Single photon K(-2) and K(-1)K(-1) double core ionization in C(2)H(2n) (n=1-3), CO, and N(2) as a potential new tool for chemical analysis

Transient responses of double core-holes generation in all-attosecond pump-probe spectroscopy

Double core-holes (DCHs) show remarkable and sensitive effects for understanding electron correlations and coherence. With advanced modulation of x-ray free-electron laser (XFEL) facility, we propose the forthcoming all-attosecond XFEL pump-probe spectroscopy can decipher the hidden photon-initiated dynamics of DCHs. The benchmark case of neon is investigated, and norm-nonconserving Monte-Carlo wavefunction method simulates non-Hermitian dynamics among vast states, which shows superiority in efficiency and reliability. In our scheme, population transfer to DCHs is sequentially irradiated by pump and probe laser. By varying time delay, Stark shifts and quantum path interference of resonant lines sensitively emerge at specific interval of two pulses. These ubiquitous multi-channel effects are also observed in phase-fluctuating pulses, derived from extra phases of impulsive Raman processes by pump laser. Non-perturbation absorption/emission verifies the uniquely interchangeable role of two pules in higher intensity. Our results reveal sensitive and robust responses on pulse parameters, which show potential capacity for XFEL attosecond pulse diagnosis and further attosecond-timescale chemical analysis.

Unraveling the variational breakdown of core valence separation calculations: Diagnostic and cure to the over relaxation error of double core hole states

The core valence separation (CVS) approximation is the most employed strategy to prevent the variational collapse of standard wave function optimization when attempting to compute electronic states bearing one or more electronic vacancies in core orbitals. Here, we explore the spurious consequences of this approximation on the properties of the computed core hole states. We especially focus on the less studied case of double core hole (DCH) states, whose spectroscopic interest has recently been rapidly growing. We show that the CVS error leads to a systematic underestimation of DCH energies, a property in stark contrast with the case of single core hole states. We highlight that the CVS error can then be interpreted as an over relaxation effect and design a new correction strategy adapted to these specificities.

Formation and relaxation of K−2 and K−2V double-core-hole states in n-butane

Using a magnetic bottle multi-electron time-of-flight spectrometer in combination with synchrotron radiation, double-core-hole pre-edge and continuum states involving the K-shell of the carbon atoms in n-butane ( n-C4H10) have been identified, where the ejected core electron(s) and the emitted Auger electrons from the decay of such states have been detected in coincidence. An assignment of the main observed spectral features is based on the results of multi-configurational self-consistent field (MCSCF) calculations for the excitation energies and static exchange (STEX) calculations for energies and intensities. MCSCF results have been analyzed in terms of static and dynamic electron relaxation as well as electron correlation contributions to double-core-hole state ionization potentials. The analysis of applicability of the STEX method, which implements the one-particle picture toward the complete basis set limit, is motivated by the fact that it scales well toward large species. We find that combining the MCSCF and STEX techniques is a viable approach to analyze double-core-hole spectra.

Specific chemical bond relaxation unraveled by analysis of shake-up satellites in the oxygen single site double core hole spectrum of CO2

We recently developed [A. Ferté, et al., J. Phys. Chem. Lett., 2020, 11, 4359] a method to compute single site double core hole (ssDCH or K^-2) spectra. We refer to that method as NOTA+CIPSI. In the present paper this method is applied to the O K^-2 spectrum of the CO₂ molecule, and we use this as an example to discuss in detail its convergence properties. Using this approach, theoretical spectra in excellent agreement with the experimental one are obtained. Thanks to a thorough interpretation of the shake-up states responsible for the main satellite peaks and through comparison with the O K^-2 spectrum of CO, we can highlight the clear signature of the two non-equivalent carbon oxygen bonds in the oxygen ssDCH CO₂ dication.

Multi-reference approach to the computation of double core-hole spectra

Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K^-2) are obtained for H₂O, N₂, CO, and C₂H_2n (n = 1-3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K^-2 shake-up spectra of H₂O and C₂H_2n molecules are here completely characterized for the first time.

The O K-2V spectrum of CO: the influence of the second core-hole

Using synchrotron radiation in the tender X-ray regime, a photoelectron spectrum showing the formation of single site double-core-hole pre-edge states, involving the K shell of the O atom in CO, has been recorded by means of high-resolution electron spectroscopy. The experimentally observed structures have been simulated, interpreted and assigned, employing state-of-the-art ab initio quantum chemical calculations, on the basis of a theoretical model, accounting for their so-called direct or conjugate character. Features appearing above the double ionization threshold have been reproduced by taking into account the strong mixing between multi-excited and continuum states. The shift of the σ* resonance below the double ionization threshold, in combination with the non-negligible contributions of multi-excited configurations in the final states reached, gives rise to a series of avoided crossings between the different potential energy curves.

Using X-ray free-electron lasers for spectroscopy of molecular catalysts and metalloenzymes

The metal centres in metalloenzymes and molecular catalysts are responsible for the rearrangement of atoms and electrons during complex chemical reactions, and they enable selective pathways of charge and spin transfer, bond breaking/making and the formation of new molecules. Mapping the electronic structural changes at the metal sites during the reactions gives a unique mechanistic insight that has been difficult to obtain to date. The development of X-ray free-electron lasers (XFELs) enables powerful new probes of electronic structure dynamics to advance our understanding of metalloenzymes. The ultrashort, intense and tunable XFEL pulses enable X-ray spectroscopic studies of metalloenzymes, molecular catalysts and chemical reactions, under functional conditions and in real time. In this Technical Review, we describe the current state of the art of X-ray spectroscopy studies at XFELs and highlight some new techniques currently under development. With more XFEL facilities starting operation and more in the planning or construction phase, new capabilities are expected, including high repetition rate, better XFEL pulse control and advanced instrumentation. For the first time, it will be possible to make real-time molecular movies of metalloenzymes and catalysts in solution, while chemical reactions are taking place.

Magnetic bottle electron spectrometer driven by electron pulses

We report an electron scattering experiment on argon gas where a keV electron beam is used as a probe and electrons are collected with a magnetic bottle spectrometer. For this purpose, we have built a thermionic gun that produces electron pulses with nanosecond duration by sweeping the beam across a small aperture. To reach the target, electrons must pass through the hole in an axially symmetric arrangement of strong permanent magnets required to operate the magnetic bottle. From the recorded multi-hit sequence of electron arrival times on the microchannel plate detector, a kinetic energy spectrum is built that allows an analysis of the elastic and inelastic electron scattering channels by means of the coincidence technique. After a description of the instrumental configuration and discussion of suitable working parameters, the results of an angle-integrated (e, 2e) experiment are presented for 800 eV electron scattering on argon atoms.

Advanced Computation Method for Double Core Hole Spectra: Insight into the Nature of Intense Shake-up Satellites

Double core hole spectroscopy is an ideal framework for investigating photoionization shake-up satellites. Their important intensity in a single site double core hole (ssDCH) spectrum allows the exploration of the subtle mix of relaxation and correlation effects associated with the inherent multielectronic character of the shake-up process. We present a high-accuracy computation method for single photon double core-shell photoelectron spectra that combines a selected configuration interaction procedure with the use of non-orthogonal molecular orbitals to obtain unbiased binding energy and intensity. This strategy leads to the oxygen ssDCH spectrum of the CO molecule that is in excellent agreement with the experimental result. Through a combined wave function and density analysis, we highlight that the most intense shake-up satellites are characterized by an electronic reorganization that opposes the core hole-induced relaxation.

Multiple Photodetachment of Carbon Anions via Single and Double Core-Hole Creation

We report on new measurements of m-fold photodetachment (m=2-5) of carbon anions via K-shell excitation and ionization. The experiments were carried out employing the photon-ion merged-beams technique at a synchrotron light source. While previous measurements were restricted to double detachment (m=2) and to just the lowest-energy K-shell resonance at about 282 eV, our absolute experimental m-fold detachment cross sections at photon energies of up to 1000 eV exhibit a wealth of new thresholds and resonances. We tentatively identify these features with the aid of detailed atomic-structure calculations. In particular, we find unambiguous evidence for fivefold detachment via double K-hole production.

Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining Sub-electronvolt Error from a Restricted Open-Shell Kohn-Sham Approach

We present the use of the recently developed square gradient minimization (SGM) algorithm for excited-state orbital optimization to obtain spin-pure restricted open-shell Kohn-Sham (ROKS) energies for core excited states of molecules. The SGM algorithm is robust against variational collapse and offers a reliable route to converging orbitals for target excited states at only 2-3 times the cost of ground-state orbital optimization (per iteration). ROKS/SGM with the modern SCAN/ωB97X-V functionals is found to predict the K-edge of C, N, O, and F to a root mean squared error of ∼0.3 eV. ROKS/SGM is equally effective at predicting L-edge spectra of third period elements, provided a perturbative spin-orbit correction is employed. This high accuracy can be contrasted with traditional time-dependent density functional theory (TDDFT), which typically has greater than 10 eV error and requires translation of computed spectra to align with experiment. ROKS is computationally affordable (having the same scaling as ground-state DFT and a slightly larger prefactor) and can be applied to geometry optimizations/ab initio molecular dynamics of core excited states, as well as condensed phase simulations. ROKS can also model doubly excited/ionized states with one broken electron pair, which are beyond the ability of linear response based methods.

Hard x-ray spectroscopy and dynamics of isolated atoms and molecules: a review

We present here a review of the most significant recent achievements in the field of HAXPES (hard x-ray photoelectron spectroscopy) on isolated atoms and molecules, and related spectroscopies. The possibility of conducting hard x-ray photoexcitation and photoionization experiments under state-of-the art conditions in terms of photon and electron kinetic energy resolution has become available only in the last few years. HAXPES has then produced structural and dynamical information at the level of detail already reached in the VUV and soft-x-ray ranges. The much improved experimental conditions have allowed extending to the hard x-ray range some methods well established in soft x-ray spectroscopies. Investigations of electron and nuclear dynamics in the femtosecond (fs, 10^-15 s) and even attosecond (as, 10^-18 s) regime have become feasible. Complex relaxation phenomena following deep-core ionization can now be enlightened in great detail. Other phenomena like e.g. recoil-induced effects are much more important in fast photoelectron emission, which can be induced by hard x-rays. Furthermore, a new kind of ionic states with double core holes can be observed by x-ray single-photon absorption. Future perspectives are also discussed.

Energy-Dependent Relative Cross Sections in Carbon 1s Photoionization: Separation of Direct Shake and Inelastic Scattering Effects in Single Molecules

We demonstrate that the possibility of monitoring relative photoionization cross sections over a large photon energy range allows us to study and disentangle shake processes and intramolecular inelastic scattering effects. In this gas-phase study, relative intensities of the carbon 1s photoelectron lines from chemically inequivalent carbon atoms in the same molecule have been measured as a function of the incident photon energy in the range of 300-6000 eV. We present relative cross sections for the chemically shifted carbon 1s lines in the photoelectron spectra of ethyl trifluoroacetate (the "ESCA" molecule). The results are compared with those of methyl trifluoroacetate and S-ethyl trifluorothioacetate as well as a series of chloro-substituted ethanes and 2-butyne. In the soft X-ray energy range, the cross sections show an extended X-ray absorption fine structure type of wiggles, as was previously observed for a series of chloroethanes. The oscillations are damped in the hard X-ray energy range, but deviations of cross-section ratios from stoichiometry persist, even at high energies. The current findings are supported by theoretical calculations based on a multiple scattering model. The use of soft and tender X-rays provides a more complete picture of the dominant processes accompanying photoionization. Such processes reduce the main photoelectron line intensities by 20-60%. Using both energy ranges enabled us to discern the process of intramolecular inelastic scattering of the outgoing electron, whose significance is otherwise difficult to assess for isolated molecules. This effect relates to the notion of the inelastic mean free path commonly used in photoemission studies of clusters and condensed matter.

Cationic double K-hole pre-edge states of CS2 and SF6

Recent advances in X-ray instrumentation have made it possible to measure the spectra of an essentially unexplored class of electronic states associated with double inner-shell vacancies. Using the technique of single electron spectroscopy, spectra of states in CS₂ and SF₆ with a double hole in the K-shell and one electron exited to a normally unoccupied orbital have been obtained. The spectra are interpreted with the aid of a high-level theoretical model giving excellent agreement with the experiment. The results shed new light on the important distinction between direct and conjugate shake-up in a molecular context. In particular, systematic similarities and differences between pre-edge states near single core holes investigated in X-ray absorption spectra and the corresponding states near double core holes studied here are brought out.

Interaction of molecular nitrogen with free-electron-laser radiation

Molecular double core hole contribution to the final atomic ion fragments of N₂ when driven by an FEL pulse.

Double-Core-Hole States in Neon: Lifetime, Post-Collision Interaction, and Spectral Assignment

Using synchrotron radiation and high-resolution electron spectroscopy, we have directly observed and identified specific photoelectrons from K^{-2}V states in neon corresponding to simultaneous 1s ionization and 1s→valence excitation. The natural lifetime broadening of the K^{-2}V states and the relative intensities of different types of shakeup channels have been determined experimentally and compared to ab initio calculations. Moreover, the high-energy Auger spectrum resulting from the decay of Ne^{2+}K^{-2} and Ne^{+}K^{-2}V states as well as from participator Auger decay from Ne^{+}K^{-1}L^{-1}V states, has been measured and assigned in detail utilizing the characteristic differences in lifetime broadenings of these core hole states. Furthermore, post collision interaction broadening of Auger peaks is clearly observed only in the hypersatellite spectrum from K^{-2} states, due to the energy sharing between the two 1s photoelectrons which favors the emission of one slow and one fast electron.

Study of double core hole excitations in molecules by X-ray double-quantum-coherence signals: a multi-configuration simulation

The multi-configurational self-consistent field method is employed to simulate the two-dimensional all-X-ray double-quantum-coherence (XDQC) spectroscopy, a four-wave mixing signal that provides direct signatures of double core hole (DCH) states. The valence electronic structure is probed by capturing the correlation between the single (SCH) and double core hole states. The state-averaged restricted-active-space self-consistent field (SA-RASSCF) approach is used which can treat the valence, SCH, and DCH states at the same theoretical level, and applies to all types of DCHs (located on one or two atoms, K-edge or L-edge), with both accuracy and efficiency. Orbital relaxation introduced by the core hole(s) and the static electron correlation is properly accounted for. The XDQC process can take place via different intermediate DCH state channels by tuning the pulse frequencies. We simulate the XDQC signals for the three isomers of aminophenol at 8 pulse frequency configurations, covering all DCH pathways involving the N1s and O1s core hole (N1sN1s, O1sO1s and N1sO1s), which reveal different patterns of valence excitations.

Direct observation of double-core-hole shake-up States in photoemission

Direct measurements of Ar^{+} 1s^{-1}2p^{-1}nl double-core-hole shake-up states are reported using conventional single-channel photoemission, offering a new and relatively easy means to study such species. The high-quality results yield accurate energies and lifetimes of the double-core-hole states. Their photoemission spectrum also can be likened to 1s absorption of an exotic argon ion with a 2p core vacancy, providing new information about the spectroscopy of both this unusual ionic state as well as the neutral atom.

Double photoionization in ring molecules: search of the cooper pair formation

We provide a final state selective experimental study on the direct double photoionization of the valence states of benzene and pyrrole. The experiment is carried out using a magnetic-bottle electron time-of-flight coincidence setup at the incident photon energy region of 25-120 eV. We discuss on the recently discovered phenomenon of so-called Cooper pair formation [R. Wehlitz et al., Phys. Rev. Lett. 109, 193001 (2012)] and show that our experiment provides contradicting evidence on its existence in the proposed form. We confirm the finding of a new two-electron continuum resonance structure observed at about 30–70 eV above the double ionization threshold in benzene, provide further information from it, and suggest an alternative explanation.

Near-edge x-ray absorption fine structures revealed in core ionization photoelectron spectroscopy

Simultaneous core ionization and core excitation have been observed in the C(2)H(2n) (n=1, 2, 3) molecular series using synchrotron radiation and a magnetic bottle time-of-flight electron spectrometer. Rich satellite patterns corresponding to (K(-2)V) core excited states of the K(-1) molecular ions have been identified by detecting in coincidence the photoelectron with the two Auger electrons resulting from the double core hole relaxation. A theoretical model is proposed providing absolute photoionization cross sections and revealing clear signatures of direct (monopolar) and conjugate (dipolar near-edge x-ray absorption fine structure) shakeup lines of comparable magnitude.