Core-excited States Research Articles

Revealing core-valence interactions in solution with femtosecond X-ray pump X-ray probe spectroscopy

Femtosecond pump-probe spectroscopy using ultrafast optical and infrared pulses has become an essential tool to discover and understand complex electronic and structural dynamics in solvated molecular, biological, and material systems. Here we report the experimental realization of an ultrafast two-color X-ray pump X-ray probe transient absorption experiment performed in solution. A 10 fs X-ray pump pulse creates a localized excitation by removing a 1s electron from an Fe atom in solvated ferro- and ferricyanide complexes. Following the ensuing Auger–Meitner cascade, the second X-ray pulse probes the Fe 1s → 3p transitions in resultant novel core-excited electronic states. Careful comparison of the experimental spectra with theory, extracts +2 eV shifts in transition energies per valence hole, providing insight into correlated interactions of valence 3d with 3p and deeper-lying electrons. Such information is essential for accurate modeling and predictive synthesis of transition metal complexes relevant for applications ranging from catalysis to information storage technology. This study demonstrates the experimental realization of the scientific opportunities possible with the continued development of multicolor multi-pulse X-ray spectroscopy to study electronic correlations in complex condensed phase systems.

Visualize the vibronic coupling in Auger final states in N2 molecule.

Vibronic coupling is a critical mechanism in chemical reactions. However, its quantitative evaluation is challenging due to mathematical complexity and programming difficulty, and its experimental proof is often elusive due to overlap among neighboring states. Here, after exciting a vibrational level (ν = 0, 1, 2) of the intermediate N 1s→πg* core-excited state in N2 molecules, we separate the resonant Auger decay channels that lead to the lowest dissociation limit in the two-dimensional energy correlation maps. From three kinetic energy release spectra of these channels at different vibrational quantum numbers, we give the first experimental proof of the vibronic coupling between two resonant Auger final states 12Πg and 22Πg.

Signatures of diradicals in x-ray absorption spectroscopy.

Theoretical simulations are critical to analyze and interpret the x-ray absorption spectrum of transient open-shell species. In this work, we propose a model of the many-body core-excited states of symmetric diradicals. We apply this model to analyze the carbon K-edge transitions of o-, m-, and p-benzyne, three organic diradicals with diverse and unusual electronic structures. The predictions of our model are compared with high-level multireference computations of the K-edge spectrum of the benzynes obtained with the driven similarity renormalization group truncated to third order. Our model shows the importance of a many-body treatment of the core-excited states of the benzynes and provides a theoretical framework to understand which properties of the ground state of these diradicals can be extracted from their x-ray spectrum.

X-ray induced electron and ion fragmentation dynamics in IBr.

Characterization of the inner-shell decay processes in molecules containing heavy elements is key to understanding x-ray damage of molecules and materials and for medical applications with Auger-electron-emitting radionuclides. The 1s hole states of heavy atoms can be produced by absorption of tunable x rays and the resulting vacancy decays characterized by recording emitted photons, electrons, and ions. The 1s hole states in heavy elements have large x-ray fluorescence yields that transfer the hole to intermediate electron shells that then decay by sequential Auger-electron transitions that increase the ion's charge state until the final state is reached. In molecules, the charge is spread across the atomic sites, resulting in dissociation to energetic atomic ions. We have used x-ray/ion coincidence spectroscopy to measure charge states and energies of Iq+ and Brq'+ atomic ions following 1s ionization at the I and Br K-edges of IBr. We present the charge states and kinetic energies of the two correlated fragment ions associated with core-excited states produced during the various steps of the cascades. To understand the dynamics leading to the ion data, we develop a computational model that combines Monte-Carlo/Molecular-Dynamics (MC/MD) simulations with a classical over-the-barrier model to track inner-shell cascades and redistribution of electrons in valence orbitals and nuclear motion of fragments.

A study of core-excited states of organic molecules computed with the generalized active space driven similarity renormalization group.

This work examines the accuracy and precision of x-ray absorption spectra computed with a multireference approach that combines generalized active space (GAS) references with the driven similarity renormalization group (DSRG). We employ the x-ray absorption benchmark of organic molecule (XABOOM) set, consisting of 116 transitions from mostly organic molecules [Fransson et al., J. Chem. Theory Comput. 17, 1618 (2021)]. Several approximations to a full-valence active space are examined and benchmarked. Absolute excitation energies and intensities computed with the GAS-DSRG truncated to second-order in perturbation theory are found to systematically underestimate experimental and reference theoretical values. Third-order perturbative corrections significantly improve the accuracy of GAS-DSRG absolute excitation energies, bringing the mean absolute deviation from experimental values down to 0.32eV. The ozone molecule and glyoxylic acid are particularly challenging for second-order perturbation theory and are examined in detail to assess the importance of active space truncation and intruder states.

Resonances close to the first ionization threshold of selenium

Relativistic multichannel theory has been used to calculate the even-parity Rydberg states and odd-parity autoionizing (AI) Rydberg spectrum converging to the limit of second and third excited core states of selenium (Se), taking into account the ionic core dipole polarization effect caused by the Rydberg electron. Six even-parity Rydberg series and are calculated, along with AI Rydberg states converging to or in or symmetry. In general, there is less than a 0.05 difference between calculated and experimental quantum defects. The influence of the perturbers on quantum defects and peak profiles has all been investigated. The accuracy of our calculations allows us to provide a reliable the assignment of the measured AI Rydberg states and the accompanying total angular momentum.

Efficient core-excited state orbital perspective on calculating x-ray absorption transitions in determinant framework

X-ray absorption spectroscopy (XAS) is an explicit probe of the unoccupied electronic structure of materials and an invaluable tool for fingerprinting various electronic properties and phenomena. Computational methods capable of simulating and analyzing such spectra are therefore in high demand for complementing experimental results and for extracting valuable insights therefrom. In particular, a recently proposed first-principles approach titled many-body XAS (MBXAS) [Y. Liang et al., Phys. Rev. Lett. 118, 096402 (2017)], which approximates the final (initial) state as a Slater determinant constructed from Kohn-Sham (KS) orbitals optimized in the absence (presence) of the relevant core electron has shown promising prospects in evaluating the transition amplitudes. In this article, we show that the MBXAS approach can be rederived using a transition operator expressed entirely in the basis of core-excited state KS orbitals and that this reformulation offers substantial practical and conceptual advantages. In addition to circumventing previous issues of convergence with respect to the number of unoccupied ground-state orbitals, the aforementioned representation reduces the computational expense by rendering the calculation of such orbitals unnecessary altogether. The reformulated approach also provides a direct pathway for comparing the many-body approximation with the so-called single-particle treatment and indicates the relative importance in observed XAS intensity of the relaxation of the valence occupied subspace induced by the core excitation. Finally, using the core-excited state basis, we define auxiliary orbitals for x-ray absorption and demonstrate their utility in explaining the spectral intensity by contrasting them with single-particle approximations to the excited state.

Bounding [AnO2]2+ (An = U, Np) covalency by simulated O K-edge and An M-edge X-ray absorption near-edge spectroscopy.

Restricted active space simulations are shown to accurately reproduce and characterise both O K-edge and U M4,5-edge spectra of uranyl in excellent agreement with experimental peak positions and are extended to the Np analogue. Analysis of bonding orbital composition in the ground and O K-edge core-excited states demonstrates that metal contribution is underestimated in the latter. In contrast, An M4/5-edge core-excited states produce bonding orbital compositions significantly more representative of those in the ground state. Quantum Theory of Atoms in Molecules analysis is employed to explain the discrepancy between K- and M-edge data and demonstrates that the location of the core-hole impacts the pattern of electron localisation in core-excited states. An apparent contradiction to this behaviour in neptunyl is rationalised in terms interelectronic repulsion between the unpaired 5f electron and the excited core-electron.

Direct dissociative recombination of HCO+via the core-excited doublet and the lowest quartet states.

The dissociative recombination of HCO+ up to 1 eV collision energy is studied. New calculations for several core-excited HCO states provide improved potential energy surfaces crossing the HCO+ ground state surface in the vicinity of its equilibrium geometry. Wave packet analysis leads to significantly higher contributions of the direct mechanism to the cross section for electron energy ε < 0.7 eV than according to earlier studies [Larson et al., Phys. Rev. A, 2012, 85, 042702]. The limit H + CO(a3Π) is found to be the most probable exit channel. We discuss the improved agreement of theory with the latest experiments [Hamberg et al., J. Phys. Chem., 2014, 118, 6034] resulting from combination with the most recent calculations of the indirect process [Fonseca dos Santos et al., J. Chem. Phys., 2014, 140, 164308]. For the lowest quartet surfaces some vibrational states and their population and depopulation (mediated by spin-orbit coupling) are examined.

Resonant double-core excitations with ultrafast, intense X-ray pulses

Intense few-to-sub-femtosecond soft X-ray pulses can produce neutral, two-site excited double-core-hole states by promoting two core electrons to the same unoccupied molecular orbital. We theoretically investigate double nitrogen K-edge excitations of nitrous oxide (N 2 O) with multiconfigurational electronic structure calculations. We show that the second core-excitation energy is reduced with respect to its ground state value. A site-selective double core-excitation mechanism using intense few-femtosecond x-rays is investigated using time-dependent Schrödinger equation (TDSE) simulations. The subsequent two-step Auger–Meitner and two-electrons-one-electron decay spectra of the double core-excited states are analysed using a Mulliken population analysis of the multiconfirational wavefunctions. The change in the electron emission lineshape between the absorption of 1 or 2 photons in the resonant core-excitation is predicted by combining this approach with the TDSE simulations. We examine the possibility of resolving the double core-excited states with X-ray pump-probe techniques by calculating the chemical shifts of the core-electron binding energy of the core-excited states and decay products.

Transition energies and transition probabilities for the core-excited state [formula omitted] of Li-like ions with [formula omitted] 6–92

The transition energies and radiative transition probabilities for the transition from the (1s2s2p)3/2 group to the ground state 1s22s involving the electric dipole (E1) and magnetic quadrupole (M2) transitions have been systematically calculated for ions along the Li isoelectronic sequence from Z=6 to Z=92. The calculations are performed by using the full relativistic multi-configuration Dirac–Fock (MCDF) method, in which the leading quantum electrodynamics (QED) shifts and the frequency dependence of the Breit interaction are also considered. The present calculation results are in good agreement with available previous results. It is found that the transition probabilities generally increase along with nuclear number Z; however, the abnormal behavior with the minima transition probabilities at Z=28 and Z=25 emerges in the [(1s2s)02p3/2]3/2→1s22s via E1 transition and the [(1s2s)12p3/2]3/2→1s22s via M2 transition, respectively; the M2 transition probabilities become comparable with that of E1 in mid-Z ions, and particularly for the q line of Z=28 ion, the M2 and E1 transition probabilities would be of the same order of magnitude. In addition, the present results show that the electron correlations impact on the energy levels and transition probabilities mainly work on the low-Z ions, while, the QED and Breit effects mainly work on the high-Z ions. This work should be of particular interest to the analysis of the spectrum and the effects of multipole mixing on the X-ray properties.

Shell-model study on spectroscopic properties in the region “south” of Pb208

Background: The properties of nuclei located in the region ``south'' of $^{208}\mathrm{Pb}$ are important for understanding the $r$-process nucleosynthesis. While some isomeric states and their spectroscopic properties have been investigated experimentally in neutron-rich Pb, Tl, and Hg isotopes recently, a large portion of the area still remains unreachable.Purpose: We aim to study the properties of nuclei in the region south of $^{208}\mathrm{Pb}$, including the binding and excitation energies and electromagnetic properties, in order to predict unknown properties of these nuclei, such as isomerism, utilizing a theoretical model which describes the experimentally known properties precisely. We also address whether the $N=126$ shell closure is robust or not when the proton number decreases from $^{208}\mathrm{Pb}$.Methods: We performed large-scale shell-model calculations with a new Hamiltonian suggested in the present work. The model space is taken as the 5 proton orbits within $50&lt;Z\ensuremath{\leqslant}82$ and the 13 neutron orbits within $82&lt;N\ensuremath{\leqslant}184$, and one-particle-one-hole excitation is allowed across the $N=126$ gap. The Hamiltonian is constructed by combining the existing Hamiltonians, KHHE (with adjustment of its proton-proton part) and KHPE, and the monopole-based universal interaction.Results: The shell-model results well reproduce the experimentally observed binding energies and spectroscopic properties, such as isomerism, core excitation, and electromagnetic properties. Some possible isomeric states in neutron-rich Pb, Tl, and Hg isotopes are predicted with transition energies and half-lives. The $N=126$ shell gap is predicted to be robust from $Z=82$ down to 72 with minor reduction. We also examine the effective charges and the quenching of the $g$ factors suitable for this region by comparisons between observed and calculated electromagnetic properties.Conclusions: A new Hamiltonian is constructed for nuclei in the region south of $^{208}\mathrm{Pb}$, mainly including Pb, Tl, Hg, Au, Pt, Ir, Os, Re, and W isotopes around $N=126$, and provides them reasonable descriptions on nuclear properties including binding energies, excitation energies, and electromagnetic properties through shell-model studies. The present Hamiltonian and discussions provide fruitful information for future measurements and theoretical investigations for nuclei in this region, especially those around the $N=126$ shell, including the recommended effective charges and $g$ factors, the predicted binding energies, isomeric states, and core-excited states.

Excitonic Effects in X-ray Absorption Spectra of Fluoride Salts and Their Surfaces

Given their natural abundance and thermodynamic stability, fluoride salts may appear as evolving components of electrochemical interfaces in Li-ion batteries and emergent multivalent ion cells. This is due to the practice of employing electrolytes with fluorine-containing species (salt, solvent, or additives) that electrochemically decompose and deposit on the electrodes. Operando X-ray absorption spectroscopy (XAS) can probe the electrode–electrolyte interface with a single-digit nanometer depth resolution and offers a wealth of insights into the evolution and Coulombic efficiency or degradation of prototype cells, provided that the spectra can be reliably interpreted in terms of local oxidation state, atomic coordination, and electronic structure about the excited atoms. To this end, we explore fluorine K-edge XAS of mono- (Li, Na, and K) and di-valent (Mg, Ca, and Zn) fluoride salts from a theoretical standpoint and discover a surprising level of detailed electronic structure information about these materials despite the relatively predictable oxidation state and ionicity of the fluoride anion and the metal cation. Utilizing a recently developed many-body approach based on the ΔSCF method, we calculate the XAS using density functional theory and experimental spectral profiles are well reproduced despite some experimental discrepancies in energy alignment within the literature, which we can correct for in our simulations. We outline a general methodology to explain shifts in the main XAS peak energies in terms of a simple exciton model and explain line-shape differences resulting from the mixing of core-excited states with metal d character (for K and Ca specifically). Given ultimate applications to evolving interfaces, some understanding of the role of surfaces and their terminations in defining new spectral features is provided to indicate the sensitivity of such measurements to changes in interfacial chemistry.

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States.

The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

A critical compilation of experimental data on the 1s2[formula omitted] core-excited states of Li-like ions from carbon to uranium

Recent advance in calculations of energy levels of the 1s2l2l′ core-excited states for ions along the Li isoelectronic sequence from carbon to uranium suggested that theoretical predictions for the 1s22l-1s2l2l′ transitions are significantly more precise than most of the experimental results available today and can thus be used for calibrating measured X-ray spectra. This suggestion is verified in the present work by comparison with benchmark experimental results. We present a critical compilation of all available experimental data on the energy levels of the 1s2l2l′ core-excited states of Li-like ions. The compiled experimental data include uncertainty estimates, which allowed proper weighted averaging and comparison with theoretical calculations. This comparison confirmed the supremacy of the most advanced theoretical calculations of the 1s2l2l′ levels over the best experimental results available today.

Assessing the performance of ΔSCF and the diagonal second-order self-energy approximation for calculating vertical core excitation energies.

Vertical core excitation energies are obtained using a combination of the ΔSCF method and the diagonal second-order self-energy approximation. These methods are applied to a set of neutral molecules and their anionic forms. An assessment of the results with the inclusion of relativistic effects is presented. For core excitations involving delocalized symmetry orbitals, the applied composite method improves upon the overestimation of ΔSCF by providing approximate values close to experimental K-shell transition energies. The importance of both correlation and relaxation contributions to the vertical core-excited state energies, the concept of local and nonlocal core orbitals, and the consequences of breaking symmetry are discussed.

Changes in polarization dictate necessary approximations for modeling electronic deexcitation intensity: Application to x-ray emission

We systematically investigate the underlying relations among different levels of approximation for simulating electronic de-excitations, with a focus on modeling X-ray emission spectroscopy (XES). Using Fermi's golden rule and explicit modeling of the initial, core-excited state and the final, valence-hole state, we show that XES can be accurately modeled by using orbital optimization for the various final states within a Slater-determinant framework. However, in this paper, we introduce a much cheaper approach reliant only on a single self-consistent field for all the final states, and show that it is typically sufficient. Further approximations reveal that these fundamentally many-body transitions can be reasonably approximated by projections of ground state orbitals, but that the ground state alone is insufficient. Furthermore, except in cases where the core-ionization induces negligible changes in polarization, linear-response approaches within the adiabatic approximation will have difficulty in accurately modeling de-excitation to the core level. Therefore, change in the net dipole moment of the valence electrons can serve as a metric for the validity of the linear-response approximation.

Generalized oscillator strength of the core-excited states of molecular nitrogen studied by nonresonant inelastic x-ray scattering

Fast electron impact was used to study the generalized oscillator strengths of the inner-shell excitations in atoms and molecules previously. In this work, a nonresonant inelastic x-ray scattering technique is extended to determine the generalized oscillator strengths of $(1{\ensuremath{\sigma}}_{g}\ensuremath{\rightarrow}1{\ensuremath{\pi}}_{g})+(1{\ensuremath{\sigma}}_{u}\ensuremath{\rightarrow}1{\ensuremath{\pi}}_{g})$ inner-shell excitations of molecular nitrogen in the squared momentum transfer range of 0.86 to 14.40 a.u. at a photon energy of about 10 keV and an energy resolution of about 1.3 eV. The present generalized oscillator strength strictly follows the first Born approximation and thus provides a rigorous test to the previously calculated results and the experimental ones measured by the electron energy loss spectroscopy. The presently extrapolated optical oscillator strength at zero momentum transfer is in accord with most experimental results and the theoretical data with the correlation effect considered carefully. This work indicates that the nonresonant inelastic x-ray scattering technique is a powerful tool to study the core excitation mechanism in atoms and molecules.

Oscillator Strengths in the Framework of Equation of Motion Multilevel CC3.

We present an efficient implementation of the equation of motion oscillator strengths for the closed-shell multilevel coupled cluster singles and doubles with perturbative triples method (MLCC3) in the electronic structure program eT. The orbital space is split into an active part treated with CC3 and an inactive part computed at the coupled cluster singles and doubles (CCSD) level of theory. Asymptotically, the CC3 contribution scales as floating-point operations, where nV is the total number of virtual orbitals while nv and no are the number of active virtual and occupied orbitals, respectively. The CC3 contribution, thus, only scales linearly with the full system size and can become negligible compared to the cost of CCSD. We demonstrate the capabilities of our implementation by calculating the ultraviolet–visible spectrum of azobenzene and a core excited state of betaine 30 with more than 1000 molecular orbitals.

Core-hole delocalization for modeling x-ray spectroscopies: A cautionary tale.

The influence of core-hole delocalization for x-ray photoelectron, x-ray absorption, and x-ray emission spectrum calculations is investigated in detail using approaches including response theory, transition-potential methods, and ground state schemes. The question of a localized/delocalized vacancy is relevant for systems with symmetrically equivalent atoms, as well as near-degeneracies that can distribute the core orbitals over several atoms. We show that the issues relating to core-hole delocalization are present for calculations considering explicit core-hole states, e.g., when using a core-excited or core-ionized reference state or for fractional occupation numbers. As electron correlation eventually alleviates the issues, but even when using coupled-cluster single-double and perturbative triple, there is a notable discrepancy between core-ionization energies obtained with localized and delocalized core-holes (0.5eV for the carbon K-edge). Within density functional theory, the discrepancy correlates with the exchange interaction involving the core orbitals of the same spin symmetry as the delocalized core-hole. The use of a localized core-hole allows for a reasonably good inclusion of relaxation at a lower level of theory, whereas the proper symmetry solution involving a delocalized core-hole requires higher levels of theory to account for the correlation effects involved in orbital relaxation. For linear response methods, we further show that if x-ray absorption spectra are modeled by considering symmetry-unique sets of atoms, care has to be taken such that there are no delocalizations of the core orbitals, which would otherwise introduce shifts in absolute energies and relative features.