamics become accessible with cold and controlled molecules. Many of these experiments use molecular beams as a starting point for the generation of molecular samples. This review gives an overview of methods to produce beams of cold molecules, starting from supersonic expansions or effusive sources, and provides examples of applications in spectroscopy and molecular dynamics studies.

Control of conformers combining cooling by supersonic expansion of seeded molecular beams with hexapole selection and alignment: experiment and theory on 2-butanol

Selection and alignment of rotamers and, more in general, of conformers in the gas phase is a challenge that we tackle experimentally by supersonic expansion of seeded molecular beams and hexapolar electrostatic fields with quadrupole mass detection. The studied system involves the nine conformers of the asymmetric-top molecule 2-butanol, which coexist because of nearly free rotations around a CC and a CO bond. From the measured time-of-flight of a 2-butanol supersonic molecular beam seeded in either He or Ar, the corresponding velocity distributions are obtained. The different nature and masses of the seeding gas decrease selectively the vibrational temperature and determine the population of the conformers, which is assessed on the basis of their statistical distribution, derived from high level accompanying quantum mechanical calculations. The use of a hexapolar electrostatic field permits us to induce a variation of the population distribution as a function of the applied voltage and of the selective focusing and alignment of the conformers. A technique, recently developed for treating asymmetric tops and involving extensive trajectory simulations, is applied to obtain the link between the focusing curves, i.e. the dependence of the beam intensity on the hexapole voltage, and the conformers' populations and alignment. Perspectives are provided for photo- and stereo-dynamics experiments, particularly appealing also on account that 2-butanol is the simplest chiral alcohol.

Alignment of D-state Rydberg molecules

We report on the formation of ultralong-range Rydberg D-state molecules via photoassociation in an ultracold cloud of rubidium atoms. By applying a magnetic offset field on the order of 10 G and high resolution spectroscopy, we are able to resolve individual rovibrational molecular states. A full theory, using a Fermi pseudopotential approach including s- and p-wave scattering terms, reproduces the measured binding energies. The calculated molecular wave functions show that in the experiment we can selectively excite stationary molecular states with an extraordinary degree of alignment or antialignment with respect to the magnetic field axis.

Spatial separation of molecular conformers and clusters

Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold molecular beams. However, these beams often contain multiple conformers and clusters, even at low rotational temperatures. We present an experimental methodology that allows the spatial separation of these constituent parts of a molecular beam expansion. Using an electric deflector the beam is separated by its mass-to-dipole moment ratio, analogous to a bender or an electric sector mass spectrometer spatially dispersing charged molecules on the basis of their mass-to-charge ratio. This deflector exploits the Stark effect in an inhomogeneous electric field and allows the separation of individual species of polar neutral molecules and clusters. It furthermore allows the selection of the coldest part of a molecular beam, as low-energy rotational quantum states generally experience the largest deflection. Different structural isomers (conformers) of a species can be separated due to the different arrangement of functional groups, which leads to distinct dipole moments. These are exploited by the electrostatic deflector for the production of a conformationally pure sample from a molecular beam. Similarly, specific cluster stoichiometries can be selected, as the mass and dipole moment of a given cluster depends on the degree of solvation around the parent molecule. This allows experiments on specific cluster sizes and structures, enabling the systematic study of solvation of neutral molecules.

Analysis of a measurement scheme for ultrafast hole dynamics by few femtosecond resolution X-ray pump–probe Auger spectroscopy

Ultrafast hole dynamics created in molecular systems as a result of sudden ionisation is the focus of much attention in the field of attosecond science. Using the molecule glycine we show through ab initio simulations that the dynamics of a hole, arising from ionisation in the inner valence region, evolves with a timescale appropriate to be measured using X-ray pulses from the current generation of SASE free electron lasers. The examined pump–probe scheme uses X-rays with photon energy below the K edge of carbon (275–280 eV) that will ionise from the inner valence region. A second probe X-ray at the same energy can excite an electron from the core to fill the vacancy in the inner-valence region. The dynamics of the inner valence hole can be tracked by measuring the Auger electrons produced by the subsequent refilling of the core hole as a function of pump–probe delay. We consider the feasibility of the experiment and include numerical simulation to support this analysis. We discuss the potential for all X-ray pump-X-ray probe Auger spectroscopy measurements for tracking hole migration.

Specific Chemical Reactivities of Spatially Separated 3-Aminophenol Conformers with Cold Ca+ Ions

Many molecules exhibit multiple rotational isomers (conformers) that interconvert thermally and are difficult to isolate. Consequently, a precise characterization of their role in chemical reactions has proven challenging. We have probed the reactivity of specific conformers by using an experimental technique based on their spatial separation in a molecular beam by electrostatic deflection. The separated conformers react with a target of Coulomb-crystallized ions in a trap. In the reaction of Ca+ with 3-aminophenol, we find a twofold larger rate constant for the cis compared with the trans conformer (differentiated by the O–H bond orientation). This result is explained by conformer-specific differences in the long-range ion-molecule interaction potentials. Our approach demonstrates the possibility of controlling reactivity through selection of conformational states.

Ultrafast charge rearrangement and nuclear dynamics upon inner-shell multiple ionization of small polyatomic molecules

Ionization and fragmentation of methylselenol (CH(3)SeH) molecules by intense (>10(17) W/cm(2)) 5 fs x-ray pulses (ħω=2 keV) are studied by coincident ion momentum spectroscopy. We contrast the measured charge state distribution with data on atomic Kr, determine kinetic energies of resulting ionic fragments, and compare them to the outcome of a Coulomb explosion model. We find signatures of ultrafast charge redistribution from the inner-shell ionized Se atom to its molecular partners, and observe significant displacement of the atomic constituents in the course of multiple ionization.

Molecular imaging using X-ray free-electron lasers

The opening of hard X-ray free-electron laser facilities, such as the Linac Coherent Light Source (LCLS) at SLAC National Accelerator Laboratory in the United States, has ushered in a new era in structural determination. With X-ray pulse durations down to 10 fs or shorter, and up to 10(13) transversely coherent photons per pulse in a narrow spectral bandwidth, focused irradiances of 10(18) to 10(21) W cm(-2) or higher can be produced at X-ray energies ranging from 500 eV to 10 keV. New techniques for determining the structure of systems that cannot be crystallized and for studying the time-resolved behavior of irreversible reactions at femtosecond timescales are now available.

Beam broadening of polar molecules and clusters in deflection experiments

A beam of rotating dipolar particles (molecules or clusters) will broaden when passed through an electric or magnetic field gradient region. This broadening, which is a common experimental observable, can be expressed in terms of the variance of the distribution of the resulting polarization orientation (the direction cosine). Here, the broadening for symmetric-top and linear rotors is discussed. These two types of rotors have qualitatively different low-field orientation distribution functions, but behave similarly in a strong field. While analytical expressions for the polarization variance can be derived from first-order perturbation theory, for experimental guidance it is important to identify the applicability and limitations of these expressions, and the general dependence of the broadening on the experimental parameters. For this purpose, the analytical results are compared with the full diagonalization of the rotational Stark-effect matrices. Conveniently for experimental estimations, it is found that for symmetric tops, the dependence of the broadening parameter on the rotational constant, the axial ratio, and the field strength remains similar to the analytical expression even outside of the perturbative regime. Also, it is observed that the shape envelope, the centroid, and the width of the orientation distribution function for a symmetric top are quite insensitive to the value of its rotational constant (except at low rotational temperatures).