Photoelectron Angular Distributions Research Articles

Time-resolved photoelectron diffraction imaging of methanol photodissociation involving molecular hydrogen ejection.

Imaging ultrafast atomic and molecular hydrogen motion with femtosecond time resolution is a challenge for ultrafast spectroscopy due to the low mass and small scattering cross section of the moving neutral hydrogen atoms and molecules. Here, we propose time- and momentum-resolved photoelectron diffraction (TMR-PED) as a way to overcome limitations of existing methodologies and illustrate its performance using a prototype molecular dissociation process involving the sequential ejection of a neutral hydrogen molecule and a proton from the methanol dication. By combining state-of-the-art molecular dynamics and electron-scattering methods, we show that TMR-PED allows for direct imaging of hydrogen atoms in action. More specifically, the fingerprint of hydrogen dynamics reflects the time evolution of polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) as would be recorded in X-ray pump/X-ray probe experiments with few-femtosecond resolution. We present the results of two precursor experiments that support the feasibility of this approach.

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).

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.

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.

Time-stretched multi-hit 3D velocity map imaging of photoelectrons.

The 2D photoelectron velocity map imaging (VMI) technique is commonly employed in gas-phase molecular spectroscopy and dynamics investigations due to its ability to efficiently extract photoelectron spectra and angular distributions in a single experiment. However, the standard technique is limited to specific light-source polarization geometries. This has led to significant interest in the development of 3D VMI techniques, which are capable of measuring individual electron positions and arrival times, obtaining the full 3D distribution without the need for inversion, forward-convolution, or tomographic reconstruction approaches. Here, we present and demonstrate a novel time-stretched, 13-lens 3D VMI photoelectron spectrometer, which has sub-camera-pixel spatial resolution and 210ps (σ) time-of-flight (TOF) resolution (currently limited by trigger jitter). We employ a kHz CMOS camera to image a standard 40mm diameter microchannel plate (MCP)/phosphor anode detector (providing x and y positions), combined with a digitizer pick-off from the MCP anode to obtain the electron TOF. We present a detailed analysis of time-space correlation under data acquisition conditions which generate multiple electrons per laser shot, and demonstrate a major advantage of this time-stretched 3D VMI approach: that the greater spread in electron TOFs permits for an accurate time- and position-stamping of up to six electrons per laser shot at a 1kHz repetition rate.

Orientation-angle-resolved photoelectron angular distribution in dissociative ionization of methanol induced by an intense ultraviolet laser pulse

We investigate dissociative ionization of methanol, $\mathrm{C}{\mathrm{H}}_{3}\mathrm{OH}\ensuremath{\rightarrow}{\mathrm{CH}}_{3}{}^{+}+\mathrm{OH}+{e}^{\ensuremath{-}}$, in a linearly polarized intense ultraviolet laser field (400 nm, 67 fs, $3.1\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}$) by photoelectron-photoion coincidence three-dimensional momentum imaging. The photoelectron angular distributions (PADs) are recorded as a function of the orientation angle between the molecular C-O bond axis and the laser polarization direction. Photoelectrons are emitted dominantly along the laser polarization direction when ${\mathrm{CH}}_{3}{\mathrm{OH}}^{+}$ is produced in the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}$ state via the four-photon absorption. By contrast, the photoelectron emission becomes prominent along the direction perpendicular to the laser polarization direction when ${\mathrm{CH}}_{3}{\mathrm{OH}}^{+}$ is produced in the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}$ state via the five-photon absorption. The orientation-angle-resolved PADs are expanded in terms of spherical harmonics in the laboratory frame, and then the anisotropy of the PADs varying as a function of the orientation angle of the C-O bond axis with respect to the laser polarization direction is examined quantitatively. We discuss how the shape of the molecular orbital from which an electron is emitted is reflected in the recorded PADs.

Probing Superatomic Orbitals of Sc-Doped and Undoped Silver Cluster Anions via Photoelectron Angular Anisotropy.

Valence s electrons in alkali- or coinage-metal clusters are conceived to delocalize over the metal frameworks. The electrons occupy so-called superatomic orbitals (SAOs, i.e., 1S, 1P, 1D, 2S, 1F, ...), which provide an essential picture for understanding the size-dependent, unique properties of these metal clusters. While such electronic shells are unambiguously identified in their photoelectron spectra and supported by electronic structure calculations, characterization of SAOs in heteroatom-doped metal clusters has remained elusive as the doping significantly affects its energy levels and even alters the ordering of SAOs. Here, we present a photoelectron imaging study to explore SAOs formed in Sc-doped and undoped silver cluster anions, AgNSc- (N = 15, 16) and AgN- (N = 18, 19). Photoelectron angular distributions from their outermost SAOs are clearly visualized, whose characters are analyzed with the aid of density functional theory calculations. The present methodology enables us to explore not only the quantized energy levels but also the spatial distributions of SAOs formed in various metal cluster anions.

Ångstrom-Depth Resolution with Chemical Specificity at the Liquid-Vapor Interface.

The determination of depth profiles across interfaces is of primary importance in many scientific and technological areas. Photoemission spectroscopy is in principle well suited for this purpose, yet a quantitative implementation for investigations of liquid-vapor interfaces is hindered by the lack of understanding of electron-scattering processes in liquids. Previous studies have shown, however, that core-level photoelectron angular distributions (PADs) are altered by depth-dependent elastic electron scattering and can, thus, reveal information on the depth distribution of species across the interface. Here, we explore this concept further and show that the experimental anisotropy parameter characterizing the PAD scales linearly with the average distance of atoms along the surface normal obtained by molecular dynamics simulations. This behavior can be accounted for in the low-collision-number regime. We also show that results for different atomic species can be compared on the same length scale. We demonstrate that atoms separated by about 1Å along the surface normal can be clearly distinguished with this method, achieving excellent depth resolution.