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The effect of inner-shell photodetachment channels on outer-shell photodetachment is investigated using the R-matrix method. The simplest multishell closed-shell negative ion, Li - , is examined near the 1s detachment threshold and the results show that the interchannel coupling significantly alters the shapes and magnitudes of the valence photodetachment cross sections in this energy region.
The fragmentation of molecular cations following inner-shell decay processes in molecules containing heavy elements underpins the X-ray damage effects observed in X-ray scattering measurements of biological and chemical materials, as well as in medical applications involving Auger electron-emitting radionuclides. Traditionally, these processes are modeled using simulations that describe the electronic structure at an atomic level, thereby omitting molecular bonding effects. This work addresses the gap by introducing a novel approach that couples Auger–Meitner decay to nuclear dynamics across multiple decay steps, by developing a decay spawning dynamics algorithm and applying it to potential energy surfaces characterized with ab initio molecular dynamics simulations. We showcase the approach on a model decay cascade following K-shell ionization of IBr and subsequent Kβ fluorescence decay. We examine two competing channels that undergo two decay steps, resulting in ion pairs with a total 3+ charge state. This approach provides a continuous description of the electron transfer dynamics occurring during the multistep decay cascade and molecular fragmentation, revealing the combined inner-shell decay and charge transfer time scale to be approximately 75 fs. In conclusion, our computed kinetic energies of ion fragments show good agreement with experimental data.
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. Here, 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.
XUV multiphoton ionization of molecules is commonly used in free-electron laser experiments to study charge transfer dynamics. However, molecular dissociation and electron dynamics, such as multiple photon absorption, Auger decay, and charge transfer, often happen on competing time scales, and the contributions of individual processes can be difficult to unravel. We experimentally investigate the Coulomb explosion dynamics of methyl iodide upon core–hole ionization of the shallow inner-shell of iodine (4d) and classically simulate the fragmentation by phenomenologically introducing ionization dynamics and charge transfer. Under our experimental conditions with medium fluence and relatively long XUV pulses (~75 fs), we find that fast Auger decay prior to charge transfer significantly contributes to the charging mechanism, leading to a yield enhancement of higher carbon charge states upon molecular dissociation. Furthermore, we argue for the existence of another charging mechanism for the weak fragmentation channels leading to triply charged carbon atoms. This study shows that classical simulations can be a useful tool to guide the quantum mechanical description of the femtosecond dynamics upon multiphoton absorption in molecular systems.
Understanding inner-shell decay processes in heavy-element molecules is essential for unraveling x-ray-induced photodynamics and advancing molecular imaging techniques. Here, in this study, we investigate the influence of atomic substitution on core-hole relaxation dynamics and molecular fragmentation in Br 2 and IBr, initiated by x-ray ionization absorption at the Br K-edge. Using a combination of x-ray/ion coincidence measurements and Monte Carlo/molecular dynamics simulations, we track the charge distribution and the kinetic energy release (KER) of fragment ions with a total charge from 2+ to 8+. For both molecules, the simulated KER values show good agreement with experiment across different fragmentation channels. Our comparison reveals that substituting Br with the heavier I atom in IBr has a minimal impact on the inner-shell electronic decay process but significantly influences nuclear motion, leading to slower dissociation and thus a KER close to the Coulomb limit—an effect attributed to the atomic mass. These findings highlight the interplay between electronic and nuclear effects in molecular fragmentation, particularly in heavy-element species, and provide new insights into medical therapies, structural biology, and astrophysics.
Molecules can sequentially absorb multiple photons when irradiated by an intense X-ray pulse from a free-electron laser. If the time delay between two photoabsorption events can be determined, this enables pump-probe experiments with a single X-ray pulse, where the absorption of the first photon induces electronic and nuclear dynamics that are probed by the absorption of the second photon. Here we show a realization of such a single-pulse X-ray pump-probe scheme on N 2 molecules, using the X-ray induced dissociation process as an internal clock that is read out via coincident detection of photoelectrons and fragment ions. By coincidence analysis of the kinetic energies of the ionic fragments and photoelectrons, the transition from a bound molecular dication to two isolated atomic ions is observed through the energy shift of the inner-shell electrons. Via ab-initio simulations, we are able to map characteristic features in the kinetic energy release and photoelectron spectrum to specific delay times between photoabsorptions. In contrast to previous studies where nuclear motions were typically revealed by measuring ion kinetics, our work shows that inner-shell photoelectron energies can also be sensitive probes of nuclear dynamics, which adds one more dimension to the study of light-matter interactions with X-ray pulses.
The chemical shifts of inner-shell atomic orbitals are highly sensitive to chemical bonding and molecular structure. In evolving systems, however, the spectra of distinct molecular species and geometries overlap, obscuring the underlying chemical dynamics. Here we demonstrate the use of electron–ion covariance analysis to combine the structural sensitivity of Coulomb explosion imaging with inner-shell spectroscopy, yielding geometry-specific spectra of transient and product species. We apply this approach to the excited state dynamics of CS 2 probed by ionization above the S 2p edge. Electron–ion covariance with time- and momentum-selected S + and S 2+ ions isolates distinct S 2p photoelectron spectra for ground-state CS 2 , bent photoexcited CS 2 , the CS photoproduct, and bare atomic sulfur ─ species whose spectra overlap strongly in the channel-averaged measurement. Clear chemical shifts are observed in the covariance photoelectron spectrum for each of these species, all of which are consistent with high-level calculations. Here, by extracting the atomic S contribution to the photoelectron spectrum in a finely time-resolved manner we can disentangle this contribution to the overall time-resolved photoelectron spectrum as the photodissociation proceeds. These results demonstrate the promise of electron–ion covariance as a general approach to geometry-resolved inner-shell spectroscopy, opening a route to tracking structural evolution through chemical shifts in complex photoexcited molecules.
When dielectrics are hit with intense infrared (IR) laser pulses, transient metalization can occur. The initial attosecond dynamics behind this metallization are not entirely understood. Therefore, simulations are needed to understand this process and to help interpret experimental observations of it, such as with attosecond transient absorption (ATA). In this paper, we present first-principles simulations of ATA based on bulk-mimicking clusters and real-time time-dependent density functional theory (RT-TDDFT), with Koopmans-tuned range-separated hybrid functionals and Gaussian basis sets. Our method gives good agreement with the experiment for the breakdown threshold in silica and diamond. This breakdown voltage corresponds to a Keldysh parameter of approximately one and thus involves a transition to a regime where the dynamics are driven by tunneling. Pumping at an amplitude just below this value causes a mixture of multiphoton and tunneling excitations across the band gap to occur. The computed extreme ultraviolet and X-ray attosecond transient spectra also agree well with the experiment and show a decrease in optical density due to the transient population of the conduction band from the IR field. First-principles approaches such as this are valuable for interpreting the complicated modulations in a spectrum and for guiding future attosecond experiments on solids.
The predissociation dynamics of the 6s (B 2 E) Rydberg state of gas-phase CH 3 I were investigated by time-resolved Coulomb-explosion imaging using extreme ultraviolet (XUV) free-electron laser pulses. Inner-shell ionization at the iodine 4d edge was utilized to provide a site-specific probe of the ensuing dynamics. The combination of a velocity-map imaging (VMI) spectrometer coupled with the pixel imaging mass spectrometry (PImMS) camera permitted three-dimensional ionic fragment momenta to be recorded simultaneously for a wide range of iodine charge states. In accord with previous studies, initial excitation at 201.2 nm results in internal conversion and subsequent dissociation on the lower-lying A-state surface on a picosecond time scale. Examination of the time-dependent yield of low kinetic energy iodine fragments yields mechanistic insights into the predissociation and subsequent charge transfer following multiple ionization of the iodine products. The effect of charge transfer was observed through differing delay-dependencies of the various iodine charge states, from which critical internuclear distances for charge transfer could be inferred and compared to a classical over-the-barrier model. Time-dependent photofragment angular anisotropy parameters were extracted from the central slice of the Newton sphere, without Abel inversion, and highlight the effect of rotation of the parent molecule before dissociation, as observed in previous works. Our results demonstrate the ability to perform three-dimensional ion imaging at high event rates and showcase the potential benefits of this approach, particularly in relation to further time-resolved studies at free-electron laser facilities.
Here, we present a time-dependent Schrödinger equation approach within a nonrelativistic quantum electrodynamics framework to investigate resonant x-ray scattering driven by intense x-ray pulses. This method enables us to explore how coherent x-ray electron dynamics influence scattering signals from Ne + . We account for both resonance fluorescence and elastic scattering channels, while also considering competing photoionization and inner-shell decay processes. By computing the angular distribution and energy spectrum of scattered photons, we uncover interference effects between elastic scattering and resonance fluorescence pathways. Notably, this interference results in a small asymmetry in the energy spectrum. We discuss the experimental potential for detecting signatures of interference. Our findings demonstrate that the x-ray Rabi dynamics can be used to control scattering responses and provide insights into interference mechanisms and scattering efficiency in high-intensity x-ray regimes.
Rapid X-ray ionization of a core electron is known to induce the attosecond motion of valence electrons; however, the effect of core-hole shape on the triggered dynamics remains relatively unknown. In this work, the sub-four fs response of prototypical functionalized/heterocyclic/polycyclic molecules was simulated using real-time time-dependent density functional theory (RT-TDDFT), a sudden approximation core-hole, and phenomenologically Auger–Meitner (AM) decay. These molecules included fluorobenzene, chlorobenzene, bromobenzene, phenol, thiophenol, pyridine, phosphorus, and azulene. It is observed that the valence electron dynamics are essentially independent of the core-hole created, provided that it is ionized from an inner-shell orbital and not an inner-valence orbital. This has broad implications for free-electron laser studies of X-ray pumped attosecond processes since the flexibility in edge allows for a wide range of experimental modalities, core-holes with longer AM lifetimes, and molecular targets.
The photodissociation dynamics of UV excited CS 2 are investigated using time-resolved Auger–Meitner (AM) spectroscopy. AM decay is initiated by inner-shell ionisation with a femtosecond duration x-ray (179.9 eV) probe generated by the FERMI free electron laser. The time-delayed x-ray probe removes an electron from the S(2p) orbital leading to secondary emission of a high energy electron through AM decay. We monitor the electron kinetic energy of the AM emission as a function of pump-probe delay and observe time-dependent changes in the spectrum that correlate with the formation of bound, excited-state CS 2 molecules at early times, and CS + S fragments on the picosecond timescale. The results are analysed based on a simplified kinetic scheme that provides a time constant for dissociation of approximately 1.2 ps, in agreement with previous time-resolved x-ray photoelectron spectroscopy measurements (Gabalski, et al 2023 J. Phys. Chem. Lett. 14 7126–7133).
Inner-shell photodetachment of Na – near the L-edge threshold was investigated using the R-matrix method. Significant structure was found in the cross section, and this structure is shown to be related to the complicated correlated electron dynamics endemic in negative ions. Comparison with experiment suggests that the absolute values of the measured cross section might be too small by a factor of two.
The interactions of hydrated ions with molecular and macromolecular solution and interface partners are strong on a chemical energy scale. Here we recount the foremost ab initio theory for the evaluation of the hydration free energies of ions, namely, quasi-chemical theory (QCT). We focus on anions, particularly halides but also the hydroxide anion, because they have been outstanding challenges for all theories. For example, this work supports understanding the high selectivity for F – over Cl – in fluoride-selective ion channels despite the identical charge and the size similarity of these ions. QCT is built by the identification of inner-shell clusters, separate treatment of those clusters, and then the integration of those results into the broader-scale solution environment. Recent work has focused on a close comparison with mass-spectrometric measurements of ion-hydration equilibria. We delineate how ab initio molecular dynamics (AIMD) calculations on ion-hydration clusters, elementary statistical thermodynamics, and electronic structure calculations on cluster structures sampled from the AIMD calculations obtain just the free energies extracted from the cluster experiments. That theory–experiment comparison has not been attempted before the work discussed here, but the agreement is excellent with moderate computational effort. This agreement reinforces both theory and experiment and provides a numerically accurate inner-shell contribution to QCT. The inner-shell complexes involving heavier halides display strikingly asymmetric hydration clusters. Asymmetric hydration structures can be problematic for the evaluation of the QCT outer-shell contribution with the polarizable continuum model (PCM). Nevertheless, QCT provides a favorable setting for the exploitation of PCM when the inner-shell material shields the ion from the outer solution environment. For the more asymmetrically hydrated, and thus less effectively shielded, heavier halide ions clustered with waters, the PCM is less satisfactory. We therefore investigate an inverse procedure in which the inner-shell structures are sampled from readily available AIMD calculations on the bulk solutions. This inverse procedure is a remarkable improvement; our final results are in close agreement with a standard tabulation of hydration free energies, and the final composite results are independent of the coordination number on the chemical energy scale of relevance, as they should be. Finally, a comparison of anion hydration structure in clusters and bulk solutions from AIMD simulations emphasize some differences: the asymmetries of bulk solution inner-shell structures are moderated compared with clusters but are still present, and inner hydration shells fill to slightly higher average coordination numbers in bulk solution than in clusters.
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 CCl 4 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.
Abstract Short-wavelength free-electron lasers with their ultrashort pulses at high intensities have originated new approaches for tracking molecular dynamics from the vista of specific sites. X-ray pump X-ray probe schemes even allow to address individual atomic constituents with a ‘trigger’-event that preludes the subsequent molecular dynamics while being able to selectively probe the evolving structure with a time-delayed second X-ray pulse. Here, we use a linearly polarized X-ray photon to trigger the photolysis of a prototypical chiral molecule, namely trifluoromethyloxirane (C 3 H 3 F 3 O), at the fluorine K-edge at around 700 eV. The created fluorine-containing fragments are then probed by a second, circularly polarized X-ray pulse of higher photon energy in order to investigate the chemically shifted inner-shell electrons of the ionic mother-fragment for their stereochemical sensitivity. We experimentally demonstrate and theoretically support how two-color X-ray pump X-ray probe experiments with polarization control enable XFELs as tools for chiral recognition.
Quantum mechanical calculations of core electron binding energies (CEBEs) are relevant to interpreting X-ray photoelectron spectroscopy (XPS). Orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge CEBEs but is challenged by the presence of significant spin–orbit coupling (SOC) at L- and higher edges involving inner-shell orbitals with nonzero angular momentum. Here, to extend OO-DFT to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted open-shell OO-DFT to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell (e.g., ionizing all six possible 2p spin orbitals). Nonorthogonal configuration interaction (NOCI) is then used to obtain the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. Using a screened 1-electron SOC operator parametrized with the Dirac-Coulomb-Breit (DCB) Hamiltonian results in doublet splitting (DS) values for third row elements that are nearly in quantitative agreement with experiment. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT CEBEs to yield CEBEs (split by SOC) corrected for dynamic correlation. Comparing calculations on gas phase molecules with experimental results establishes that NO-QDPT with the SCAN functional (NO-QDPT/SCAN), using the DCB screened 1-electron SOC operator is accurate to about 0.2 eV for L-edge CEBEs of molecules containing third row atoms. However, this NO-QDPT approach becomes less accurate for fourth-row elements starting in the middle of the 3d transition metal series, with errors increasing as atomic number increases.
We report resonant inelastic x-ray scattering (RIXS) spectra of neon atoms interacting with intense x-ray pulses generated using an x-ray free-electron laser (XFEL). We find that an unexpected peak emerges near the 𝐾𝛼 line of Ne, which does not coincide with any physical resonances of neon ions. We perform theoretical calculations based on a quantum-state-resolved rate-equation approach with x-ray-induced processes including possible resonant excitations. Our dynamics simulations demonstrate that a sequence of multiple resonant photoabsorption events are involved and the interplay of those multiple resonances in combination with the relatively large spectral bandwidth of XFEL radiation leads to the emergent resonance-like structure at a position where no resonances exist. Our finding offers critical guidance for future applications of high-intensity RIXS at XFEL facilities.