Outer- and inner-valence satellites of carbon dioxide: Electron momentum spectroscopy compared with symmetry-adapted-cluster configuration interaction general-Rcalculations

Reference Energies for Valence Ionizations and Satellite Transitions

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

Multi-electron excitation contributions towards primary and satellite states in the photoelectron spectrum

The computation of Dyson orbitals and corresponding ionization energies has been implemented within the Equation of Motion Coupled Cluster Singles, Doubles and Perturbative Triples (EOM-CC3) method. Coupled to an accurate...

Photon-electron coincidence experiments at synchrotron radiation facilities with arbitrary bunch modes

We report the adaptation of an electron-photon coincidence detection scheme to the multibunch hybrid mode of the synchrotron radiation source BESSY II (Helmholtz-Zentrum Berlin). Single-event-based data acquisition and evaluation, combined with the use of relative detection times between the coincident particles, enable the acquisition of proper coincidence signals from a quasi-continuous excitation pattern. The background signal produced by accidental coincidences in the time difference representation is modeled using the non-coincident electron and photon spectra. We validate the method by reproducing previously published results, which were obtained in the single bunch mode, and illustrate its usability for the multibunch hybrid mode by investigating the photoionization of CO₂ into CO₂ ⁺ B satellite states, followed by subsequent photon emission. The radiative lifetime obtained and the electron binding energy are in good agreement with earlier publications. We expect this method to be a useful tool to extend the versatility of coincident particle detection to arbitrary operation modes of synchrotron radiation facilities and other excitation sources without the need for additional experimental adjustments.

Restricted Correlation Space B-Spline ADC Approach to Molecular Ionization: Theory and Applications to Total Photoionization Cross-Sections

Herein is presented a new approach to the ab initio algebraic diagrammatic construction (ADC) schemes for the polarization propagator, which is explicitly designed to accurately and efficiently describe molecular ionization. The restricted correlation space (RCS) version of the ADC methods up to second order of perturbation theory is derived via the intermediate state representation (ISR) and implemented in the multicenter B-spline basis set for the electronic continuum. Remarkably a general close-coupling structure of the RCS-ADC many-electron wave function, connecting the N-particle to the ( N - 1)-particle ADC intermediate states, emerges naturally as a nontrivial result of the RCS ansatz. Moreover, the introduced RCS-ADC schemes prove to be particularly manageable from a computational point of view, overcoming the practical limitations of the conventional ADC approaches. The quality of the new RCS-ADC( n) approaches is verified by performing a series of total photoionization cross-section calculations on a test set of molecules. The excellent agreement of the results with existing accurate benchmarks demonstrates that the RCS versions of the ADC schemes are optimal and quantitatively accurate methods for studying multichannel molecular photoionization.

Electron correlation effects in the photoionization of CO and isoelectronic diatomic molecules

This paper investigates the first sigma satellite band, which is by far the most prominent, in the valence photoelectron spectra for a set of isoelectronic diatomic molecules: carbon monoxide, carbon monosulfide, carbon monoselenide, silicon monoxide and boron monofluoride. In particular, we analyze the effect of the electronic structure, with the change of the atomic pair along the row and column of the periodic table on the position of the satellite peak as well as on the related dynamical observables profiles. For this investigation, highly correlated calculations have been performed on the primary ionic states and the satellite band for all the molecules considered. Cross sections for the primary ionic states, calculated using Dyson orbitals, have been compared with those obtained with Hartree-Fock and Density Functional Theory to probe the impact of the correlation in the bound states on the photoionization observables. Limitations of a simple intensity borrowing mechanism clearly result from the analysis of the satellite state, characterized by different features with respect to the relevant primary states.

Development of an electron momentum spectrometer for time-resolved experiments employing nanosecond pulsed electron beam

The low count rate of (e, 2e) electron momentum spectroscopy (EMS) has long been a major limitation of its application to the investigation of molecular dynamics. Here we report a new EMS apparatus developed for time-resolved experiments in the nanosecond time scale, in which a double toroidal energy analyzer is utilized to improve the sensitivity of the spectrometer and a nanosecond pulsed electron gun with a repetition rate of 10 kHz is used to obtain an average beam current up to nA. Meanwhile, a picosecond ultraviolet laser with a repetition rate of 5 kHz is introduced to pump the sample target. The time zero is determined by photoionizing the target using a pump laser and monitoring the change of the electron beam current with time delay between the laser pulse and electron pulse, which is influenced by the plasma induced by the photoionization. The performance of the spectrometer is demonstrated by the EMS measurement on argon using a pulsed electron beam, illustrating the potential abilities of the apparatus for investigating the molecular dynamics in excited states when employing the pump-probe scheme.

Electron Momentum Spectroscopy Investigation of Molecular Conformations of Ethanol Considering Vibrational Effects

The interpretation of experimental electron momentum distributions (EMDs) of ethanol, one of the simplest molecules having conformers, has confused researchers for years. High-level calculations of Dyson orbital EMDs by thermally averaging the gauche and trans conformers as well as molecular dynamical simulations failed to quantitatively reproduce the experiments for some of the outer valence orbitals. In this work, the valence shell electron binding energy spectrum and EMDs of ethanol are revisited by the high-sensitivity electron momentum spectrometer employing symmetric noncoplanar geometry at an incident energy of 1200 eV plus binding energy, together with a detailed analysis of the influence of vibrational motions on the EMDs for the two conformers employing a harmonic analytical quantum mechanical (HAQM) approach by taking into account all of the vibrational modes. The significant discrepancies between theories and experiments in previous works have now been interpreted quantitatively, indicating that the vibrational effect plays a significant role in reproducing the experimental results, not only through the low-frequency OH and CH₃ torsion modes but also through other high-frequency ones. Rational explanation of experimental momentum profiles provides solid evidence that the trans conformer is slightly more stable than the gauche conformer, in accordance with thermodynamic predictions and other experiments. The case of ethanol demonstrates the significance of considering vibrational effects when performing a conformational study on flexible molecules using electron momentum spectroscopy.

Imaging molecular geometry with electron momentum spectroscopy

Electron momentum spectroscopy is a unique tool for imaging orbital-specific electron density of molecule in momentum space. However, the molecular geometry information is usually veiled due to the single-centered character of momentum space wavefunction of molecular orbital (MO). Here we demonstrate the retrieval of interatomic distances from the multicenter interference effect revealed in the ratios of electron momentum profiles between two MOs with symmetric and anti-symmetric characters. A very sensitive dependence of the oscillation period on interatomic distance is observed, which is used to determine F-F distance in CF₄ and O-O distance in CO₂ with sub-Ångström precision. Thus, using one spectrometer, and in one measurement, the electron density distributions of MOs and the molecular geometry information can be obtained simultaneously. Our approach provides a new robust tool for imaging molecules with high precision and has potential to apply to ultrafast imaging of molecular dynamics if combined with ultrashort electron pulses in the future.

Yields and Time-of-Flight Spectra of Neutral High-Rydberg Fragments at the K Edges of the CO2 Molecule

We have studied the production of neutral fragments in high-Rydberg (HR) states at the C 1s and O 1s edges of the CO2 molecule by performing two kinds of experiments. First, the yields of neutral HR fragments were measured indirectly by ionizing such fragments in a static electric field and by collecting resulting singly charged positive ions as a function of the photon energy. Such measurements reveal not only excitations below the core ionization thresholds but also thresholds for single core-hole and shakeup photoionization. Second, we obtained the mass spectra of neutral HR fragments at selected photon energies by exploiting pulsed field ionization; they show atomic fragments C(HR) and O(HR). We discuss dissociation pathways leading to the production of neutral HR fragments in core excitation and ionization of CO2.

From double-slit interference to structural information in simple hydrocarbons

Interferences in coherent emission of photoelectrons from two equivalent atomic centers in a molecule are the microscopic analogies of the celebrated Young's double-slit experiment. By considering inner-valence shell ionization in the series of simple hydrocarbons C2H2, C2H4, and C2H6, we show that double-slit interference is widespread and has built-in quantitative information on geometry, orbital composition, and many-body effects. A theoretical and experimental study is presented over the photon energy range of 70-700 eV. A strong dependence of the oscillation period on the C-C distance is observed, which can be used to determine bond lengths between selected pairs of equivalent atoms with an accuracy of at least 0.01 Å. Furthermore, we show that the observed oscillations are directly informative of the nature and atomic composition of the inner-valence molecular orbitals and that observed ratios are quantitative measures of elusive many-body effects. The technique and analysis can be immediately extended to a large class of compounds.