Core-excited States Research Articles

Enhanced 5f-δ bonding in [U(C7H7)2]-: C K-edge XAS, magnetism, and ab initio calculations.

5f covalency in [U(C7H7)2]- was probed with carbon K-edge X-ray absorption spectroscopy (XAS) and electronic structure theory. The results revealed U 5f orbital participation in δ-bonding in both the ground- and core-excited states; additional 5f ϕ-mixing is observed in the core-excited states. Comparisons with U(C8H8)2 show greater δ-covalency for [U(C7H7)2]-.

Manipulating valence and core electronic excitations of a transition-metal complex using UV/Vis and X-ray cavities.

We demonstrate how optical cavities can be exploited to control both valence- and core-excitations in a prototypical model transition metal complex, ferricyanide ([Fe(iii)(CN)6]3−), in an aqueous environment. The spectroscopic signatures of hybrid light-matter polariton states are revealed in UV/Vis and X-ray absorption, and stimulated X-ray Raman signals. In an UV/Vis cavity, the absorption spectrum exhibits the single-polariton states arising from the cavity photon mode coupling to both resonant and off-resonant valence-excited states. We further show that nonlinear stimulated X-ray Raman signals can selectively probe the bipolariton states via cavity-modified Fe core-excited states. This unveils the correlation between valence polaritons and dressed core-excitations. In an X-ray cavity, core-polaritons are generated and their correlations with the bare valence-excitations appear in the linear and nonlinear X-ray spectra.

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.

Fragmentation pathways of methylbenzoate cations following core excitation: Theoretical approach using graph theory

We performed theoretical calculations to elucidate the detailed pathways following the core excitation of methylbenzoate. The classical molecular dynamics were expanded to include geometry relaxation on the resonant core-excited state at the O K-edge. The fragmentation pathways of cationic state as the Auger final state were examined. We found that the chemical bonds around methoxy oxygen are dissociative on the core-excited state; furthermore, the yields of fragment ions produced by bond scission of methoxy oxygen increased. Thus, OCH3+ and CH3+ ions were dissociated selectively after core excitation.

Vibrationally resolved coupled-cluster x-ray absorption spectra from vibrational configuration interaction anharmonic calculations.

Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the adaptive density-guided approach scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecules.

Probing Delocalized Current Densities in Selenophene by Resonant X-ray Sum-Frequency Generation

Time-resolved, resonant X-ray sum-frequency generation in aligned selenophene molecules is calculated. A wave packet of valence-excited states, prepared by an extreme-ultraviolet pump pulse, is probed by two 12-keV X-ray probe pulses resonant with the Se core-excited states for variable time delays. At these hard-X-ray frequencies, the angström wavelength of the X-ray probe is comparable to the molecular size. We thus employ a nonlocal description of the light-matter interaction based on the minimal-coupling Hamiltonian. The wavevector-resolved resonant stimulated sum-frequency-generation signal, obtained by varying the propagation direction of hard-X-ray pulses, can thus directly monitor the transition current densities between core and ground/valence states. This is in contrast to off-resonant diffraction, which detects the transition charge densities.

Resonant propagation of x rays from the linear to the nonlinear regime

We present a theoretical study of temporal, spectral, and spatial reshaping of intense, ultrafast x-ray pulses propagating through a resonant medium. Our calculations are based on the solution of a 3D time-dependent Schr\"odinger-Maxwell equation, with the incident x-ray photon energy on resonance with the core-level 1s-3p transition in neon. We study the evolution of the combined incident and medium-generated field, including the effects of stimulated emission, absorption, ionization and Auger decay, as a function of the input pulse energy and duration. We find that stimulated Raman scattering between core-excited states $1s^{-1}3p$ and $2p^{-1}3p$ occurs at high x-ray intensity, and that the emission around this frequency is strongly enhanced when also including the similar $1s^{-1}-2p^{-1}$ response of the ion. We also explore the dependence of x-ray self-induced transparency (SIT) and self-focusing on the pulse intensity and duration, and we find that the stimulated Raman scattering plays an important role in both effects. Finally, we discuss how these nonlinear effects may potentially be exploited as control parameters for pulse properties of x-ray free-electron laser sources.

Attosecond spectroscopy reveals alignment dependent core-hole dynamics in the ICl molecule

The removal of electrons located in the core shells of molecules creates transient states that live between a few femtoseconds to attoseconds. Owing to these short lifetimes, time-resolved studies of these states are challenging and complex molecular dynamics driven solely by electronic correlation are difficult to observe. Here, we obtain few-femtosecond core-excited state lifetimes of iodine monochloride by using attosecond transient absorption on iodine 4d−16p transitions around 55 eV. Core-level ligand field splitting allows direct access of excited states aligned along and perpendicular to the ICl molecular axis. Lifetimes of 3.5 ± 0.4 fs and 4.3 ± 0.4 fs are obtained for core-hole states parallel to the bond and 6.5 ± 0.6 fs and 6.9 ± 0.6 fs for perpendicular states, while nuclear motion is essentially frozen on this timescale. Theory shows that the dramatic decrease of lifetime for core-vacancies parallel to the covalent bond is a manifestation of non-local interactions with the neighboring Cl atom of ICl.

Analysis of low-lying states, neutron-core excitations, and electromagnetic transitions in tellurium isotopes Te130–134

The neutron-rich $^{130--134}\mathrm{Te}$ isotopes are investigated by large-scale shell-model calculations with the extended pairing plus multipole-multipole force (EPQQM model). The orbits of $(0{g}_{7/2},1{d}_{5/2},1{d}_{3/2},2{s}_{1/2},0{h}_{11/2})$ are included for both proton and neutron model space, while two more neutron orbits $(1{f}_{7/2},2{p}_{3/2})$ above the $N=82$ shell gap are included to study neutron-core excitations. The higher core-excited states in $^{132,133}\mathrm{Te}$ are calculated for the first time in this region. The present work well describes both the low-lying and the high-energy states for $^{134}\mathrm{Te}$, $^{133}\mathrm{Te}$, and $^{132}\mathrm{Te}$, as well as the low-lying levels of $^{131}\mathrm{Te}$ and $^{130}\mathrm{Te}$. The several multiplets with clear boundary exist in $^{134,133}\mathrm{Te}$, while a new configuration lying between 4.8 and 6.0 MeV is found as a theoretical prediction in $^{134}\mathrm{Te}$. Finally, the transition probabilities in these nuclei are calculated and compared with available data. The predicted energy levels and electromagnetic transition will be useful for planning future experiments.

Lifetimes of core-excited states in semi-magic ^{95}mathrm {Rh}

Lifetimes of negative-parity states have been determined in the neutron deficient semi-magic (N = 50) nucleus ^{95}mathrm {Rh}. The fusion-evaporation reaction ^{58}Ni(^{40}Ca, 3p) was used to populate high-spin states in ^{95}mathrm {Rh} at the Grand Accélérateur National d’Ions Lourds (GANIL) accelerator facility. The results were obtained using the Doppler Shift Attenuation Method (DSAM) based on the Doppler broadened line shapes produced during the slowing down process of the residual nuclei in a thick 6;mathrm {mg/cm}^2 metallic target. B(M1) and B(E2) reduced transition strengths are compared with predictions from large-scale shell-model calculations.

Influence of spin orbit splitting and satellite transitions on nickel soft X-ray optical properties near its L2,3 absorption edge region.

Transition elements exhibit strong correlations and configuration interactions between core and valence excited states, which give rise to different excitations inside materials. Nickel exhibits satellite features in its emission and absorption spectra. Effects of such transitions on the optical constants of nickel have not been reported earlier and the available database of Henke et al. does not represent such fine features. In this study, the optical behaviour of ion beam sputter deposited Ni thin film near the L2,3-edge region is investigated using reflection spectroscopy techniques, and distinct signatures of various transitions are observed. The soft X-ray reflectivity measurements in the 500-1500 eV photon energy region are performed using the soft X-ray reflectivity beamline atthe Indus-2 synchrotron radiation source. Kramers-Kronig analysis of the measured reflectivity data exhibit features corresponding to spin orbital splitting and satellite transitions in the real and imaginary part of the refractive index (refraction and absorption spectra). Details of fine features observed in the optical spectra are discussed. To the best of our knowledge, this is the first study reporting fine features in the measured optical spectra of Ni near its L2,3-edge region.

The effect of 5f states on the nd → 5f transition energies and spectra of americium ions

The spectra originating from the electric dipole transitions of nd (n = 3 − 5) core excited states to the 5f valence states of Am2+ to Am8+ ions have been calculated using the Dirac-Hartee-Fock method, which are compared with the results from the Flexible Atomic Code for the explanation of accuracy. It is found that both the and spectra of these ions consist of two peaks that are well separated in energy respectively by 202.11 eV and 49.10 eV due to strong spin-orbit interaction of the and hole state, while the spectra show a broad quasi-continuum profile.

Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations.

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted due to the risk of "variational collapse" down to the ground state. We employ the recently developed square gradient minimization [D. Hait and M. Head-Gordon, J. Chem. Theory Comput. 16, 1699 (2020)] algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP, and ωB97X-D3) are found to predict excitation energies from the core to singly occupied levels with high accuracy (≤0.3 eV RMS error) against available experimental data. Higher excited states are, however, more challenging by virtue of being intrinsically multiconfigurational. We thus present a configuration interaction inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO+, and the N K-edge of NO2 with high accuracy relative to experiment, indicating substantial promise in using this approach for the computation of core-level spectra for doublet species [vs more traditional time dependent DFT, equation of motion coupled cluster singles and doubles (EOM-CCSD), or using unrecoupled mixed configurations]. We also present general guidelines for computing core-excited states from orbital optimized DFT.

Theoretical investigation of an intense ultrashort xuv pulse-induced Auger cascade in krypton

This paper theoretically investigates an Auger cascade triggered upon exposure of a Kr atom to an intense ultrashort xuv laser. In the first step of the cascade, Auger electrons are released from a coherent superposition of core-excited states to form an intermediate ionic state, which further decays through the Auger process to form a double ionic final state. Results show that the interference due to electrons released from a coherent superposition of closely spaced core-excited states, in their common continuum, in the first step of the cascade significantly modifies the line shape of the coincidence spectrum of the two Auger electrons of the cascade. The variation of the laser peak intensity not only influences the peak magnitude and linewidth but also induces a peak shift in the coincidence electron spectrum; further, the high-intensity-induced Rabi oscillations between ground and core-excited state induce line-shape splitting in the coincidence electron spectrum of the two Auger electrons, thereby manifesting the effect of Rabi oscillations even for the second Auger electron of the cascade. This work shows that the inter-related decay widths of the core-excited state and intermediate ionic state significantly influence the line shape of the coincidence electron spectrum of a cascade decay. The angular distribution of the second electron released from the cascade system of krypton is also investigated.

Observation of Double Excitations in the Resonant Inelastic X-ray Scattering of Nitric Oxide.

The nitrogen K-edge resonant inelastic X-ray scattering (RIXS) map of nitric oxide (NO) has been measured and simulated to provide a detailed analysis of the observed features. High-resolution experimental RIXS maps were collected using an in situ gas flow cell and a high-transmission soft X-ray spectrometer. Accurate descriptions of the ground, excited, and core-excited states are based upon restricted active space self-consistent-field calculations using second order multiconfigurational perturbation theory. The nitrogen K-edge RIXS map of NO shows a range of features that can be assigned to intermediate states arising from 1s → π* and 1s → Rydberg excitations; additional bands are attributed to doubly excited intermediate states comprising 1s → π* and π → π* excitations. These results provide a detailed picture of RIXS for an open-shell molecule and an extensive description of the core-excited electronic structure of NO, an important molecule in many chemical and biological processes.

Quantifying the error of the core-valence separation approximation.

For the calculation of core-excited states probed through X-ray absorption spectroscopy, the core-valence separation (CVS) scheme has become a vital tool. This approach allows us to target such states with high specificity, albeit introducing an error. We report the implementation of a post-processing step for CVS excitations obtained within the algebraic-diagrammatic construction scheme for the polarization propagator, which removes this error. Based on this, we provide a detailed analysis of the CVS scheme, identifying its accuracy to be dominated by an error balance between two neglected couplings, one between core and valence single excitations and the other between single and double core excitations. The selection of the basis set is shown to be vital for a proper description of both couplings, with tight polarizing functions being necessary for a good balance of errors. The CVS error is confirmed to be stable across multiple systems, with an element-specific spread for K-edge spectrum calculations of only about ±0.02 eV. A systematic lowering of the CVS error by 0.02 eV-0.03 eV is noted when considering excitations to extremely diffuse states, emulating ionization.

Vibrationally resolved photoemissions of N2 (C3Πu → B3Πg) and CO (b3Σ+ → a3Π) by low-energy electron impacts

Vibrationally resolved photoemission spectra of the electronic-state transitions C3Πu → B3Πg of N2 and b3Σ+ → a3Π of CO following low-energy electron impacts are measured with a crossed-beam experimental arrangement. The absolute cross sections of C3Πu (ν') → B3Πg (ν″) of N2 are presented for the vibrational state-to-state transitions (ν',ν″) = (0,0), (0,1), (1,0), (1,2), and (2,1). The excitation cross sections of the metastable state C3Πu of N2 show the maxima at the electron-impact energies 14.10 (ν' = 0) eV and 14.50 (ν' = 1) eV, which are potentially related to the core-excited vibrational Feshbach resonant state 2Σu + of N2 - formed by electron attachment. The absolute cross sections of b3Σ+ (ν' = 0) → a3Π (ν″ = 0, 1, 2, 3, 4) of CO are given by the calibrations with those of N2 measured in this work. Besides the maximum excitation cross section 5.85 × 10-18 cm2 at 10.74 eV of the CO b3Σ+ (ν' = 0) state, some fine structures on the excitation function profile are attributed to different shapes and Feshbach resonant states of CO- formed by electron attachment, while the others arise from the direct electron-impact excitation. Some discrepancies, particularly for N2, between the present data and the results available in the literature studies arise from different experimental techniques and data-processing procedures. Furthermore, contributions of physical processes such as wave-packet evolution and non-Franck-Condon dynamics are highlighted here.

Density Functional Theory Based Methods for the Calculation of X-ray Spectroscopy.

The availability of new light sources combined with the realization of the unique capabilities of spectroscopy in the X-ray region has driven tremendous advances in the field of X-ray spectroscopy. Currently, these techniques are emerging as powerful analytical tools for the study of a wide range of problems encompassing liquids, materials, and biological systems. Time-resolved measurements add a further dimension to X-ray spectroscopy, opening up the potential to resolve ultrafast chemical processes at an atomic level. X-ray spectroscopy encompasses a range of techniques which provide complementary information, and these include X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES), and resonant inelastic X-ray scattering (RIXS). In many studies, the interpretation of the experimental data relies upon calculations to enable the nature of the underlying molecular structure, electronic structure, and bonding to be revealed. Density functional theory (DFT) based methods are some of the most widely used methods for the simulation of X-ray spectra. In this Account, we focus on our recent contributions to the simulation of a range of X-ray spectroscopic techniques using DFT and linear-response time-dependent density functional theory (TDDFT) and show how these methods can provide a computational toolkit for the simulation of X-ray spectroscopy. The importance of the exchange-correlation functional for the calculation of XAS is discussed, and the introduction of short-range corrected functionals is described. The application of these calculations to study large systems through the use of efficient implementations of TDDFT will be highlighted, with the use of these methods illustrated through studies of ionic liquids and transition metal complexes. The extension of TDDFT to calculate XES through the use of a reference determinant for the core-ionized state will be described, and the factors that affect the accuracy of the computed spectra discussed. The application of these approaches will be illustrated through the study of a range of organic molecules and transition metal complexes, which also show how going beyond the dipole approximation in determining the transition intensities can be critical. The application of these approaches to the simulation of the RIXS spectrum of water will also be described, highlighting how ultrafast dynamics on the femtoscale time scale are evident in the measured spectra. In these calculations, the description of the core-ionized and core-excited states becomes increasingly important, and the role of the basis set in accurately describing these states will be explored.

Effects of intense chirped x-ray laser on resonant Auger process through multiple core-excited states

In the context of the recent reported results indicating chirped laser induced suppression of resonant Auger effect the author investigates the effects of chirping on the resonant Auger process from a coherent superposition of core-excited states and direct ionization from the ground state. It is found that for the positive chirping case total electron yield initially increases with increase in chirp rate eventually decreasing with further increase in chirp rate. However, in the case of negative chirping total electron yield always decreases with increase in chirp rate. The results demonstrate the possibility of controlling Rabi oscillations between ground and core-excited states through the variation of chirp rate. It is also found that the variation of chirp rate significantly influences the peak magnitude of the two peaks visible in the electron spectrum. The author also studies the effects of chirping of the laser on the electron spectrum computed for direct ionization from the ground state. The calculated results indicate that chirping of x-ray pulse can modify the signatures of interference between two competing pathways in the electron spectrum.

X-Ray Absorption Spectrum of the N_{2}^{+} Molecular Ion.

The x-ray absorption spectrum of N_{2}^{+} in the K-edge region has been measured by irradiation of ions stored in a cryogenic radio frequency ion trap with synchrotron radiation. We interpret the experimental results with the help of restricted active space multiconfiguration theory. Spectroscopic constants of the 1σ_{u}^{-1} ^{2}Σ_{u}^{+} state, and the two 1σ_{u}^{-1}3σ_{g}^{-1}1π_{g} ^{2}Π_{u} states are determined from the measurements. The charge of the ground state together with spin coupling involving several open shells give rise to double excitations and configuration mixing, and a complete breakdown of the orbital picture for higher lying core-excited states.