Core-excited States Research Articles

Nonlinear spectral dispersion in resonant Auger scattering from SF6 for studying nuclear potentials and dynamics

In this study, we integrate experimental observations and theoretical models to elucidate the complex phenomena observed in the resonant S K-edge Auger scattering spectra of the SF6 molecule. A two-dimensional spectral map, constructed of incident photon energy and kinetic energy of the emitted Auger electron, is shown to be a versatile tool for understanding a character of the core-excited potential energy surface and change of the molecular geometry. Our findings reveal how the distinct dispersion behavior of multiple spectral lines enables mapping of ultrafast dynamics within the short-lived core-excited states. Our results confirm the presence of nuclear dynamics in the S1s−16a1g1 and S1s−16t1u1 core-excited states, while dynamics is absent in the S1s−17t1u1 state. Using a combination of analysis, simulations with Coulomb model potentials, and a simple analytical approximation, we qualitatively demonstrate how the varying characteristics of spectral dispersion—classified as Raman, non-Raman, and anti-Raman—mirror the relative gradients of the intermediate and final states in the resonant x-ray scattering process. This insight allows for the effective mapping of molecular potential energy curves, offering a prospective tool on the underlying mechanisms of resonant Auger scattering and its potential for probing molecular dynamics. Published by the American Physical Society 2024

Capturing Coupled Structural and Electronic Motions During Excited-State Intramolecular Proton Transfer via Computational Multiedge Resonant Inelastic X-ray Scattering.

Proton transfer processes form the foundation of many chemical processes. In excited-state intramolecular proton transfer (ESIPT) processes, ultrafast proton transfer is impulsively initiated through light. Here, we explore time-dependent coupled atomic and electronic motions during and following ESIPT through computational time-resolved resonant inelastic X-ray scattering (RIXS). Excited-state ab initio molecular dynamics simulations combined with time-dependent density functional theory calculations were performed for a model ESIPT system, 10-hydroxybenzo[h]quinoline, to obtain transient RIXS signatures. The RIXS spectra at both the nitrogen and oxygen K-edges were computed to resolve the electronic and atomic structural dynamics from both the proton donor and acceptor perspective. The results demonstrate that RIXS provides unprecedented details of the local electronic structure, the coupling between different core and valence excited electronic states, and the reorganization of the electronic structure coupled to the proton transfer process. We also develop a spectroscopic ruler correlating spectral shifts of a RIXS peak to the proton transfer distance during ESIPT. This work highlights the exciting potential of time-resolved RIXS experiments at newly commissioned soft X-ray free electron laser facilities for measuring coupled electronic and structural changes during ultrafast chemical processes.

Exploring the Influence of Approximations for Simulating Valence Excited X-ray Spectra.

First-principles simulations of excited-state X-ray spectra are becoming increasingly important to interpret the wealth of electronic and geometric information contained within femtosecond X-ray absorption spectra recorded at X-ray Free Electron Lasers (X-FELs). However, because the transition dipole matrix elements must be calculated between two excited states (i.e., the valence excited state and the final core excited state arising from the initial valence excited state) of very different energies, this can be challenging and time-consuming to compute. Herein using two molecules, protonated formaldimine and cyclobutanone, we assess the ability of n-electron valence-state perturbation theory (NEVPT2), equation-of-motion coupled-cluster theory (EOM-CCSD), linear-response time-dependent density functional theory (LR-TDDFT) and the maximum overlap method (MOM) to describe excited state X-ray spectra. Our study focuses in particular on the behavior of these methods away from the Franck-Condon geometry and in the vicinity of important topological features of excited-state potential energy surfaces, namely, conical intersections. We demonstrate that the primary feature of excited-state X-ray spectra is associated with the core electron filling the hole created by the initial valence excitation, a process that all of the methods can capture. Higher energy states are generally weaker, but importantly much more sensitive to the nature of the reference electronic wave function. As molecular structures evolve away from the Franck-Condon geometry, changes in the spectral shape closely follow the underlying valence excitation, highlighting the importance of accurately describing the initial valence excitation to simulate the excited-state X-ray absorption spectra.

Core-excited states leading to the high-spin band structure in $$^{93}$$Nb nucleus

Core-excited states leading to the high-spin band structure in $$^{93}$$Nb nucleus

Highly Accurate and Robust Constraint-Based Orbital-Optimized Core Excitations.

We adapt our recently developed constraint-based orbital-optimized excited-state method (COOX) for the computation of core excitations. COOX is a constrained density functional theory (cDFT) approach based on excitation amplitudes from linear-response time-dependent DFT (LR-TDDFT), and has been shown to provide accurate excitation energies and excited-state properties for valence excitations within a spin-restricted formalism. To extend COOX to core-excited states, we introduce a spin-unrestricted variant which allows us to obtain orbital-optimized core excitations with a single constraint. Using a triplet purification scheme in combination with the constrained unrestricted Hartree-Fock formalism, scalar-relativistic zero-order regular approximation corrections, and a semiempirical treatment of spin-orbit coupling, COOX is shown to produce highly accurate results for K- and L-edge excitations of second- and third-period atoms with subelectronvolt errors despite being based on LR-TDDFT, for which core excitations pose a well-known challenge. L- and M-edge excitations of heavier atoms up to uranium are also computationally feasible and numerically stable, but may require more advanced treatment of relativistic effects. Furthermore, COOX is shown to perform on par with or better than the popular ΔSCF approach while exhibiting more robust convergence, highlighting it as a promising tool for inexpensive and accurate simulations of X-ray absorption spectra.

Attosecond Probing of Coherent Vibrational Dynamics in CBr4.

A coherent vibrational wavepacket is launched and manipulated in the symmetric stretch (a1) mode of CBr4, by impulsive stimulated Raman scattering (ISRS) from nonresonant 400 nm laser pump pulses with various peak intensities on the order of tens of 1012 W/cm2. Extreme ultraviolet (XUV) attosecond transient absorption spectroscopy (ATAS) records the wavepacket dynamics as temporal oscillations in XUV absorption energy at the bromine M4,5 3d3/2,5/2 edges around 70 eV. The results are augmented by nuclear time-dependent Schrödinger equation simulations. Slopes of the (Br 3d3/2,5/2)-110a1* core-excited state potential energy surface (PES) along the a1 mode are calculated to be -9.4 eV/Å from restricted open-shell Kohn-Sham calculations. Using analytical relations derived for the small-displacement limit and the calculated slopes of the core-excited state PES, a deeper insight into the vibrational dynamics is obtained by retrieving the experimental excursion amplitude of the vibrational wavepacket and the amount of population transferred to the vibrational first-excited state as a function of pump-pulse peak intensity. Experimentally, the results show that XUV ATAS is capable of resolving oscillations in the XUV absorption energy on the order of a few to tens of meV with tens of femtosecond time precision. This corresponds to change in C-Br bond length on the order of 10-4 to 10-3 Å. The results and the analytic relationships offer a clear physical picture, on multiple levels of understanding, of how the pump-pulse peak intensity controls the vibrational dynamics launched by nonresonant ISRS in the small-displacement limit.

Attosecond impulsive stimulated X-ray Raman scattering in liquid water.

We report the measurement of impulsive stimulated x-ray Raman scattering in neutral liquid water. An attosecond pulse drives the excitations of an electronic wavepacket in water molecules. The process comprises two steps: a transition to core-excited states near the oxygen atoms accompanied by transition to valence-excited states. Thus, the wavepacket is impulsively created at a specific atomic site within a few hundred attoseconds through a nonlinear interaction between the water and the x-ray pulse. We observe this nonlinear signature in an intensity-dependent Stokes Raman sideband at 526 eV. Our measurements are supported by our state-of-the-art calculations based on the polarization response of water dimers in bulk solvation and propagation of attosecond x-ray pulses at liquid density.

Bonding and Interactions in UO22+ for Ground and Core Excited States: Extracting Chemistry from Molecular Orbital Calculations.

Theoretical analyses of actinyls are necessary in order to understand and correctly interpret the chemical and physical properties of these molecules. Here, wave functions of Uranyl, UO22+, are considered for the ground state and for the core excited states where an electron is promoted from the U 3d5/2 shell into a low-lying unoccupied orbital that is U 5f antibonding with the ligand, O, orbitals. A focus is on the application of novel theoretical methods to the analysis of these wave functions so that measurements, especially with X-ray absorption, can be related to the UO22+ chemical bonding. The bond covalency is examined with these theoretical methods. The study includes how the covalent character is different for the ground and excited configurations and how this character changes as the U-O distance is changed. Furthermore, analyses are mode of how many-body effects may modify excitation energies and X-ray adsorption intensities. This includes determining the extent to which a single configuration provides a satisfactory model for the UO22+ wave functions. Two distinct types of many-body effects are considered. One involves the angular momentum coupling of the open shell electrons in the excited states to yield correct multiplets. The second adds excitations from shells that are bonding into the antibonding open shell space. These excitations are essential to properly describe the X-ray adsorption. While these many-body effects must be taken into account, their importance and their role can be explained and understood using orbitals and orbital occupations.

Measurement of coherent vibrational dynamics with X-ray Transient Absorption Spectroscopy simultaneously at the Carbon K- and Chlorine L2,3- edges

X-ray Transient Absorption Spectroscopy (XTAS) is a powerful probe for ultrafast molecular dynamics. The evolution of XTAS signal is controlled by the shapes of potential energy surfaces of the associated core-excited states, which are difficult to directly measure. Here, we study the vibrational dynamics of Raman activated CCl4 with XTAS targeting the C 1s and Cl 2p electrons. The totally symmetric stretching mode leads to concerted elongation or contraction in bond lengths, which in turn induce an experimentally measurable red or blue shift in the X-ray absorption energies associated with inner-shell electron excitations to the valence antibonding levels. The ratios between slopes of different core-excited potential energy surfaces (CEPESs) thereby extracted agree very well with Restricted Open-Shell Kohn-Sham calculations. The other, asymmetric, modes do not measurably contribute to the XTAS signal. The results highlight the ability of XTAS to reveal coherent nuclear dynamics involving < 0.01 Å atomic displacements and also provide direct measurement of forces on CEPESs.

Observation of a core-excited dipole-bound state ∼1eV above the electron detachment threshold in cryogenically cooled acetylacetonate.

Dipole-bound states in anions exist when a polar neutral core binds an electron in a diffuse orbital through charge-dipole interaction. Electronically excited polar neutral cores can also bind an electron in a diffuse orbital to form Core-Excited Dipole-Bound States (CE-DBSs), which are difficult to observe because they usually lie above the electron detachment threshold, leading to very short lifetimes and, thus, unstructured transitions. We report here the photodetachment spectroscopy of cryogenically cooled acetylacetonate anion (C5H7O2-) recorded by detecting the neutral radical produced upon photodetachment and the infrared spectroscopy in He-nanodroplets. Two DBSs were identified in this anion. One of them lies close to the electron detachment threshold (∼2.74eV) and is associated with the ground state of the radical (D0-DBS). Surprisingly, the other DBS appears as resonant transitions at 3.69eV and is assigned to the CE-DBS associated with the first excited state of the radical (D1-DBS). It is proposed that the resonant transitions of the D1-DBS are observed ∼1eV above the detachment threshold because its lifetime is determined by the internal conversion to the D0-DBS, after which the fast electron detachment takes place.

Quantifying Covalency and Environmental Effects in RASSCF-Simulated O K-Edge XANES of Uranyl.

A RASSCF approach to simulate the O K-edge XANES spectra of uranyl is employed, utilizing three models that progressively improve the representation of the local crystal environment. Simulations successfully reproduce the observed three-peak profile of the experimental spectrum and confirm peak assignments made by Denning. The [UO2Cl4]2- model offers the best agreement with experiment, with peak positions (to within 1 eV) and relative peak separations accurately reproduced. Establishing a direct link between a specific electronic transition and peak intensity is complicated, as a large number of possible transitions can contribute to the overall peak profile. Furthermore, a relationship between oxygen character in the antibonding orbital and the strength of the transition breaks down when using a variety of orbital composition approaches at larger excitation energy. Covalency analysis of the U-O bond in both the ground- and excited-state reveals a dependence on the crystal environment. Orbital composition analysis reveals an underestimation of the uranium contribution to ground-state bonding orbitals when probing O K-edge core-excited states, regardless of the uranyl model employed. However, improving the environmental model provides core-excited state electronic structures that are better representative of that of the ground-state, validating their use in the determination of covalency and bonding.

Detailed structure of Sn131 populated in the β decay of isomerically purified In131 states

The excited structure of the single-hole nucleus Sn131 populated by the β− decay of In131 was investigated in detail at the ISOLDE facility at CERN. This new experiment took advantage of isomeric purification capabilities provided by resonant ionization, making it possible to independently study the decay of each isomer for the first time. The position of the first-excited νh11/2 neutron-hole state was confirmed via an independent mass spectroscopy experiment performed at the Ion Guide Isotope Separator On-Line facility at the University of Jyväskylä. The level scheme of Sn131 was notably expanded with the addition of 31 new γ-ray transitions and 22 new excited levels. The γ-emitting excited levels above the neutron separation energy in Sn131 were investigated, revealing a large number of states, which in some cases decay by transitions to other neutron-unbound states. Our analysis showed the dependence between the population of these states in Sn131 and the β-decaying In131 state feeding them. Profiting from the isomer selectivity, it was possible to estimate the direct β feeding to the 3/2+ ground and 11/2− isomeric states, disentangling the contributions from the three indium parent states. This made possible to resolve the discrepancies in logft for first-forbidden transitions observed in previous studies, and to determine the β-delayed neutron decay probability (Pn) values of each indium isomers independently. The first measurement of subnanosecond lifetimes in Sn131 was performed in this work. A short T1/2=18(4)−ps value was measured for the 1/2+ neutron single-hole 332-keV state, which indicates an enhanced l-forbidden M1 behavior for the ν3s1/2−1→ν3d3/2−1 transition. The measured half-lives of high-energy states populated in the β decay of the (21/2+) second isomeric state (In131m2) provided valuable information on transition rates, supporting the interpretation of these levels as core-excited states analogous to those observed in the doubly-magic Sn132. Published by the American Physical Society 2024

The x-ray absorption spectrum of the tert-butyl radical: An experimental and computational investigation.

We report the x-ray absorption spectrum (XAS) of the tert-butyl radical, C4H9. The radical was generated pyrolytically from azo-tert-butane, and the XAS of the pure radical was obtained by subtraction of spectra recorded at different temperatures. The bands in the XAS were assigned by abinitio calculations that are in very good agreement with the experimental data. The lowest energy signal in the XAS is assigned to the C1s electron transition from the central carbon atom to the singly occupied molecular orbital (SOMO), while higher transitions correspond to C1s excitations from terminal carbon atoms. Furthermore, we investigated the fragmentation of the radical following resonant C1s excitation by electron-ion-coincidence spectroscopy. Several fragmentation channels were identified. The C1s excitation of the terminal carbons is associated with a stronger fragmentation tendency compared to the lowest C1s excitation of the central carbon into the SOMO. For this core excited state, we still observe an intact parent ion, C4H9+, and a comparatively higher tendency to dissociate into CH3+ + C3H6+.

Core-excited states in 105Cd

105Cd was produced in the 96Mo+12C fusion/evaporation reaction, performed at NIPNE, Bucharest-Magurele, Romania. Various excited states of positive- and negative-parities were populated. Picosecond half-lives were measured by using the Differential Decay Curve Method (DDCM) method, allowing to control the side feeding of the states of interest. New data were obtained for the half-lives of the 11/2+, 15/2− and 19/2− 105Cd states. Reduced electric quadrupole transition strengths were calculated and compared to the neighboring odd-A and even-A cadmium nuclei. The particle-core weak coupling approach was used to interpret excited states of 105Cd in the light of the new data.

Core-Hole Coherent Spectroscopy in Molecules.

We study the ultrafast dynamics initiated by a coherent superposition of core-excited states of nitrous oxide molecule. Using high-level abinitio methods, we show that the decoherence caused by the electronic decay and the nuclear dynamics is substantially slower than the induced ultrafast quantum beatings, allowing the system to undergo several oscillations before it dephases. We propose a proof-of-concept experiment using the harmonic up-conversion scheme available at x-ray free-electron laser facilities to trace the evolution of the created core-excited-state coherence through a time-resolved x-ray photoelectron spectroscopy.

Influence of Selective Carbon 1s Excitation on Auger-Meitner Decay in the ESCA Molecule.

Two-dimensional spectral mapping is used to visualize how resonant Auger-Meitner spectra are influenced by the site of the initial core-electron excitation and the symmetry of the core-excited state in the trifluoroethyl acetate molecule (ESCA). We observe a significant enhancement of electron yield for excitation of the COO 1s → π* and CF3 1s → σ* resonances unlike excitation at resonances involving the CH3 and CH2 sites. The CF3 1s → π* and CF3 1s → σ* resonance spectra are very different from each other, with the latter populating most valence states equally. Two complementary electronic structure calculations for the photoelectron cross section and Auger-Meitner intensity are shown to effectively reproduce the site- and state-selective nature of the resonant enhancement features. The site of the core-electron excitation and the respective final state hole locality increase the sensistivity of the photoelectron signal at specific functional group sites. This showcases resonant Auger-Meitner decay as a potentially powerful tool for selectively probing structural changes at specific functional group sites of polyatomic molecules.

GUGA-based MRCI approach with core-valence separation approximation (CVS) for the calculation of the core-excited states of molecules.

We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core-Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states.

Resonant Auger decay of dissociating CH3I near the I 4d threshold.

Resonant Auger processes provide a unique perspective on electronic interactions and excited vibrational and electronic states of molecular ions. Here, new data are presented on the resonant Auger decay of excited CH3I in the region just below the I 4d-1 ionization threshold. The resonances include the Rydberg series converging to the five spin-orbit and ligand-field split CH3I (I 4d-1) thresholds, as well as resonances corresponding to excitation from the I 4d5/2,3/2 orbitals into the σ* lowest unoccupied molecular orbital. This study focuses on participator decay that populates the lowest lying states of CH3I+, in particular, the X̃2E3/2 and 2E1/2 states, and on spectator decay that populates the lowest-lying (CH3I2+)σ* states of CH3I+. The CH3I (I 4d-1)σ* resonances are broad, and dissociation to CH3 + I competes with the autoionization of the core-excited states. Auger decay as the molecule dissociates produces a photoelectron spectrum with a long progression (up to v3+ ∼ 25) in the C-I stretching mode of the X̃2E3/2 and 2E1/2 states, providing insights into the shape of the dissociative core-excited surface. The observed spectator decay processes indicate that CH3I+ is formed on the repulsive wall of the lower-lying (CH3I2+)σ* potentials, and the photon-energy dependence of the processes provides insights into the relative slopes of the (4d-1)σ* and (CH3I2+)σ* potential surfaces. Data are also presented for the spectator decay of higher lying CH3I (I 4d-1)nl Rydberg resonances. Photoelectron angular distributions for the resonant Auger processes provide additional information that helps distinguish these processes from the direct ionization signal.

Time-Dependent Resonant Inelastic X-ray Scattering of Pyrazine at the Nitrogen K-Edge: A Quantum Dynamics Approach.

We calculate resonant inelastic X-ray scattering spectra of pyrazine at the nitrogen K-edge in the time domain including wavepacket dynamics in both the valence and core-excited state manifolds. Upon resonant excitation, we observe ultrafast non-adiabatic population transfer between core-excited states within the core-hole lifetime, leading to molecular symmetry distortions. Importantly, our time-domain approach inherently contains the ability to manipulate the dynamics of this process by detuning the excitation energy, which effectively shortens the scattering duration. We also explore the impact of pulsed incident X-ray radiation, which provides a foundation for state-of-the-art time-resolved experiments with coherent pulsed light sources.

Rebuilding the vibrational wavepacket in TRAS using attosecond X-ray pulses

Time-resolved X-ray photoelectron spectroscopy (TXPS) is a well-established technique to probe coherent nuclear wavepacket dynamics using both table-top and free-electron-based ultrafast X-ray lasers. Energy resolution, however, becomes compromised for a very short pulse duration in the sub-femtosecond range. By resonantly tuning the X-ray pulse to core-excited states undergoing Auger decay, this drawback of TXPS can be mitigated. While resonant Auger-electron spectroscopy (RAS) can recover the vibrational structures not hidden by broadband excitation, the full reconstruction of the wavepacket is a standing challenge. Here, we theoretically demonstrate how the complete information of a nuclear wavepacket, i.e., the populations and relative phases of the vibrational states constituting the wavepacket, can be retrieved from time-resolved RAS (TRAS) measurements. Thus, TRAS offers key insights into coupled nuclear and electronic dynamics in complex systems on ultrashort timescales, providing an alternative to leverage femtosecond and attosecond X-ray probe pulses.