Photoelectron Angular Distributions Research Articles

Fourier-Hankel-Abel Nyquist-limited tomography: A spherical harmonic basis function approach to tomographic velocity-map image reconstruction.

A new method for the fully generalized reconstruction of three-dimensional (3D) photoproduct distributions from velocity-map imaging (VMI) projection data is presented. This approach, dubbed Fourier-Hankel-Abel Nyquist-limited TOMography (FHANTOM), builds on recent previous work in tomographic image reconstruction [C. Sparling and D. Townsend, J. Chem. Phys. 157, 114201 (2022)] and takes advantage of the fact that the distributions produced in typical VMI experiments can be simply described as a sum over a small number of spherical harmonic functions. Knowing the solution is constrained in this way dramatically simplifies the reconstruction process and leads to a considerable reduction in the number of projections required for robust tomographic analysis. Our new method significantly extends basis set expansion approaches previously developed for the reconstruction of photoproduct distributions possessing an axis of cylindrical symmetry. FHANTOM, however, can be applied generally to any distribution-cylindrically symmetric or otherwise-that can be suitably described by an expansion in spherical harmonics. Using both simulated and real experimental data, this new approach is tested and benchmarked against other tomographic reconstruction strategies. In particular, the reconstruction of photoelectron angular distributions recorded in a strong-field ionization regime-marked by their extensive expansion in terms of spherical harmonics-serves as a key test of the FHANTOM methodology. With the increasing use of exotic optical polarization geometries in photoionization experiments, it is anticipated that FHANTOM and related reconstruction techniques will provide an easily accessible and relatively low-cost alternative to more advanced 3D-VMI spectrometers.

Wave packet dynamics and control in excited states of molecular nitrogen.

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N2. Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ∼ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.

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.

Resonant Auger decay of dissociating CH3I near the I 4d threshold.

Resonant Auger processes provide a unique perspective on electronic interactions and excited vibrational and electronic states of molecular ions. Here, new data are presented on the resonant Auger decay of excited CH3I in the region just below the I 4d-1 ionization threshold. The resonances include the Rydberg series converging to the five spin-orbit and ligand-field split CH3I (I 4d-1) thresholds, as well as resonances corresponding to excitation from the I 4d5/2,3/2 orbitals into the σ* lowest unoccupied molecular orbital. This study focuses on participator decay that populates the lowest lying states of CH3I+, in particular, the X̃2E3/2 and 2E1/2 states, and on spectator decay that populates the lowest-lying (CH3I2+)σ* states of CH3I+. The CH3I (I 4d-1)σ* resonances are broad, and dissociation to CH3 + I competes with the autoionization of the core-excited states. Auger decay as the molecule dissociates produces a photoelectron spectrum with a long progression (up to v3+ ∼ 25) in the C-I stretching mode of the X̃2E3/2 and 2E1/2 states, providing insights into the shape of the dissociative core-excited surface. The observed spectator decay processes indicate that CH3I+ is formed on the repulsive wall of the lower-lying (CH3I2+)σ* potentials, and the photon-energy dependence of the processes provides insights into the relative slopes of the (4d-1)σ* and (CH3I2+)σ* potential surfaces. Data are also presented for the spectator decay of higher lying CH3I (I 4d-1)nl Rydberg resonances. Photoelectron angular distributions for the resonant Auger processes provide additional information that helps distinguish these processes from the direct ionization signal.

Tracing Photoinduced Hydrogen Migration in Alcohol Dications from Time-Resolved Molecular-Frame Photoelectron Angular Distributions.

The recent implementation of attosecond and few-femtosecond X-ray pump/X-ray probe schemes in large-scale free-electron laser facilities has opened the way to visualize fast nuclear dynamics in molecules with unprecedented temporal and spatial resolution. Here, we present the results of theoretical calculations showing how polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) can be used to visualize the dynamics of hydrogen migration in methanol, ethanol, propanol, and isopropyl alcohol dications generated by X-ray irradiation of the corresponding neutral species. We show that changes in the PA-MFPADs with the pump-probe delay as a result of intramolecular photoelectron diffraction carry information on the dynamics of hydrogen migration in real space. Although visualization of this dynamics is more straightforward in the smaller systems, methanol and ethanol, one can still recognize the signature of that motion in propanol and isopropyl alcohol and assign a tentative path to it. A possible pathway for a corresponding experiment requires an angularly resolved detection of photoelectrons in coincidence with molecular fragment ions used to define a molecular frame of reference. Such studies have become, in principle, possible since the first XFELs with sufficiently high repetition rates have emerged. To further support our findings, we provide experimental evidence of H migration in ethanol-OD from ion-ion coincidence measurements performed with synchrotron radiation.

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.

Photoionization cross sections and photoelectron angular distributions of molecules with XCHEM-2.0

The XCHEM code was introduced in 2017 [1] to provide an accurate description of electron correlation and exchange in the electronic continuum of molecules at the same level as complete or restricted active-space self-consistent field (CASSCF or RASSCF) methods. This has allowed for an accurate description of molecular photoionization in the region of Feshbach resonances, shake up processes in which ionization is accompanied by excitation of one or several of the remaining electrons, and interchannel couplings. The success of XCHEM for small molecules has led us to improve its performance in several aspects, which now allows for the description of resonant molecular photoionization in larger systems. In addition, we have incorporated the possibility to calculate photoelectron angular distributions in the laboratory and molecular frames, which are essential to interpret angularly resolved photoionization experiments. Here we show its performance in the N2 and pyrazine molecules. The new version of the code, XCHEM-2.0, is freely available at https://gitlab.com/xchem/xchem_public. Program summaryProgram Title: XCHEM-2.0CPC Library link to program files:https://doi.org/10.17632/t8tbk9gdt2.1Developer's repository link:https://gitlab.com/xchem/xchem_public/-/archive/2.0.0/xchem_public-2.0.0.tar.gzLicensing provisions: LGPLProgramming language: Fortran, pythonNature of problem: Understanding photoionization of molecules is a recurrent goal in Atomic, Molecular and Optical physics, even more nowadays with the advent of XUV and X-ray high-harmonic generation sources and free electron lasers. Photoionization can be employed to induce electron dynamics in molecules, e.g., by using ultrashort XUV or X-ray pulses, or as a probe of these dynamics by recording time-resolved photoelectron spectra. At low photoelectron energies, photoionization may result from various competing processes, such as direct ionization, autoionization of Feshbach and shape resonances, shake up, etc., each of these leaving its trace in the measured spectra. So, interpretation of these spectra can be a difficult task and theoretical simulations are often required to separate the different contributions. However, a method able to do so must be able to describe electron correlation in the electronic continuum beyond the Hartree-Fock (HF) and configuration interaction singles (CIS) approximations. XCHEM-2.0 has been designed to account for all these processes by providing an accurate description of electron correlation in the ionization continuum of molecules.Solution method: XCHEM-2.0 employs a close coupling formalism to describe the electronic continuum of molecules at the level of multiference configuration interaction (MRCI) methods in combination with a hybrid Gaussian-Bspline basis set (the so-called GABs basis). In particular, it makes use of a restricted active space self-consistent field (RASSCF) approximation to evaluate the bound electronic states of the remaining molecular cation using localized Gaussian functions. These localized Gaussians are then supplemented with a single centered Gaussian expansion to allow the electron to leave the nuclear environment. Finally, the basis set includes a set of B-spline functions, centered at the same position as the single-centered Gaussians, which reach the asymptotic region. Thanks to the last B-spline function, which does not vanish at the box boundary, XCHEM-2.0 can determine continuum states fulfilling any required asymptotic behavior. The present version of the code improves on the original version by incorporating a more efficient augmentation procedure to build Ne-electron configurations from (Ne−1) ones, reducing the space to store data, providing a more efficient removal of linear dependencies resulting from the over-completeness of the polycentric+GABS basis and a more efficient solution of the scattering equations, and including new routines to calculate photoelectron angular distributions in the laboratory and molecular frames.Additional comments including restrictions and unusual features: The proposed method focuses on RASSCF methodology, so part of electron correlation is still not included. Also, one- and two electron integrals involving exclusively Gaussian functions are done using a modified version of the OpenMOLCAS software, so the installation of this code is also required and limitation associated with the latter is applicable. The code is limited to include a few ionization channels (around 20) with medium angular momentum (limited to ℓ = 15 as in OpenMOLCAS).

Theoretical study of time-resolved photoelectron circular dichroism in the photodissociation of a chiral molecule.

Photoelectron circular dichroism (PECD), the forward-backward asymmetry of the photoelectron angular distribution when ionizing randomly oriented chiral molecules with circularly polarized light, is an established method to investigate chiral properties of molecules in their electronic ground state. Here, we develop a computational strategy for predicting time-resolved PECD (TRPECD) of chemical reactions and demonstrate the method on the photodissociation of 1-iodo-2-methylbutane. Our approach combines multi-configurational quantum-chemical calculations of the relevant potential-energy surfaces of the neutral and singly ionized molecule with ab initio molecular-dynamics (AIMD) calculations. The PECD parameters along the AIMD trajectories are calculated with the aid of electron-molecule scattering calculations based on the Schwinger variational principle implemented in ePolyScat. Our calculations have been performed for two probe wavelengths (133 and 160 nm) accessible through low-order harmonic generation in gases. Our results show that the TRPECD is a highly sensitive probe of photochemical reaction dynamics. Most interestingly, the TRPECD is found to change sign multiple times along the photodissociation coordinate, in agreement with recent experiments on CHBrFI [Svoboda et al., "Femtosecond photoelectron circular dichroism of chemical reactions," Sci. Adv. 8, eabq2811 (2022)]. The computational protocol introduced in the present work is general and readily applicable to other chiral photochemical processes.

Quadrupole Effects in the Photoionisation of Sodium 3s in the Vicinity of the Dipole Cooper Minimum

A procedure to obtain relativistic expressions for photoionisation angular distribution parameters using the helicity formulation is discussed for open-shell atoms. Electric dipole and quadrupole transition matrix elements were considered in the present work, to study the photoionisation dynamics of the 3s electron of the sodium atom in the vicinity of the dipole Cooper minimum. We studied dipole–quadrupole interference effects on the photoelectron angular distribution in the region of the dipole Cooper minimum. Interference with quadrupole transitions was found to alter the photoelectron angular distribution, even at rather low photon energies. The initial ground and final ionised state discrete wavefunctions of the atom were obtained in the present work using GRASP, and we employed RATIP with discrete wavefunctions, to construct continuum wavefunctions and to calculate transition amplitudes, total cross-sections and angular distribution asymmetry parameters.

Coordination-induced bond weakening in NiC3: An experimental and theoretical investigation.

Mass-selected photoelectron velocity-map imaging spectroscopy in conjunction with the density functional theory calculations was employed to investigate the geometrical and chemical bonding properties of NiC3-/0. Both the photoelectron spectrum and photoelectron angular distribution were measured from the spectra, yielding useful geometrical and electronic information about NiC3-/0. The complementary theoretical calculations suggest that the linear and fan-like structures were both populated experimentally in the cluster beam. Further comparative study on the synergistic donor-acceptor interactions in both isomers revealed the side-on coordination-induced bond weakening in the fan-like isomer as compared to the linear isomer. These findings will shed light on the structure-dependent reactivity of transition metal carbides.

Molecular-frame photoelectron angular distributions during double core-hole generation in and molecules

Angular distributions of photoelectrons emitted upon double core-hole (DCH) generation in nitrogen and oxygen molecules are studied theoretically in the frame of a molecular reference. The respective electronic structure calculations are performed by the single center method for photoelectron kinetic energies up to 40 eV in the relaxed-core Hartree–Fock approximation. The molecular frame photoelectron angular distributions are computed for single-site and two-site DCH creation processes and further analyzed for different orientations of the molecular axis with respect to the electric field vector of linearly polarized incident light and for localized or delocalized emitting atomic site scenarios. The present theoretical results provide reliable predictions for future experiments with high-repetition free-electron lasers.

Photoelectron Velocity Map Imaging Spectroscopy of the Beryllium Trimer and Tetramer.

Computational studies of small beryllium clusters (BeN) predict dramatic, nonmonotonic changes in the bonding mechanisms and per-atom cohesion energies with increasing N. To date, experimental tests of these quantum chemistry models are lacking for all but the Be2 molecule. In the present study, we report spectroscopic data for Be3 and Be4 obtained via anion photodetachment spectroscopy. The trimer is predicted to have D3h symmetric equilibrium structures for both the neutral molecule and the anion. Photodetachment spectra reveal transitions that originate from the X2A2″ ground state and the 12A1' electronically excited state. The state symmetries were assigned on the basis of anisotropic photoelectron angular distributions. The neutral and anionic forms of Be4 are predicted to be tetrahedral. Franck-Condon diagonal photodetachment was observed with a photoelectron angular distribution consistent with the expected Be4-X2A1 → Be4X1A1 transition. The electron affinities of Be3 and Be4 were determined to be 11363 ± 60 and 13052 ± 50 cm-1, respectively.

Electron impact resonances of uracil in an aqueous environment from anion photoelectron imaging

The effect that solvation has on electron attachment to uracil, U, was studied by probing the electronic resonances of the uracil radical anion, U−, in gas-phase water clusters, U−(H2O) n , using photoelectron imaging across a range of photon energies. Specifically, the π 3* shape resonance was probed in detail and the spectral signatures following excitation to this resonance are considered. Several new methods for analysis are provided to capture the different actions of the resonance on the photoelectron emission, which in turn provide insight into the location of the π 3* resonance and its subsequent dynamics. The effect of solvation on each action observed through the photoelectron emission is studied for n ⩽ 10. We find that the actions—be they related to statistical emission, prompt autodetachment, or the photoelectron angular distributions—all become less sensitive as the cluster size increases, suggesting that their use for very large clusters may be limited. Additionally, we consider the correlation between electron detachment from the anion, as probed in the experiments, and electron attachment to the neutral. Specifically, they are linked through the reorganisation energy in a linear response picture and we show how the cluster approach developed here allows one to decompose the total reorganisation energy into intramolecular (associated with the anion to neutral geometry change in U) and intermolecular (associated with the change in hydration sphere) contributions. For U in a bulk aqueous environment, we find that the total reorganisation energy, λ ∼ 1.2 eV, shows equal contributions from both intra- and intermolecular changes.

Angular distribution of photoelectrons generated in atomic ionization by twisted radiation

Angular distribution of photoelectrons generated in atomic ionization by twisted radiation

The photoelectron angular distributions of H atoms in two-color linearly polarized laser fields

By calculating the photoelectron angular distributions of H atoms driven by two-color linear polarization laser pulses, we investigate the influence of ionization channels on the photoelectron angular distributions. For a fixed final kinetic energy of photoelectron E k = qω1, qω1 = lω1 + mω2, in which l is the number of photons absorbed from laser with a wavelength of λ1, m is the number of photons absorbed from laser with a wavelength of λ2, and the combination ( l, m) is an ionization channel. We find that the photoelectron angular distributions are obviously dependent on ionization channels. For a given ionization channel, the low-order phased Bessel function, which corresponds to the smaller number of photon absorbed, has the main contribution to the photoelectron angular distributions. We also find that the relative direction of the polarization vector of two laser pulses has significant influence on the photoelectron angular distributions. By changing the relative direction between two polarization vectors, we can control the emission direction of photoelectrons.

Identifying photoelectron releasing order in strong-field dissociative ionization of H2.

Driven by intense laser fields, the outgoing photoelectrons in molecules possess a quiver motion, resulting in the rise of the effective ionization potential. The coupling of the field-dressed ionization potential with abundant molecular dynamics complicates the laser-molecule interactions. Here, we demonstrate an approach to resolve photoelectron releasing order in the dissociative and non-dissociative channels of multiphoton ionization driven by an orthogonally polarized two-color femtosecond laser pulse. The photoelectron kinetic energy releases and the regular nodes in the photoelectron angular distributions due to the participation of different continuum partial waves allow us to deduce the field-dressed ionization potential of various channels. It returns the ponderomotive energy experienced by the outgoing electron and reveals the corresponding photoionization instants within the laser pulse. Our results provide a route to explore the complex strong-field ionization dynamics of molecules using two-dimensional photoelectron momentum spectroscopy.

Ultrastable, high-repetition-rate attosecond beamline for time-resolved XUV–IR coincidence spectroscopy

The implementation of attosecond photoelectron–photoion coincidence spectroscopy for the investigation of atomic and molecular dynamics calls for a high-repetition-rate driving source combined with experimental setups characterized by excellent stability for data acquisition over time intervals ranging from a few hours up to a few days. This requirement is crucial for the investigation of processes characterized by low cross sections and for the characterization of fully differential photoelectron(s) and photoion(s) angular and energy distributions. We demonstrate that the implementation of industrial-grade lasers, combined with a careful design of the delay line implemented in the pump–probe setup, allows one to reach ultrastable experimental conditions leading to an error in the estimation of the time delays of only 12 as over an acquisition time of 6.5 h. This result opens up new possibilities for the investigation of attosecond dynamics in simple quantum systems.

Is Pseudohalide CN− a Real Halide? A General Symmetry Consideration

Recently, in light of the significant attention devoted to pseudohalide CN− and cyano radical CN physico-chemical property studies and superhalide behavior exploration in CN−-ligated metal compounds, the photoelectron angular distribution nature of pseudohalide CN− has been directly demonstrated via the photoelectron velocity map imaging technique to be comparable to Cl−. For the halide Cl−, photoelectrons were observed at 266 nm (4.66 eV) to peak, perpendicular to the laser polarization associated with the detachment of p-orbital symmetry. For the analogous pseudohalide CN−, photoelectrons were present at a peak in laser polarization at 266 nm, which can be explained as detachment from mainly atomic s-like orbital symmetry. Although both are often regarded as having the same high electron affinity and similarly strong chemical bonding capabilities to stabilize complexes, their photoelectron angular distributions are distinctly different, which indicates their intrinsically different electronic–structure symmetry (HOMO nature). The approach based on symmetry consideration in this work could be utilized to explain the photoelectron angular distributions of pseudohalide and classic halide ligands via the advanced photoelectron velocity map imaging tool.

Autoionization from the plasmon resonance in isolated 1-cyanonaphthalene.

Polycyclic aromatic hydrocarbons have widely been conjectured to be ubiquitous in space, as supported by the recent discovery of two isomers of cyanonaphthalene, indene, and 2-cyanoindene in the Taurus molecular cloud-1 using radioastronomy. Here, the photoionization dynamics of 1-cyanonaphthalene (1-CNN) are investigated using synchrotron radiation over the hν = 9.0-19.5eV range, revealing that prompt autoionization from the plasmon resonance dominates the photophysics for hν = 11.5-16.0eV. Minimal photo-induced dissociation, whether originating from an excited state impulsive bond rupture or through internal conversion followed by a statistical bond cleavage process, occurs over the microsecond timescale (as limited by the experimental setup). The direct photoionization cross section and photoelectron angular distributions are simulated using an ezDyson model combining Dyson orbitals with Coulomb wave photoejection. When considering these data in conjunction with recent radiative cooling measurements on 1-CNN+, which showed that cations formed with up to 5eV of internal energy efficiently stabilize through recurrent fluorescence, we conclude that the organic backbone of 1-CNN is resilient to photodestruction by VUV and soft XUV radiation. These dynamics may prove to be a common feature for the survival of small polycyclic aromatic hydrocarbons in space, provided that the cations have a suitable electronic structure to support recurrent fluorescence.

Attosecond interferometry of neon atom: photoelectron angular distributions

In the paper we present the angular distributions of photoelectrons in ionization of neon atom by a field of several multiple frequencies. The considered setup is refered to the RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) spectroscopy under condition that the field frequencies are selected in such a way that resonant transitions through discrete states play an important role. The role of the phase of the seed infrared field on the angular distributions of photoemission is analyzed. A significant difference in the anisotropy parameters at the near-threshold sideband caused by transitions through discrete states is shown. Two methods are compared: numerical solution of rate equations with continuum discretization and third-order perturbation theory.