Core Hole States Research Articles

Double core hole valence-to-core x-ray emission spectroscopy: A theoretical exploration using time-dependent density functional theory.

With the help of newly developed X-ray free-electron laser (XFEL) sources, creating double core holes (DCHs) simultaneously at the same or different atomic sites in a molecule has now become possible. DCH X-ray emission is a new form of X-ray nonlinear spectroscopy that can be studied with a XFEL. Here, we computationally explore the metal K-edge valence-to-core (VtC) X-ray emission spectroscopy (XES) of metal/metal and metal/ligand DCH states in a series of transition metal complexes with time-dependent density functional theory. The simulated DCH VtC-XES signals are compared with conventional single core hole (SCH) XES signals. The energy shifts and intensity changes of the DCH emission lines with respect to the corresponding SCH-XES features are fingerprints of the coupling between the second core hole and the occupied orbitals around the DCHs that contain important chemical bonding information of the complex. The difference between delocalized/localized core hole models on DCH VtC-XES is also briefly discussed. We theoretically demonstrate that DCH XES provides subtle information on the local electronic structure around metal centers in transition metal complexes beyond conventional linear XES. Our predicted changes from calculations between SCH-XES and DCH-XES features should be detectable with modern XFEL sources.

Xcalib: a focal spot calibrator for intense X-ray free-electron laser pulses based on the charge state distributions of light atoms.

The xcalib toolkit has been developed to calibrate the beam profile of an X-ray free-electron laser (XFEL) at the focal spot based on the experimental charge state distributions (CSDs) of light atoms. Characterization of the fluence distribution at the focal spot is essential to perform the volume integrations of physical quantities for a quantitative comparison between theoretical and experimental results, especially for fluence-dependent quantities. The use of the CSDs of light atoms is advantageous because CSDs directly reflect experimental conditions at the focal spot, and the properties of light atoms have been well established in both theory and experiment. Theoretical CSDs are obtained using xatom, a toolkit to calculate atomic electronic structure and to simulate ionization dynamics of atoms exposed to intense XFEL pulses, which involves highly excited multiple core-hole states. Employing a simple function with a few parameters, the spatial profile of an XFEL beam is determined by minimizing the difference between theoretical and experimental results. The optimization procedure employing the reinforcement learning technique can automatize and organize calibration procedures which, before, had been performed manually. xcalib has high flexibility, simultaneously combining different optimization methods, sets of charge states, and a wide range of parameter space. Hence, in combination with xatom, xcalib serves as a comprehensive tool to calibrate the fluence profile of a tightly focused XFEL beam in the interaction region.

Auger-induced charge migration

Novel perspectives of controlling molecular systems have recently arisen from the possibility of generating attosecond pulses in the ultraviolet regime and tailoring electron dynamics in its natural time scale. The cornerstone mechanism is the so-called charge migration, he production of a coherent charge transfer with subfemtosecond oscillations across a molecule. Typically, charge migration is induced by the ionization of valence molecular orbitals. However, recent technological developments allow the generation of attosecond pulses in the x-ray regime. In this case, the absorption of photons creates core-hole states. In light elements, core-hole states mainly decay by Auger processes that, driven by electron correlations, involve valence orbitals. We theoretically demonstrate in a fluoroacetylene molecule a double-hole charge migration triggered by attosecond core-electron photoionization, followed by Auger electron relaxations. This opens a new route for inducing with x rays charge transfer processes in the subfemtosecond time scale.

Selectivity of the Br 3d−1 Auger decays in HBr

The Auger decay of the spin-orbit and molecular-field split Br $3{d}^{\ensuremath{-}1}$ core holes in HBr is investigated, both by a photoelectron--Auger-electron coincidence experiment and by ab initio calculations based on the one-center approximation. The branching ratios for the Auger decay of the five different core-hole states to the $4p{(\ensuremath{\sigma},\ensuremath{\pi})}^{\ensuremath{-}2}$ dicationic final states are determined. Experimental and theoretical data are in good agreement and conform to results for the $4p{\ensuremath{\pi}}^{\ensuremath{-}2}$ final states from a previous analysis of the high-resolution conventional Auger-electron spectrum. The branching ratios for the Br $3{d}^{\ensuremath{-}1}$ Auger decay to the $4p{(\ensuremath{\sigma},\ensuremath{\pi})}^{\ensuremath{-}2}$ with \ensuremath{\Sigma} symmetry follow the propensity rule of ${L}_{2,3}VV$ Auger decay [S. Svensson, A. Ausmees, S. J. Osborne, G. Bray, F. Gel'mukhanov, H. \AA{}gren, A. Naves de Brito, O.-P. Sairanen, A. Kivim\aki, E. N\~ommiste, H. Aksela, and S. Aksela, Phys. Rev. Lett. 72, 3021 (1994)] stating that the oriented core holes decay preferentially by involving a valence electron from an orbital with the same spatial orientation. For the ${M}_{4,5}VV$ decay in HBr this propensity rule has to be supplemented by the requirement that the Auger-electron channel and the other valence orbital have the same preferential orientation. We also probe the influence of the Auger kinetic energy on the distortion of the photoline caused by the postcollision interaction effect. For small kinetic energies, differences between experimental results and theoretical predictions are identified.

Ab initiocalculation of electron-impact-ionization cross sections for ions in exotic electron configurations

Atomic or molecular assemblies irradiated with intense hard x-ray pulses, such as those emitted from x-ray free-electron lasers (XFELs), are subject to a strong ionization, which also releases electrons from atomic inner shells. The resulting core-hole states relax via various channels, including fluorescence and Auger decay. The latter is the predominant relaxation channel for light elements and typically occurs on a time scale of 1--10 fs. In dense samples, the core-hole ions may already undergo electron-impact ionizations during this time due to the abundance of highly energetic photoelectrons and Auger electrons. In this study we perform an ab initio calculation of the electron-impact-ionization cross sections of ions with an arbitrary electronic configuration at zero temperature. This allows us to evaluate and compare impact-ionization cross sections for ions in ground and ``exotic'' electronic states (e.g., with a few core holes), which may be formed during their interaction with intense x-ray pulses. We show that the impact-ionization cross sections for ions of the same charge, but with varying electronic configurations, may significantly differ. This finding has to be taken into account in any modeling tool treating the relaxation of atoms after high-energy-impact collision, e.g., simulations dedicated for coherent x-ray diffraction imaging of nanocrystals and single biological macromolecules, or laser-created plasma studies. Our computationally efficient ab initio calculation scheme can be easily incorporated in such simulation schemes.

A New Mechanism For XPS Line Broadening: The 2p-XPS of Ti(IV)

There is almost a factor of 2 increase in the full width at half maximum (FWHM) of the main Ti 2p1/2 XPS peak compared to the 2p3/2 in the closed-shell Ti(IV) compounds TiO2 and strontium titanate, STO. Although the spectra of anatase and rutile forms of TiO2 differ slightly from STO, the 2p1/2 broadening over 2p3/2 is very similar. For STO, we show that ascribing this differential broadening to a short 2p1/2 lifetime is unphysical. For STO, rigorous and fully relativistic electronic structure calculations have been carried out for both the initial state and the 2p core-hole states; these calculations include many-body effects as well as the one-body effects of spin–orbit and ligand field splittings. The agreement of the theoretical and measured XPS data for the main 2p1/2 and 2p3/2 peaks indicate that the necessary one- and many-body effects have been included. They show that the broadening is due to the presence of XPS intensity distributed over many unresolved final states for a 2p1/2 core-hole, wherea...

Ab initio calculation of the calorimetric electron-capture spectrum of Ho163 : Intra-atomic decay into bound states

The determination of the electron neutrino mass by electron capture in $^{163}$Ho relies on a precise understanding of the deexcitation of a core hole after an electron capture event. We here present an \textit{ab intio} calculation of the electron capture spectrum in $^{163}$Ho, including all intra-atomic decay channels into bound-states. We use theoretical methods developed for the calculation of core level spectroscopy on correlated electron compounds. Our comparison critically tests the reality of these theories. We find that relativistic interactions beyond the Dirac equation, i.e. quantum-electro dynamics, only lead to minor shifts of the spectral peaks. The electronic relaxation after an electron capture event due to the changed nuclear potential leads to a mixing of different edges, but due to conservation of angular momentum of each scattered electron, no additional structures emerge. Many-body Coulomb interactions lead to the formation of multiplets and to additional peaks with multiple core-holes due to Auger decay. Multiplets crucially change the appearance of the resonances on a Rydberg energy scale. The additional structures due to Auger decay are, although clearly visible, relatively weak compared to the one core hole states and accidentally far away from the end-point region of the spectrum. As the end-point of the spectrum is effected most by the neutrino mass these additional states do not influence the statistics for determining the neutrino mass directly. The multiplet broadening and Auger shake-up of the main core-level edges do change the apparent line-width and accompanying lifetime of these edges, thereby invalidating experimentally obtained lifetimes at the resonance for regions far away from the resonance.

Ionization potential depression in an atomic-solid-plasma picture

Exotic solid density matter such as heated hollow crystals allow extended material studies while their physical properties and models such as the famous ionization potential depression are presently under renewed controversial discussion. Here we develop an atomic-solid-plasma (ASP) model that permits ionization potential depression studies also for single and multiple core hole states. Numerical calculations show very good agreement with recently available data not only in absolute values but also for Z-scaled properties while currently employed methods fail. For much above solid density compression, the ASP model predicts increased K-edge energies that are related to a Fermi surface rising. This is in good agreement with recent quantum molecular dynamics simulations. For hot dense matter a quantum number dependent optical electron finite temperature ion sphere model is developed that fits well with line shift and line disappearance data from dense laser produced plasma experiments. Finally, the physical transparency of the ASP picture allows a critical discussion of current methods.

Changes in site-specific shape resonances in nitrogen K-shell photoionization of N2O induced by vibrational excitation

The central (Nc) and terminal (Nt) nitrogen K-shell photoelectron spectra (PESs) of N2O molecules have been measured in the σ shape resonance energy region at temperatures of ∼300 and ∼630 K. Estimating vibrational populations based on the Boltzmann distribution at these temperatures, PESs of vibrationally ground and bending-excited levels in the initial electronic ground state were extracted. Vibrationally integrated partial cross sections and asymmetry parameters for ionization from vibrationally ground and bending-excited levels were obtained as a function of the incident photon energy by integrating PESs over the vibrational levels of the core-hole states. In Nc photoionization, the shape resonance from the bending-excited level was found to be shifted to the lower photon energy side and to become narrower than that from the ground vibrational level. In Nt photoionization from the bending-excited level, the downward shift of the resonance is more significant than that in Nc ionization. These experimental findings are qualitatively consistent with theoretical predictions and suggest that the shape resonance associated with the Nt core hole is more sensitive to the bending angle of the initial state than is the shape resonance associated with the Nc core hole. The asymmetry parameters for photoionization from the bending-excited level, however, showed almost the same behavior as those from the ground vibrational level for both K-shell photoionization channels and in the photon energy range studied here.

Quantitative analysis of Yb 4d photoelectron spectrum of metallic Yb

The measured Yb 4d3/2 intensity is larger than the Yb 4d5/2 in X‐ray photoelectron (XPS) emission of metallic Yb, which is unexpected. The shape and intensity of photoelectron peaks are strongly affected by extrinsic excitations due to electron transport out of the surface (including bulk and surface effects) and to intrinsic excitations due to the sudden creation of the static core hole. To quantitatively extract from experimental XPS the primary excitation spectrum (ie, the initial excitation process) of the considered transition, these effects must be included within the theoretical description. The combined effect of both extrinsic and intrinsic excitations can be described by an effective energy‐differential inelastic electron scattering cross section for XPS evaluated by a dielectric response model with the dielectric function as only input. Then, using this cross section, a direct evaluation of the primary excitation spectrum is performed by standard peak shape analysis for thick homogeneous samples. We use this approach in the present paper to determine the Yb 4d photoemission spectrum for metallic Yb. We show that the unexpected larger intensity of Yb 4d3/2 compared to 4d5/2 can be fully accounted for by our model and that the total spectrum consists of a sum of symmetric primary excitation peaks.

Fragmentation of Methanol Molecules after Core Excitation and Core Ionization Studied by Negative-Ion/Positive-Ion Coincidence Experiments.

We have studied the fragmentation of the methanol molecule after core excitation and core ionization by observing coincidences between negative and positive ions. Five different negative ions (H-, C-, CH-, O-, and OH-) were observed at both the C 1s and O 1s edges. As negative ion formation occurs after resonant and normal Auger decay of core-hole states, it is necessarily linked with the release of positively charged fragments. Our data show that such fragmentation can happen in many different ways: We found approximately 30 negative-ion/positive-ion/positive-ion coincidence (NIPIPICO) channels. All involve only singly charged positive ions. Fragmentation channels leading to atomic ions are the most probable, but positive molecular ions are also frequently found in the context of anion formation. Coincidence yields as a function of photon energy were determined for the most intense NIPIPICO channels. Adding together the data measured at different photon energies, we could also verify the occurrence of four-ion coincidences, which involved one negative ion (H- or O-) and three positive ions.

A Chemical View on X-ray Photoelectron Spectroscopy: the ESCA Molecule and Surface-to-Bulk XPS Shifts.

In this paper we remind the reader of a simple, intuitive picture of chemical shifts in X-ray photoelectron spectroscopy (XPS) as the difference in chemical bonding between the probed atom and its neighbor to the right in the periodic table, the so called Z+1 approximation. We use the classical ESCA molecule, ethyl trifluoroacetate, and 4d-transition metals to explicitly demonstrate agreement between core-level shifts computed as differences between final core-hole states and the approach where each core-ionized atom is replaced by a Z+1 atom. In this final state, or total energy picture, the XPS shift arises due to the more or less unfavorable chemical bonding of the effective nitrogen in the carbon geometry for the ESCA molecule. Surface core level shifts in metals are determined by whether the Z+1 atom as an alloy segregates to the surface or is more soluble in the bulk. As further illustration of this more chemical picture, we compare the geometry of C 1s and O 1s core-ionized CO with that of, respectively, NO+ and CF+ . The scope is not to propose a new method to compute XPS shifts but rather to stress the validity of this simple interpretation.

Experimental and theoretical study of the double-core-hole hypersatellite Auger spectrum of Ne

We present the hypersatellite Auger spectrum of neon which contains the decay transitions of the ${K}^{\ensuremath{-}2}, {K}^{\ensuremath{-}2}V, {K}^{\ensuremath{-}2}{L}^{\ensuremath{-}1}, {K}^{\ensuremath{-}2}{L}^{\ensuremath{-}1}V$, and ${K}^{\ensuremath{-}1}{L}^{\ensuremath{-}1}V$ states. The Auger decays of these types of core-hole states show different line shapes and linewidths which can be distinguished due to the high experimental resolution available for the present experiments. The individual Auger transitions are assigned based on various approaches. Complementary calculations are performed to assign the ${K}^{\ensuremath{-}2}{L}^{\ensuremath{-}1}\ensuremath{\rightarrow}{K}^{\ensuremath{-}1}{L}^{\ensuremath{-}3}$ and the ${K}^{\ensuremath{-}2}{L}^{\ensuremath{-}1}V\ensuremath{\rightarrow}{K}^{\ensuremath{-}1}{L}^{\ensuremath{-}3}V$ Auger transitions. Based on the obtained results we were able to derive the ratio for the double to single ionization yield.

Optimized pulses for Raman excitation through the continuum: Verification using the multiconfigurational time-dependent Hartree-Fock method

We have verified a mechanism for Raman excitation of atoms through continuum levels previously obtained by quantum optimal control using the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method. For the optimal control, which requires running multiple propagations to determine the optimal pulse sequence, we used the computationally inexpensive time-dependent configuration interaction singles (TDCIS) method. TDCIS captures all of the necessary correlation of the desired processes but assumes that ionization pathways reached via double excitations are not present. MCTDHF includes these pathways and all multiparticle correlations in a set of time-dependent orbitals. The mechanism that was determined to be optimal in the Raman excitation of the Ne $1{s}^{2}2{s}^{2}2{p}^{5}3{p}^{1}$ valence state via the metastable $1{s}^{2}2{s}^{1}2{p}^{6}3{p}^{1}$ resonance state involves a sequential resonance-valence excitation. First, a long pump pulse excites the core-hole state, and then a shorter Stokes pulse transfers the population to the valence state. This process represents the first step in a multidimensional x-ray spectroscopy scheme that will provide a local probe of valence electronic correlations. Although at the optimal pulse intensities at the TDCIS level of theory the MCTDHF method predicts multiple ionization or excitation ionization of the atom, at slightly lower intensities (reduced by a factor of about 4) the TDCIS mechanism is shown to hold qualitatively. Quantitatively, the MCTDHF populations are reduced from the TDCIS calculations by a factor of 4.

Towards core-excitation spectra in attosecond spectroscopy: A coupled-cluster study of ClF

The increasing availability of short timescale spectroscopy techniques allows for more accurate probing of nuclear and electronic dynamics. This work studies the underlying potential energy curves for the core-ionized and core-excited states of ClF. The variational collapse that can occur using conventional variational methods make electronic states involving core-holes particularly challenging to describe. Coupled-cluster methods can avoid such problems. This work applies extensions of ground and excited state coupled-cluster methods to compute potential curves for core-hole states of ClF. The ability to obtain accurate potential curves for such elusive states, and generate core-absorption spectra, opens the door for exciting developments.

Potential Energy Surfaces of Core-Hole and Shake-Up States for Dissociative Ionization Studies.

The theoretical description of core-hole and core-hole excited (shake-up) states resulting from the interaction of a molecule with X-ray free-electron lasers, attosecond pulses, and synchrotron radiation is a challenging task, as these states lie in the ionization continuum and, therefore, are subject to variational collapse. Although much effort has been devoted in the past to describe core-hole states in the Franck-Condon (FC) region, very few attempts, even less for shake-up states, have been reported near the dissociation threshold, where multistate degeneracy introduces additional complications. Knowledge of the whole potential energy surface (PES) is, however, essential when dissociative ionization resulting from the interaction with XUV or X-ray light occurs. In this work, we gauge the accuracy of two widely used multiconfigurational methods, CASSCF and MRCI, to obtain the potential energy curves of core-hole states of CO, N2, and the small polyatomic molecule BF3, from the FC region up to the dissociation limit, and show that CASSCF in combination with a triple-ζ basis set provides a very reasonable compromise between accuracy and computational cost to correctly describe core-hole and shake-up states in the entire PES. Besides providing the vibrational spectroscopic constants associated with these states, we also analyze the corresponding bonding and dissociation properties, which, in some cases, are counterintuitive and significantly different from those of bound states.

Electronic-state–lifetime interference in the hard-x-ray regime: Argon as a showcase

Electronic-state--lifetime interference is a phenomenon specific for ionization of atoms and molecules in the hard-x-ray regime. Using resonant $K{L}_{2,3}{L}_{2,3}$ Auger decay in argon as a showcase, we present a model that allows extracting the interference terms directly from the cross sections of the final electronic states. The analysis provides fundamental information on the excitation and decay processes such as probabilities of various decay paths and the values of the dipole matrix elements for transitions to the excited states. Our results shed light on the interplay between spectator, shake-down, and shake-up processes in the relaxation of deep core-hole states.

Interaction of molecular nitrogen with free-electron-laser radiation.

We compute molecular continuum orbitals in the single center expansion scheme. We then employ these orbitals to obtain molecular Auger rates and single-photon ionization cross sections to study the interaction of N2 with Free-Electron-Laser (FEL) pulses. The nuclei are kept fixed. We formulate rate equations for the energetically allowed molecular and atomic transitions and we account for dissociation through additional terms in the rate equations. Solving these equations for different parameters of the FEL pulse, allows us to identify the most efficient parameters of the FEL pulse for obtaining the highest contribution of double core hole states (DCH) in the final atomic ion fragments. Finally we identify the contribution of DCH states in the electron spectra and show that the DCH state contribution is more easily identified in the photo-ionization rather than the Auger transitions.

XAS and XES studies of carbonate and bicarbonate ions in aqueous solutions

We perform theoretical calculations to reproduce the site-selective X-ray emission spectroscopy (XES) spectrum for carbonate and bicarbonate ions in aqueous solution at the oxygen K-edge. We perform structure sampling, and using an ab initio molecular dynamics simulation, we reproduce the solute-solvent model. Relative XES peak intensities with core-hole excited state molecular dynamics simulations are calculated using density functional theory. A comparison of several models shows that a cluster model with surrounding water can describe the experimental XES spectra, and these calculations provide electronic and molecular structure information in an aqueous solution.

Auger decay rates of core hole states using equation of motion coupled cluster method

The recent development of Linac coherent light source high intense X-ray laser makes it possible to create double core ionization in the molecule. The generation of double core hole state and its decay is identified by Auger spectroscopy. The decay of this double core hole (DCH) states can be used as a powerful spectroscopic tool in chemical analysis. In the present work, we have implemented a promising approach, known as CAP-EOMCC method, which is a combination of complex absorbing potential (CAP) and equation-of-motion coupled cluster (EOMCC) approach to calculate the lifetime of single and double core hole states. We have applied this method to calculate the lifetime of the single core hole (K-LL) and double core hole (KK-KLL) states of CH4, NH3 and HF molecules. The predicted lifetime is found to be extremely short.