Imaging photoelectron circular dichroism of chiral molecules by femtosecond multiphoton coincidence detection

Control of circular dichroism in ion yield of 3-methyl cyclopentanone with femtosecond laser pulses

Circular dichroism (CD) in ion yield in the gas phase is a promising chiral recognition technique. Combining it with broadband ultrafast laser pulses allows us to examine the possibility of coherent control. We used shaped femtosecond laser pulses to control the CD in ion yield of 3-methylcyclopentanone observed from a 1 + 1 + 1 resonance-enhanced multiphoton ionisation around 309 nm. The duration of the pulses is increased via their spectral width or a frequency chirp, and a pulse pair with adjustable delay is employed to study the effect on the CD in ion yield. Furthermore, we used strongly chirped pulses of different central wavelengths to control the observed anisotropy. A clear enhancement of the anisotropy can be achieved, and possible mechanisms are discussed.

Photoelectron circular dichroism of aqueous-phase alanine

Amino acids and other small chiral molecules play key roles in biochemistry. However, in order to understand how these molecules behave in vivo, it is necessary to study them under aqueous-phase conditions. Photoelectron circular dichroism (PECD) has emerged as an extremely sensitive probe of chiral molecules, but its suitability for application to aqueous solutions had not yet been proven. Here, we report on our PECD measurements of aqueous-phase alanine, the simplest chiral amino acid. We demonstrate that the PECD response of alanine in water is different for each of alanine's carbon atoms, and is sensitive to molecular structure changes (protonation states) related to the solution pH. For C 1s photoionization of alanine's carboxylic acid group, we report PECD of comparable magnitude to that observed in valence-band photoelectron spectroscopy of gas-phase alanine. We identify key differences between PECD experiments from liquids and gases, discuss how PECD may provide information regarding solution-specific phenomena - for example the nature and chirality of the solvation shell surrounding chiral molecules in water - and highlight liquid-phase PECD as a powerful new tool for the study of aqueous-phase chiral molecules of biological relevance.

Determination of the Molar Fraction and Enantiomeric Excess of Electrosprayed Amino Acid Anions Employing Photoelectron Circular Dichroism

The quantification of molar fractions and enantiomeric excess has been demonstrated in mixtures of d- and l-tryptophan and d- and l-phenylalanine, respectively, avoiding derivatization of the analyte with additional reagents or separation steps. The technique is based on electrospray ionization (ESI), which allows the generation of anions of nonvolatile compounds such as amino acids or large biomolecules. Electrons are photodetached from these anions. The distribution of forward and backward scattered photoelectrons is analyzed, leading to photoelectron circular dichroism (PECD), the observable of interest. The quantification of the concept is proven by blind measurements analyzing mixtures of unknown composition. The quantification of enantiomeric excess (ee) values is not only possible for signals originating from the molecular anion but also for the molecular dimer anion. The ESI-PECD technique is known to be applicable to large chemical entities of several thousand Daltons.

Characterization of the photoelectron circular dichroism of fixed-in-space molecules through an asymmetry of the ionic potential

Photoelectron circular dichroism (PECD) in the ionization of chiral molecules by circularly polarized radiation is a well-established tool for chiral recognition in the gas phase. The effect consists in a forward-backward asymmetry in angular emission distributions of photoelectrons with respect to the light propagation direction, which survives averaging over molecular orientations. Its magnitude is governed by the ability of the outgoing photoelectron to probe an asymmetry of the ionic potential by multiple scattering effects, and it can be significantly enhanced by fixing molecular orientation in space. Even achiral fixed-in-space molecules can exhibit such a forward-backward asymmetry in the photoemission. In the present work, we establish a qualitative correspondence between the PECD in one-photon ionization of fixed-in-space molecules and a degree of the asymmetry of their ionic potential. For this purpose, we introduce an enantiosensitive dichroic characteristic of the ionic potential, which describes a physical mechanism behind the forward-backward asymmetry in the photoemission from fixed-in-space molecules ionized by circularly polarized light. This characteristic, as a function of molecular orientation angles, can be compared to the respective PECD landscape. The present findings are exemplified by several applications to achiral and chiral species.

Two decades of imaging photoelectron circular dichroism: from first principles to future perspectives

There has been a significant recent surge in the number of studies interrogating chiral molecules in the gas phase using photoelectron circular dichroism (PECD) and related techniques. These investigations have revealed new fundamental insights into the structure and dynamics of chiral species and, furthermore, have the potential to revolutionize the field of chiral analysis for more practical and industrial applications. As it has been just over 20 years since the first PECD imaging experiments were demonstrated - and 10 years since the last dedicated general perspective article on the topic - a new overview now seems extremely timely. This article will introduce PECD to the general reader and give a synopsis of developments in the field, focusing particularly on the last decade, where the use of multiphoton ionization schemes has brought PECD to a wider experimental audience. We will discuss the novel applications of the general methodology and highlight the challenges that must be overcome to fully cement PECD and adjacent techniques as powerful chiral analysis probes.

The role of intramolecular hydrogen bonding in photoelectron circular dichroism: the diastereoisomers of 1-amino-2-indanol

(1R,2R)-trans-Aminoindanol and (1S,2R)-cis-aminoindanol, denoted as trans-AI and cis-AI, are diastereoisomer aromatic aminoalcohols differing by the presence of a weak intramolecular hydrogen bond in cis-AI, which is absent in trans-AI. They also differ by the number of conformers under supersonic jet conditions, one for trans-AI and two for cis-AI. One-photon and resonance-enhanced two-photon photoelectron circular dichroism (PECD) spectra are obtained for the two molecules. One-photon ionisation above 11 eV results in molecular fragmentation, with very similar fragmentation pathways for trans-AI and cis-AI. Identical PECD spectra for different fragments allow associating them with reactions occurring from the same parent ion within the same electronic state. The shape of the PECD spectra is sensitive to configuration, conformation, and intramolecular hydrogen bonding. Two-photon PECD, being conformer specific, shows that the PECDs of the two ring-puckering conformers of cis-AI have identical signs but different values.

Numerical evaluation of orientation averages and its application to molecular physics

In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modeling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely related to integration over two- or three-dimensional unit spheres, a common problem discussed in numerical analysis. The computational cost of the integration depends significantly on the quadrature method, making the selection of an appropriate method crucial for the feasibility of simulations. After reviewing several classes of spherical quadrature methods in terms of their efficiency and error distribution, we derive guidelines for choosing the best quadrature method for orientation averages and illustrate these with three examples from chiral molecule physics. While Gauss quadratures allow for achieving numerically exact integration for a wide range of applications, other methods offer advantages in specific circumstances. Our guidelines can also be applied to higher-dimensional spherical domains and other geometries. We also present a Python package providing a flexible interface to a variety of quadrature methods.

High-order above-threshold ionisation of diatomic molecules by few-cycle bicircular and orthogonally polarised two-colour pulses

Improved molecular strong-field approximation theory is used to calculate the ionisation probability for the high-order above-threshold ionisation process induced by a few-cycle pulse with two carrier frequencies and one envelope. The asymmetry in the photoelectron momentum distribution is due to the ultrashort nature of the driving pulse and due to the relative orientation of the molecule with respect to the laser field. We introduce the generalised asymmetry parameter, which can be used to quantitatively measure the asymmetry between the photoelectron spectra along arbitrarily many selected directions. We investigate the difference between the asymmetry parameters calculated for atomic and molecular targets and show that the contributions to the asymmetry strongly depend on the type of the employed driving pulse. For the driving pulse with components that are linearly polarised with mutually orthogonal polarisations, we find that the main source of the asymmetry, especially in the high-energy part of the spectrum, is the ultrashort nature of the pulse. The relative orientation of the molecule with respect to the laser pulse only affects the low- and medium-energy parts of the spectrum. On the other hand, for the driving pulse with circularly polarised counterrotating components, the asymmetry introduced by molecular orientation is more pronounced. We also analyse the influence of the characteristics of molecular orbitals on the asymmetries using the examples of N2 and O2 molecules.

Optimal photoelectron circular dichroism of a model chiral system

We optimize the internuclear geometry and electronic structure of a model chiral system to achieve a maximal photoelectron circular dichroism (PECD) in its one-photon ionization by circularly polarized light. The electronic structure calculations are performed by the single center method, while the optimization is done using quantum alchemy employing a Taylor series expansion. Thereby, the effect of bond lengths and uncompensated charge distributions on the chiral response of the model is investigated theoretically in some detail. It is demonstrated that manipulating a chiral asymmetry of the ionic potential may enhance the dichroic parameter (i.e., the PECD) of the randomly oriented model system well beyond β1 = 25%. Furthermore, we demonstrate that quantum alchemy is applicable to PECD despite the unusually strong coupling of spatial and electronic degrees of freedom and discuss the relative impact of the individual degrees of freedom in this model system. We define the necessary conditions for the computational design of PECD for real (non-model) chiral molecules using our approach.

Capturing electron-driven chiral dynamics in UV-excited molecules

Chiral molecules, used in applications such as enantioselective photocatalysis1, circularly polarized light detection2 and emission3 and molecular switches4,5, exist in two geometrical configurations that are non-superimposable mirror images of each other. These so-called (R) and (S) enantiomers exhibit different physical and chemical properties when interacting with other chiral entities. Attosecond technology might enable influence over such interactions, given that it can probe and even direct electron motion within molecules on the intrinsic electronic timescale6 and thereby control reactivity7-9. Electron currents in photoexcited chiral molecules have indeed been predicted to enable enantiosensitive molecular orientation10, but electron-driven chiral dynamics in neutral molecules have not yet been demonstrated owing to the lack of ultrashort, non-ionizing and perturbative light pulses. Here we use time-resolved photoelectron circular dichroism (TR-PECD)11-15 with an unprecedented temporal resolution of 2.9 fs to map the coherent electronic motion initiated by ultraviolet (UV) excitation of neutral chiral molecules. We find that electronic beatings between Rydberg states lead to periodic modulations of the chiroptical response on the few-femtosecond timescale, showing a sign inversion in less than 10 fs. Calculations validate this and also confirm that the combination of the photoinduced chiral current with a circularly polarized probe pulse realizes an enantioselective filter of molecular orientations following photoionization. We anticipate that our approach will enable further investigations of ultrafast electron dynamics in chiral systems and reveal a route towards enantiosensitive charge-directed reactivity.

Conformer-Selective Photoelectron Circular Dichroism

Conformational flexibility and chirality both play a key role in molecular recognition. It is therefore very useful to develop spectroscopic methods that simultaneously probe both properties. It has been theoretically predicted that photoelectron circular dichroism (PECD) should be very sensitive to conformational isomerism. However, experimental proof has been less forthcoming and only exists for a very few favorable cases. Here, we present a new PECD scheme based on resonance-enhanced two-photon ionization (RE2PI) using UV/Vis nanosecond laser excitations. The spectral resolution obtained thereby guarantees conformer-selectivity by inducing resonant conformer-specific ππ* S1←S0 transitions. We apply this experimental scheme to the study of chiral 1-indanol, which exists in two conformers linked by a ring inversion and defined by the position of the hydroxyl group, namely axial and equatorial. We show that the PECD of the equatorial and axial forms considerably differ in sign, magnitude and shape. We also discuss the influence of the total ionization energy, vibronic excitation of intermediate and final states, and relative polarization of the excitation and ionization lasers. Conformer-specificity adds a new dimension to the applications of PECD in analytical chemistry addressing now the general case of floppy systems.

Photoelectron Circular Dichroism in the Spin-Polarized Spectra of Chiral Molecules

We studied strong-field multiphoton ionization of 1-iodo-2-methylbutane enantiomers with 395 nm circularly polarized laser pulses experimentally and theoretically. For randomly oriented molecules, we observe spin polarization up to about 15%, which is independent of the molecular enantiomer. Our experimental findings are explained theoretically as an intricate interplay between three contributions from HOMO, HOMO-1, and HOMO-2, which are formed of 5p-electrons of the iodine atom. For uniaxially oriented molecules, our theory demonstrates even larger spin polarization. Moreover, we predict a sizable enantiosensitive photoelectron circular dichroism of about 10%, which is different for different spin states of photoelectrons.

Anisotropy Parameters for Two-Color Photoionization Phases in Randomly Oriented Molecules: Theory and Experiment in Methane and Deuteromethane

We present combined theoretical and experimental work investigating the angle-resolved phases of the photoionization process driven by a two-color field consisting of an attosecond pulse train and an infrared pulse in an ensemble of randomly oriented molecules. We derive a general form for the two-color photoelectron (and time-delay) angular distribution valid also in the case of chiral molecules and when relative polarizations of the photons contributing to the attosecond photoelectron interferometer differ. We show a comparison between the experimental data and theoretical predictions in an ensemble of methane and deuteromethane molecules, discussing the effect of nuclear dynamics on the photoionization phases. Finally, we demonstrate that the oscillating component and the phase of the two-color signal can be fitted by using complex asymmetry parameters, in perfect analogy to the atomic case.

The importance of molecular axis alignment and symmetry-breaking in photoelectron elliptical dichroism

Photoelectron angular distributions (PADs) produced from the photoionization of chiral molecules using elliptically polarized light exhibit a forward/backward asymmetry with respect to the optical propagation direction. By recording these distributions using the velocity-map imaging (VMI) technique, the resulting photoelectron elliptical dichroism (PEELD) has previously been demonstrated as a promising spectroscopic tool for studying chiral molecules in the gas phase. The use of elliptically polarized laser pulses, however, produces PADs (and consequently, PEELD distributions) that do not exhibit cylindrical symmetry about the propagation axis. This leads to significant limitations and challenges when employing conventional VMI acquisition and data processing strategies. Using novel photoelectron image analysis methods based around Hankel transform reconstruction tomography and machine learning, however, we have quantified-for the first time-significant symmetry-breaking contributions to PEELD signals that are of a comparable magnitude to the symmetric terms in the multiphoton ionization of (1R,4R)-(+)- and (1S,4S)-(-)-camphor. This contradicts any assumptions that symmetry-breaking can be ignored when reconstructing VMI data. Furthermore, these same symmetry-breaking terms are expected to appear in any experiment where circular and linear laser fields are used together. This ionization scheme is particularly relevant for investigating dynamics in chiral molecules, but it is not limited to them. Developing a full understanding of these terms and the role they play in the photoionization of chiral molecules is of clear importance if the potential of PEELD and related effects for future practical applications is to be fully realized.

Induced photoelectron circular dichroism onto an achiral chromophore

An achiral chromophore can acquire a chiral spectroscopic signature when interacting with a chiral environment. This so-called induced chirality is documented in electronic or vibrational circular dichroism, which arises from the coupling between electric and magnetic transition dipoles. Here, we demonstrate that a chiroptical response is also induced within the electric dipole approximation by observing the asymmetric scattering of a photoelectron ejected from an achiral chromophore in interaction with a chiral host. In a phenol-methyloxirane complex, removing an electron from an achiral aromatic π orbital localised on the phenol moiety results in an intense and opposite photoelectron circular dichroism (PECD) for the two enantiomeric complexes with (R) and (S) methyloxirane, evidencing the long-range effect (~5 Å) of the scattering chiral potential. This induced chirality has important structural and analytical implications, discussed here in the context of growing interest in laser-based PECD, for in situ, real time enantiomer determination.

Elliptic Dichroism in the Above-Threshold Ionization of Molecules Induced by a Strong Laser Field

Using a strong-field-approximation theory, we investigate the high-order above-threshold ionization of diatomic molecules exposed to the monochromatic and bichromatic elliptically polarized fields. We devote particular attention to the difference between the photoelectron momentum distributions obtained with fields with opposite helicity. This difference is quantified using the elliptic-dichroism parameter, which represents the normalized difference between the differential ionization rates calculated with driving fields with opposite helicity. We find that this parameter strongly depends on the molecular orientation with respect to the laser field. In addition, this dependence is different for molecules with different types of highest-occupied molecular orbital. In other words, we show that the molecular structure is imprinted onto the elliptic-dichroism parameter for both monochromatic and bichromatic driving fields. This is explained by analyzing the interferences between various partial contributions to the differential ionization rate. In this way, elliptic dichroism also serves as a tool to analyze the electron dynamics. Finally, for heteronuclear diatomic molecules, we show that the elliptic dichroism is different from zero even for the direct electrons, i.e., the electrons that after liberation go directly to the detector. In this case, the dependence on the molecular orientation is far more pronounced for a bichromatic driving field.

Ultrafast control over chiral sum-frequency generation

We introduce an ultrafast all-optical approach for efficient chiral recognition that relies on the interference between two low-order nonlinear processes that are ubiquitous in nonlinear optics: sum-frequency generation and third-harmonic generation. In contrast to traditional sum-frequency generation, our approach encodes the medium's handedness in the intensity of the emitted harmonic signal, rather than in its phase, and it enables full control over the enantiosensitive response. We show how, by sculpting the sub-optical-cycle oscillations of the driving laser field, we can force one molecular enantiomer to emit bright light while its mirror twin remains dark, thus reaching the ultimate efficiency limit of chiral sensitivity via low-order nonlinear light-matter interactions. Our work paves the way for ultrafast and highly efficient imaging and control of the chiral electronic clouds of chiral molecules using lasers with moderate intensities, in all states of matter: from gases to liquids to solids, with molecular specificity and on ultrafast time scales.

Tilting light's polarization plane to spatially separate the ultrafast nonlinear response of chiral molecules

Distinguishing between the left- and right-handed versions of a chiral molecule (enantiomers) is vital, but also inherently difficult. Traditional optical methods using elliptically/circularly polarized light rely on linear effects which arise beyond the electric-dipole approximation, posing major limitations for ultrafast spectroscopy. Here we show how to turn an ultrashort elliptical pulse into an efficient chiro-optical tool: by tilting its polarization plane towards its propagation direction. This forward tilt can be achieved by focusing the beam tightly, creating structured light which exhibits a nontrivial polarization pattern in space. Using state-of-the-art computational modelling, we show that our structured field realizes a near-field interferometer for efficient chiral recognition that separates the nonlinear optical response of left- and right-handed molecules in space. Our work provides a simple, yet highly efficient, way of spatially structuring the polarization of light to image molecular chirality, with extreme enantio-efficiency and on ultrafast time scales.

Velocity-map imaging of photoelectron circular dichroism in non-volatile molecules using a laser-based desorption source

We present an initial demonstration of a velocity-map imaging (VMI) experiment using a back-irradiation laser-based desorption source directly integrated into the electrode assembly. This has the potential to greatly expand the utility of the popular VMI approach by permitting its use with high density plumes of non-volatile molecular samples. Photoelectron circular dichroism measurements on the phenylalanine molecule using 400 nm multiphoton ionization are used to illustrate this novel method, revealing forward-backward emission asymmetries on the order of 7%.

Carrier envelope phase sensitivity of photoelectron circular dichroism

We report on a combined experimental and numerical study of photoelectron circular dichroism (PECD) induced by intense few-cycle laser pulses, using methyloxirane as the molecular example. Our experiments reveal a remarkably pronounced sensitivity of the PECD strength of double-ionization on the carrier-envelope phase (CEP) of the laser pulses. By comparison to the simulations, which reproduce the measured CEP-dependence for specific orientations of the molecules in the lab frame, we attribute the origin of the observed CEP-dependence of PECD to the CEP-induced modulation of ionization from different areas of the wave functions of three dominant orbitals.

Imaging Photoelectron Circular Dichroism in the Detachment of Mass-Selected Chiral Anions

Photoelectron Circular Dichroism (PECD) is a forward-backward asymmetry in the photoemission from a non-racemic sample induced by circularly polarized light. PECD spectroscopy has potential analytical advantages for chiral discrimination over other chiroptical methods due to its increased sensitivity to the chiral potential of the molecule. The use of anions for PECD spectroscopy allows for mass-selectivity and provides a path to simple experimental schemes that employ table-top light sources. Evidence of PECD for anions is limited, and insight into the forces that govern PECD electron dynamics in photodetachment is absent. Here, we demonstrate a PECD effect in the photodetachment of mass-selected deprotonated 1-indanol anions. By utilizing velocity map imaging photoelectron spectroscopy with a tunable light source, we determine the energy-resolved PECD over a wide range of photon energies. The observed PECD reaches up to 11 %, similar to what has been measured for neutral species.

Molecular Chirality and Its Monitoring by Ultrafast X-ray Pulses

Major advances in X-ray sources including the development of circularly polarized and orbital angular momentum pulses make it possible to probe matter chirality at unprecedented energy regimes and with Ångström and femtosecond spatiotemporal resolutions. We survey the theory of stationary and time-resolved nonlinear chiral measurements that can be carried out in the X-ray regime using tabletop X-ray sources or large scale (XFEL, synchrotron) facilities. A variety of possible signals and their information content are discussed.

Ultrafast chirality: the road to efficient chiral measurements

Today we are witnessing the electric-dipole revolution in chiral measurements. Here we reflect on its lessons and outcomes, such as the perspective on chiral measurements using the complementary principles of "chiral reagent" and "chiral observer", the hierarchy of scalar, vectorial and tensorial enantio-sensitive observables, the new properties of the chiro-optical response in the ultrafast and non-linear domains, and the geometrical magnetism associated with the chiral response in photoionization. The electric-dipole revolution is a landmark event. It has opened routes to extremely efficient enantio-discrimination with a family of new methods. These methods are governed by the same principles but work in vastly different regimes - from microwaves to optical light; they address all molecular degrees of freedom - electronic, vibrational and rotational, and use flexible detection schemes, i.e. detecting photons or electrons, making them applicable to different chiral phases, from gases to liquids to amorphous solids. The electric-dipole revolution has also enabled enantio-sensitive manipulation of chiral molecules with light. This manipulation includes exciting and controlling ultrafast helical currents in vibronic states of chiral molecules, enantio-sensitive control of populations in electronic, vibronic and rotational molecular states, and opens the way to efficient enantio-separation and enantio-sensitive trapping of chiral molecules. The word "perspective" has two meanings: an "outlook" and a "point of view". In this perspective article, we have tried to cover both meanings.

Tomographic reconstruction techniques optimized for velocity-map imaging applications

Examples of extracting meaningful information from image projection data using tomographic reconstruction techniques can be found in many areas of science. Within the photochemical dynamics community, tomography allows for complete three-dimensional (3D) charged particle momentum distributions to be reconstructed following a photodissociation or photoionization event. This permits highly differential velocity- and angle-resolved measurements to be made simultaneously. However, the generalized tomographic reconstruction strategies typically adopted for use with photochemical imaging-based around the Fourier-slice theorem and filtered back-projection algorithms-are not optimized for these specific types of problems. Here, we discuss pre-existing alternative strategies-namely, the simultaneous iterative reconstruction technique and Hankel Transform Reconstruction (HTR)-and introduce them in the context of velocity-map imaging applications. We demonstrate the clear advantages they afford, and how they can perform considerably better than approaches commonly adopted at present. Most notably, with HTR we can set a bound on the minimum number of projections required to reliably reconstruct 3D photoproduct distributions. This bound is significantly lower than what is currently accepted and will help make tomographic imaging far more accessible and efficient for many experimentalists working in the field of photochemical dynamics.

Femtosecond photoelectron circular dichroism of chemical reactions

Understanding the chirality of molecular reaction pathways is essential for a broad range of fundamental and applied sciences. However, the current ability to probe chirality on the time scale of primary processes underlying chemical reactions remains very limited. Here, we demonstrate time-resolved photoelectron circular dichroism (TRPECD) with ultrashort circularly polarized vacuum-ultraviolet (VUV) pulses from a tabletop source. We demonstrate the capabilities of VUV-TRPECD by resolving the chirality changes in time during the photodissociation of atomic iodine from two chiral molecules. We identify several general key features of TRPECD, which include the ability to probe dynamical chirality along the complete photochemical reaction path, the sensitivity to the local chirality of the evolving scattering potential, and the influence of electron scattering off dissociating photofragments. Our results are interpreted by comparison with high-level ab-initio calculations of transient PECDs from molecular photoionization calculations. Our experimental and theoretical techniques define a general approach to femtochirality.

Photoelectron Circular Dichroism of Electrosprayed Gramicidin Anions

Many sophisticated approaches for analyzing properties of chiral matter have been developed in recent years. But in general, the available chiroptical methods are limited to either solvated or small gaseous molecules. Studying the chirality of large biopolymers in the gas phase, including aspects of the secondary structure, becomes accessible by combining the electrospray ionization technique with chiroptical detection protocols. Here, laser-induced photodetachment from gramicidin anions, a peptide consisting of 15 amino acids has been investigated. The angular distribution of photoelectrons is demonstrated to be sensitive to the substitution of protons by cesium ions, which is accompanied by a conformational change. The photoelectron circular dichroism (PECD) is -0.5% for bare gramicidin, whereas gramicidin with several Cs⁺ ions attached exhibits a PECD of +0.5%. The results are complemented and supported by ion mobility studies. The presented approach offers the prospect of studying chirality and the secondary structure of various biopolymers.

Enantiosensitive steering of free-induction decay

Chiral discrimination, a problem of vital importance, has recently become an emerging frontier in ultrafast physics, with remarkable progress achieved in multiphoton and strong-field regimes. Rydberg excitations, unavoidable in the strong-field regime and intentional for few-photon processes, arise in all these approaches. Here, we show how to harness this ubiquitous feature by introducing a new phenomenon, enantiosensitive free-induction decay, steered by a tricolor chiral field at a gentle intensity, structured in space and time. We demonstrate theoretically that an excited chiral molecule accumulates an enantiosensitive phase due to perturbative interactions with the tricolor chiral field, resulting in a spatial phase gradient steering the free-induction decay in opposite directions for opposite enantiomers. Our work introduces a general, extremely sensitive, all-optical enantiosensitive detection technique that avoids strong fields and takes full advantage of recent advances in structuring light.

A geometric approach to decoding molecular structure and dynamics from photoionization of isotropic samples

We propose a geometric approach to the description and analysis of photoelectron angular distributions resulting from isotropic samples in the case of few-photon ionization by electric fields of arbitrary polarization. This approach formulates the standard photoionization observables - the b_l,m expansion coefficients of the photoelectron angular distribution, in terms of geometrical properties of the vector field D⃑(k⃑) ≡ 〈k⃑|d⃑|0〉 describing the electronic transition from a bound state |0〉 into a scattering state |k⃑〉 - the photoionization transition dipole. Besides revealing selection rules for the enantio-sensitivity of b_l,m coefficients in multiphoton ionization, our approach yields very compact expressions for both chiral and achiral molecules revealing how the molecular rotational invariants couple to the rotational invariants of the setup defined by the electric field polarization and the arrangement of photoelectron detectors. We apply this approach to one-photon ionization and find that the forward-backward asymmetry parameter b_1,0, emerging exclusively in chiral molecules and encoded in the field B⃑(k⃑) ≡ iD⃑*(k⃑) × D⃑(k⃑), is sensitive only to the components of D⃑(k⃑) perpendicular to k⃑, while the regular asymmetry parameter b_2,0 emerging in chiral and achiral molecules is sensitive only to the component of D⃑(k⃑) parallel to k⃑. Next, we analyze resonantly enhanced two-photon ionization and show that b_0,0 and b_1,0 can be written in terms of an effectively stretched D⃑(k⃑), and how b_1,0 and b_3,0 can be used to probe B⃑(k⃑).

New opportunities for ultrafast and highly enantio-sensitive imaging of chiral nuclear dynamics enabled by synthetic chiral light

Synthetic chiral light [D. Ayuso et al., Nat. Photon., 2019, 13, 866-871] has opened up new opportunities for ultrafast and highly efficient imaging and control of chiral matter. Here we show that the giant enantio-sensitivity enabled by such light could be exploited to probe chiral nuclear rearrangements during chemical reactions in a highly enantio-sensitive manner. Using a state-of-the-art implementation of real-time time-dependent density functional theory, we explore how the nonlinear response of the prototypical chiral molecule H₂O₂ changes as a function of its dihedral angle, which defines its handedness. The macroscopic intensity emitted from randomly oriented molecules at even harmonic frequencies (of the fundamental) depends strongly on this nuclear coordinate. Because of the ultrafast nature of such nonlinear interactions, the direct mapping between the dissymmetry factor and the nuclear geometry provides a way to probe chiral nuclear dynamics at their natural time scales. Our work paves the way for ultrafast and highly efficient imaging of enantio-sensitive dynamics in more complex chiral systems, including biologically relevant molecules.

Generation and complete polarimetry of ultrashort circularly polarized extreme-ultraviolet pulses

The generation of ultrashort circularly polarized pulses in the extreme-ultraviolet spectral range has recently attracted considerable interest for applications in time-resolved circular-dichroism experiments. Here, we demonstrate a simple approach to generate near-circularly polarized femtosecond pulses in the vacuum-ultraviolet. The ellipticity of the generated light can be continuously tuned from linear to near-circular, as demonstrated by detailed polarimetry measurements. Combining optical polarimetry with photoelectron circular-dichroism (PECD) measurements, we demonstrate a novel approach to characterizing the polarization state of light in terms of all four Stokes parameters. For photon energies of 9.3 eV, we obtained S₃ = 0.96 ± 0.02 and a degree of polarization of 97±2%, i.e. the highest values reported from any harmonic-generation source so far. This source is directly applicable to circular-dichroism experiments, also enabling time-resolved PECD in the extreme-ultraviolet, a general approach to probing time-dependent chirality during chemical processes on (sub)-femtosecond time scales.

Photoelectron circular dichroism in angle-resolved photoemission from liquid fenchone

We present an experimental X-ray photoelectron circular dichroism (PECD) study of liquid fenchone at the C 1s edge. A novel setup to enable PECD measurements on a liquid microjet [Malerz et al., Rev. Sci. Instrum., 2022, 93, 015101] was used. For the C 1s line assigned to fenchone's carbonyl carbon, a non-vanishing asymmetry is found in the intensity of photoelectron spectra acquired under a fixed angle in the backward-scattering plane. This experiment paves the way towards an innovative probe of the chirality of organic/biological molecules in aqueous solution.

Elliptic dichroism in strong-field ionization of atoms subjected to tailored laser fields

The differential ionization rate for strong-field ionization by tailored laser fields of atomic systems averaged over the magnetic quantum number satisfies particular inversion and reflection symmetries. The symmetries of the elliptic-dichroism parameter, which is related to the change of sign of the ellipticity of the laser field, are considered in detail, with particular emphasis on high-order above-threshold ionization. The general results are illustrated by the examples of an elliptically polarized laser field and a bi-elliptical orthogonally polarized two-color (BEOTC) field. For the BEOTC field the differential ionization rate and the elliptic-dichroism parameter are investigated for the ω-2ω and ω-3ω field combinations and for various relative phases between the laser-field components. The inversion and reflection symmetries of the photoelectron momentum distribution in the polarization plane of the field depend on the parities of r and s in the rω--sω BEOTC field combination and on the relative phase between the field components. We suggest that, by analyzing the symmetry properties of the measured momentum distribution of the elliptic-dichroism parameter, one can identify the mechanism of strong-field ionization. If the rescattering mechanism is dominant one can use these distributions to obtain information about the atomic and molecular structure and dynamics.

Photoelectron elliptical dichroism spectroscopy of resonance-enhanced multiphoton ionization via the 3s, 3p and 3d Rydberg series in fenchone

The resonance-enhanced multiphoton ionization of chiral molecules by elliptically polarized laser pulses produces photoelectron angular distributions that are forward/backward asymmetric with respect to the light propagation axis. We investigate this photoelectron elliptical dichroism in the (2 + 1)-photon ionization of fenchone molecules, using wavelength tunable femtosecond UV pulses. We show that the photoelectron elliptical asymmetry is extremely sensitive to the intermediate resonant states involved in the ionization process, and enables electronic couplings to be revealed that do not show up so clearly when using circularly polarized light.

Strong chiral response in non-collinear high harmonic generation driven by purely electric-dipole interactions

High harmonic generation (HHG) records the ultrafast electronic response of matter to light, encoding key properties of the interrogated quantum system, such as chirality. The first implementation of chiral HHG [Cireasa et al, Nat. Phys.11, 654 (2015)10.1038/nphys3369] relied on the weak electronic response of a medium of randomly oriented chiral molecules to the magnetic component of an elliptically polarized wave, yielding relatively weak chiro-optical signals. Here we apply state-of-the-art semi-analytical modelling to show that elliptically polarized light can drive a strong chiral response in chiral molecules via purely electric-dipole interactions - the magnetic component of the wave does not participate at all. This strong chiro-optical response, which remains hidden in standard HHG experiments, can be mapped into the macroscopic far-field signal using a non-collinear configuration, creating new opportunities for imaging chiral matter and chiral dynamics on ultrafast time scales.

Fragmentation dynamics of doubly charged camphor molecule following C 1s Auger decay

The fragmentation dynamics of the gas-phase, doubly charged camphor molecule, formed by Auger decay following carbon 1s ionisation, using soft X-ray synchrotron radiation, is presented in this work. The technique of velocity map imaging combined with a photoelectron-photoion-photoion coincidence (VMI-PEPIPICO) is used for both electron energy and ion momentum (in-sequence) measurements. The experimental study is complemented by molecular dynamics simulation, performed with an NVT (moles, volume, and temperature) ensemble. Velocity Verlet algorithms were used for time integration at various internal energies. These simulations validate observed dissociation pathways. From these, we successfully deduce that the internal energy of the doubly charged molecular ion has a significant contribution to the fragmentation mechanism. Notably, a prominent signature of the internal energy was observed in the experimentally determined energies of the neutral fragment in these deferred charge separation pathways, entailing a more detailed theoretical study to uncover the exact dissociation dynamics.

Arbitrary image reinflation: A deep learning technique for recovering 3D photoproduct distributions from a single 2D projection

Many charged particle imaging measurements rely on the inverse Abel transform (or related methods) to reconstruct three-dimensional (3D) photoproduct distributions from a single two-dimensional (2D) projection image. This technique allows for both energy- and angle-resolved information to be recorded in a relatively inexpensive experimental setup, and its use is now widespread within the field of photochemical dynamics. There are restrictions, however, as cylindrical symmetry constraints on the overall form of the distribution mean that it can only be used with a limited range of laser polarization geometries. The more general problem of reconstructing arbitrary 3D distributions from a single 2D projection remains open. Here, we demonstrate how artificial neural networks can be used as a replacement for the inverse Abel transform and-more importantly-how they can be used to directly "reinflate" 2D projections into their original 3D distributions, even in cases where no cylindrical symmetry is present. This is subject to the simulation of appropriate training data based on known analytical expressions describing the general functional form of the overall anisotropy. Using both simulated and real experimental data, we show how our arbitrary image reinflation (AIR) neural network can be utilized for a range of different examples, potentially offering a simple and flexible alternative to more expensive and complicated 3D imaging techniques.

Detecting chirality in mixtures using nanosecond photoelectron circular dichroism

We report chirality detection of structural isomers in a gas phase mixture using nanosecond photoelectron circular dichroism (PECD). Combining pulsed molecular beams with high-resolution resonance enhanced multi-photon ionization (REMPI) allows specific isolated transitions belonging to distinct components in the mixture to be targeted.

Photoelectron Circular Dichroism as a Probe of Chiral Hydrocarbons

The sensitivity of Photoelectron Circular Dichroism (PECD) in the angular distribution of photoelectrons, a recent chiral technique, to detect chirality in pure hydrocarbons is investigated in a number of benchmark molecules. It is found that a very large chiral signal is expected, surpassing most current examples, giving a sure fingerprint of absolute configuration. On the other hand, the sensitivity to specific isomers or closely related molecules is relatively modest.

Coincident measurement of photo-ion circular dichroism and photo-electron circular dichroism on 1-Phenylethylamine

Here we report the coincident measurement of the PICD and PECD effect in 1-Phenylethylamine upon multiphoton ionisation. Photo-ion circular dichroism (PICD) and photo-electron circular dichroism (PECD) are both methods to...

Pulse length dependence of photoelectron circular dichroism

We investigated photoelectron circular dichroism (PECD) using pulses with various durations. From the experiment with fenchone, we found constancy of the PECD over a wide range of pulse durations and estimated lifetimes of internal conversions.

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.

Fundamentals and applications of molecular photoelectron spectroscopy – Festschrift for Ivan Powis

This themed collection includes a collection of articles on fundamentals and applications of molecular photoelectron spectroscopy.

Influence of Vibrational Excitation and Nuclear Dynamics in Multiphoton Photoelectron Circular Dichroism of Fenchone

We report photoelectron circular dichroism of S-(+)-fenchone enantiomers recorded with state-state vibrational level resolution using picosecond laser (2 + 1) resonance enhanced multiphoton ionization via 3s and 3p Rydberg intermediate states. The 3p state decays to the 3s state on a picosecond time scale so that, above the 3p Rydberg excitation threshold, ionization of vibrationally hot 3s states competes with direct 3p^-1 ionization. Complex vibronic dynamics of the 3p → 3s internal conversion weaken the Rydberg Δv = 0 propensity rule in both the 3p^-1 and 3s^-1 ionization channels. Large variations of the forward-backward chiral asymmetry factors are observed between the Δv = 0 and Δv > 0 vibrational transitions, including dramatic swings from up to ±17%. Such changes of sign indicate complete reversal of the preferred direction for photoelectron emission in the laboratory frame, associated with vibrational motion. These asymmetry switches easily exceed the amplitude and frequency of such vibrationally induced flips previously observed in single photon ionization.

Ultrafast relaxation investigated by photoelectron circular dichroism: an isomeric comparison of camphor and fenchone

We study the isomeric effects using time resolved photoelectron circular dichroism (TR-PECD). Using a (1 + 1') pump-probe ionisation scheme with photoelectrons collected by the velocity map imaging technique, we compare the relaxation dynamics from the 3s-Rydberg state in 1R,4R-(+)-camphor with the one in its chiral isomer, 1R,4S-(-)-fenchone [Comby et al., 2016, JPCL, 7, 4514]. Our measurements revealed a similar lifetime for both isomers. However, the circular dichroism in the photoelectron angular distribution decays exponentially in ∼730 fs from a +9% forward amplitude during the first hundreds of femtoseconds to reach an asymptotic -2% backward amplitude. This time-scale is drastically shorter than in fenchone. Our analysis allows us to evaluate the impact of the anisotropy of excitation; the relaxation dynamics, following photoexcitation by the linearly polarized pump, is then compared to that induced by a circularly polarized pump pulse (CPL). With such a CPL pump, we then retrieve time constants of our chiral observables similar to the ones recorded in fenchone. Quantum and classical simulations are developed and used to decipher the dependence of the PECD on the anisotropy of excitation and the spatial distribution of the 3s-Rydberg electron wavefunction. Our experimental investigations, supported by our simulations, suggest that varying the pump ellipticity enables us to reveal the breakdown of the Franck-Condon approximation.

Fourfold Differential Photoelectron Circular Dichroism

We report on a joint experimental and theoretical study of photoelectron circular dichroism (PECD) in methyloxirane. By detecting O 1s photoelectrons in coincidence with fragment ions, we deduce the molecule's orientation and photoelectron emission direction in the laboratory frame. Thereby, we retrieve a fourfold differential PECD clearly beyond 50%. This strong chiral asymmetry is reproduced by ab initio electronic structure calculations. Providing such a pronounced contrast makes PECD of fixed-in-space chiral molecules an even more sensitive tool for chiral recognition in the gas phase.

Site-specific interrogation of an ionic chiral fragment during photolysis using an X-ray free-electron laser

Short-wavelength free-electron lasers with their ultrashort pulses at high intensities have originated new approaches for tracking molecular dynamics from the vista of specific sites. X-ray pump X-ray probe schemes even allow to address individual atomic constituents with a 'trigger'-event that preludes the subsequent molecular dynamics while being able to selectively probe the evolving structure with a time-delayed second X-ray pulse. Here, we use a linearly polarized X-ray photon to trigger the photolysis of a prototypical chiral molecule, namely trifluoromethyloxirane (C₃H₃F₃O), at the fluorine K-edge at around 700 eV. The created fluorine-containing fragments are then probed by a second, circularly polarized X-ray pulse of higher photon energy in order to investigate the chemically shifted inner-shell electrons of the ionic mother-fragment for their stereochemical sensitivity. We experimentally demonstrate and theoretically support how two-color X-ray pump X-ray probe experiments with polarization control enable XFELs as tools for chiral recognition.

Photoelectron Circular Dichroism in the Photodetachment of Amino Acid Anions

The chirality of chemical compounds is of undisputed importance in science and technology. In particular with respect to pharmacological application most molecules of interest cannot be accessed by the powerful techniques developed in recent years for gas phase analytes. Here, we demonstrate that the combination of electrospray ionization (ESI) with the detection of photoelectron circular dichroism (PECD) provides access to chirality information applicable to molecular materials with negligible vapor pressure, for example, amino acids. To this end, glutamic acid and 3,4-dihydroxyphenylalanine (DOPA) have been electrosprayed into the source of a chirality spectrometer, where photodetachment is enforced and the PECD is detected. The technique can be expected to be conceptually applicable to all chemical systems with chirality based on molecular properties.

Photoelectron circular dichroism of O 1s-photoelectrons of uniaxially oriented trifluoromethyloxirane: energy dependence and sensitivity to molecular configuration

The photoelectron circular dichroism (PECD) of the O 1s-photoelectrons of trifluoromethyloxirane (TFMOx) is studied experimentally and theoretically for different photoelectron kinetic energies. The experiments were performed employing circularly polarized synchrotron radiation and coincident electron and fragment ion detection using cold target recoil ion momentum spectroscopy. The corresponding calculations were performed by means of the single center method within the relaxed-core Hartree-Fock approximation. We concentrate on the energy dependence of the differential PECD of uniaxially oriented TFMOx molecules, which is accessible through the employed coincident detection. We also compare the results for the differential PECD of TFMOx to those obtained for the equivalent fragmentation channel and similar photoelectron kinetic energy of methyloxirane (MOx), studied in our previous work. Thereby, we investigate the influence of the substitution of the methyl group by the trifluoromethyl group at the chiral center on the molecular chiral response. Finally, the presently obtained angular distribution parameters are compared to those available in the literature.