Parity violation in resonant inelastic soft x-ray scattering at entangled core holes.

Resonant inelastic x-ray scattering (RIXS) is a major method for investigation of electronic structure and dynamics, with applications ranging from basic atomic physics to materials science. In RIXS applied to inversion-symmetric systems, it has generally been accepted that strict parity selectivity applies in the sub-kilo-electron volt region. In contrast, we show that the parity selection rule is violated in the RIXS spectra of the free homonuclear diatomic O2 molecule. By analyzing the spectral dependence on scattering angle, we demonstrate that the violation is due to the phase difference in coherent scattering at the two atomic sites, in analogy with Young's double-slit experiment. The result also implies that the interpretation of x-ray absorption spectra for inversion symmetric molecules in this energy range must be revised.

Role of the Cohen-Fano interference in recoil-induced rotation.

We study the rotational dynamics induced by the recoil effect in diatomic molecules using time-resolved two-color x-ray pump-probe spectroscopy. A short pump x-ray pulse ionizes a valence electron inducing the molecular rotational wave packet, whereas the second time-delayed x-ray pulse probes the dynamics. An accurate theoretical description is used for analytical discussions and numerical simulations. Our main attention is paid to the following two interference effects that influence the recoil-induced dynamics: (i) Cohen-Fano (CF) two-center interference between partial ionization channels in diatomics and (ii) interference between the recoil-excited rotational levels manifesting as the rotational revival structures in the time-dependent absorption of the probe pulse. The time-dependent x-ray absorption is computed for the heteronuclear CO and homonuclear N2 molecules as showcases. It is found that the effect of CF interference is comparable with the contribution from independent partial ionization channels, especially for the low photoelectron kinetic energy case. The amplitude of the recoil-induced revival structures for the individual ionization decreases monotonously with a decrease in the photoelectron energy, whereas the amplitude of the CF contribution remains sufficient even at the photoelectron kinetic energy below 1 eV. The profile and intensity of the CF interference depend on the phase difference between the individual ionization channels related to the parity of the molecular orbital emitting the photoelectron. This phenomenon provides a sensitive tool for the symmetry analysis of molecular orbitals.

Time-resolved study of recoil-induced rotation by X-ray pump - X-ray probe spectroscopy.

Modern stationary X-ray spectroscopy is unable to resolve rotational structure. In the present paper, we propose to use time-resolved two color X-ray pump-probe spectroscopy with picosecond resolution for real-time monitoring of the rotational dynamics induced by the recoil effect. The proposed technique consists of two steps. The first short pump X-ray pulse ionizes the valence electron, which transfers angular momentum to the molecule. The second time-delayed short probe X-ray pulse resonantly excites a 1s electron to the created valence hole. Due to the recoil-induced angular momentum the molecule rotates and changes the orientation of transition dipole moment of core-excitation with respect to the transition dipole moment of the valence ionization, which results in a temporal modulation of the probe X-ray absorption as a function of the delay time between the pulses. We developed an accurate theory of the X-ray pump-probe spectroscopy of the recoil-induced rotation and study how the energy of the photoelectron and thermal dephasing affect the structure of the time-dependent X-ray absorption using the CO molecule as a case-study. We also discuss the feasibility of experimental observation of our theoretical findings, opening new perspectives in studies of molecular rotational dynamics.

Ultrafast dissociation of ammonia: Auger Doppler effect and redistribution of the internal energy.

We study vibrationally-resolved resonant Auger (RAS) spectra of ammonia recorded in coincidence with the NH2+ fragment, which is produced in the course of dissociation either in the core-excited 1s-14a11 intermediate state or the first spectator 3a-24a11 final state. Correlation of the NH2+ ion flight times with electron kinetic energies allows directly observing the Auger-Doppler dispersion for each vibrational state of the fragment. The median distribution of the kinetic energy release EKER, derived from the coincidence data, shows three distinct branches as a function of Auger electron kinetic energy Ee: Ee + 1.75EKER = const for the molecular band; EKER = const for the fragment band; and Ee + EKER = const for the region preceding the fragment band. The deviation of the molecular band dispersion from Ee + EKER = const is attributed to the redistribution of the available energy to the dissociation energy and excitation of the internal degrees of freedom in the molecular fragment. We found that for each vibrational line the dispersive behavior of EKERvs. Ee is very sensitive to the instrumental uncertainty in the determination of EKER causing the competition between the Raman (EKER + Ee = const) and Auger (Ee = const) dispersions: increase in the broadening of the finite kinetic energy release resolution leads to a change of the dispersion from the Raman to the Auger one.

Hydrogen bond effects in multimode nuclear dynamics of acetic acid observed via resonant x-ray scattering.

A theoretical and experimental study of the gas phase and liquid acetic acid based on resonant inelastic x-ray scattering (RIXS) spectroscopy is presented. We combine and compare different levels of theory for an isolated molecule for a comprehensive analysis, including electronic and vibrational degrees of freedom. The excitation energy scan over the oxygen K-edge absorption reveals nuclear dynamic effects in the core-excited and final electronic states. The theoretical simulations for the monomer and two different forms of the dimer are compared against high-resolution experimental data for pure liquid acetic acid. We show that the theoretical model based on a dimer describes the hydrogen bond formation in the liquid phase well and that this bond formation sufficiently alters the RIXS spectra, allowing us to trace these effects directly from the experiment. Multimode vibrational dynamics is accounted for in our simulations by using a hybrid time-dependent stationary approach for the quantum nuclear wave packet simulations, showing the important role it plays in RIXS.

Vibrational resonant inelastic X-ray scattering in liquid acetic acid: a ruler for molecular chain lengths.

Quenching of vibrational excitations in resonant inelastic X-ray scattering (RIXS) spectra of liquid acetic acid is observed. At the oxygen core resonance associated with localized excitations at the O-H bond, the spectra lack the typical progression of vibrational excitations observed in RIXS spectra of comparable systems. We interpret this phenomenon as due to strong rehybridization of the unoccupied molecular orbitals as a result of hydrogen bonding, which however cannot be observed in x-ray absorption but only by means of RIXS. This allows us to address the molecular structure of the liquid, and to determine a lower limit for the average molecular chain length.

Nuclear dynamics in resonant inelastic X-ray scattering and X-ray absorption of methanol.

We report on a combined theoretical and experimental study of core-excitation spectra of gas and liquid phase methanol as obtained with the use of X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS). The electronic transitions are studied with computational methods that include strict and extended second-order algebraic diagrammatic construction [ADC(2) and ADC(2)-x], restricted active space second-order perturbation theory, and time-dependent density functional theory-providing a complete assignment of the near oxygen K-edge XAS. We show that multimode nuclear dynamics is of crucial importance for explaining the available experimental XAS and RIXS spectra. The multimode nuclear motion was considered in a recently developed "mixed representation" where dissociative states and highly excited vibrational modes are accurately treated with a time-dependent wave packet technique, while the remaining active vibrational modes are described using Franck-Condon amplitudes. Particular attention is paid to the polarization dependence of RIXS and the effects of the isotopic substitution on the RIXS profile in the case of dissociative core-excited states. Our approach predicts the splitting of the 2a″ RIXS peak to be due to an interplay between molecular and pseudo-atomic features arising in the course of transitions between dissociative core- and valence-excited states. The dynamical nature of the splitting of the 2a″ peak in RIXS of liquid methanol near pre-edge core excitation is shown. The theoretical results are in good agreement with our liquid phase measurements and gas phase experimental data available from the literature.

Probing hydrogen bond strength in liquid water by resonant inelastic X-ray scattering.

Local probes of the electronic ground state are essential for understanding hydrogen bonding in aqueous environments. When tuned to the dissociative core-excited state at the O1s pre-edge of water, resonant inelastic X-ray scattering back to the electronic ground state exhibits a long vibrational progression due to ultrafast nuclear dynamics. We show how the coherent evolution of the OH bonds around the core-excited oxygen provides access to high vibrational levels in liquid water. The OH bonds stretch into the long-range part of the potential energy curve, which makes the X-ray probe more sensitive than infra-red spectroscopy to the local environment. We exploit this property to effectively probe hydrogen bond strength via the distribution of intramolecular OH potentials derived from measurements. In contrast, the dynamical splitting in the spectral feature of the lowest valence-excited state arises from the short-range part of the OH potential curve and is rather insensitive to hydrogen bonding.

Recoil-induced ultrafast molecular rotation probed by dynamical rotational Doppler effect.

Observing and controlling molecular motion and in particular rotation are fundamental topics in physics and chemistry. To initiate ultrafast rotation, one needs a way to transfer a large angular momentum to the molecule. As a showcase, this was performed by hard X-ray C1s ionization of carbon monoxide accompanied by spinning up the molecule via the recoil "kick" of the emitted fast photoelectron. To visualize this molecular motion, we use the dynamical rotational Doppler effect and an X-ray "pump-probe" device offered by nature itself: the recoil-induced ultrafast rotation is probed by subsequent Auger electron emission. The time information in our experiment originates from the natural delay between the C1s photoionization initiating the rotation and the ejection of the Auger electron. From a more general point of view, time-resolved measurements can be performed in two ways: either to vary the "delay" time as in conventional time-resolved pump-probe spectroscopy and use the dynamics given by the system, or to keep constant delay time and manipulate the dynamics. Since in our experiment we cannot change the delay time given by the core-hole lifetime τ, we use the second option and control the rotational speed by changing the kinetic energy of the photoelectron. The recoil-induced rotational dynamics controlled in such a way is observed as a photon energy-dependent asymmetry of the Auger line shape, in full agreement with theory. This asymmetry is explained by a significant change of the molecular orientation during the core-hole lifetime, which is comparable with the rotational period.

Compatibility of quantitative X-ray spectroscopy with continuous distribution models of water at ambient conditions.

The phase diagram of water harbors controversial views on underlying structural properties of its constituting molecular moieties, its fluctuating hydrogen-bonding network, as well as pair-correlation functions. In this work, long energy-range detection of the X-ray absorption allows us to unambiguously calibrate the spectra for water gas, liquid, and ice by the experimental atomic ionization cross-section. In liquid water, we extract the mean value of 1.74 ± 2.1% donated and accepted hydrogen bonds per molecule, pointing to a continuous-distribution model. In addition, resonant inelastic X-ray scattering with unprecedented energy resolution also supports continuous distribution of molecular neighborhoods within liquid water, as do X-ray emission spectra once the femtosecond scattering duration and proton dynamics in resonant X-ray-matter interaction are taken into account. Thus, X-ray spectra of liquid water in ambient conditions can be understood without a two-structure model, whereas the occurrence of nanoscale-length correlations within the continuous distribution remains open.

Ultrafast dissociation features in RIXS spectra of the water molecule.

In this combined theoretical and experimental study we report on an analysis of the resonant inelastic X-ray scattering (RIXS) spectra of gas phase water via the lowest dissociative core-excited state |1s-1O4a11. We focus on the spectral feature near the dissociation limit of the electronic ground state. We show that the narrow atomic-like peak consists of the overlapping contribution from the RIXS channels back to the ground state and to the first valence excited state |1b-114a11 of the molecule. The spectral feature has signatures of ultrafast dissociation (UFD) in the core-excited state, as we show by means of ab initio calculations and time-dependent nuclear wave packet simulations. We show that the electronically elastic RIXS channel gives substantial contribution to the atomic-like resonance due to the strong bond length dependence of the magnitude and orientation of the transition dipole moment. By studying the RIXS for an excitation energy scan over the core-excited state resonance, we can understand and single out the molecular and atomic-like contributions in the decay to the lowest valence-excited state. Our study is complemented by a theoretical discussion of RIXS in the case of isotopically substituted water (HDO and D2O) where the nuclear dynamics is significantly affected by the heavier fragments' mass.

Far-Zone Resonant Energy Transfer in X-ray Photoemission as a Structure Determination Tool.

Near-zone Förster resonant energy transfer is the main effect responsible for excitation energy flow in the optical region and is frequently used to obtain structural information. In the hard X-ray region, the Förster law is inadequate because the wavelength is generally shorter than the distance between donors and acceptors; hence, far-zone resonant energy transfer (FZRET) becomes dominant. We demonstrate the characteristics of X-ray FZRET and its fundamental differences with the ordinary near-zone resonant energy-transfer process in the optical region by recording and analyzing two qualitatively different systems: high-density CuO polycrystalline powder and SF6 diluted gas. We suggest a method to estimate geometrical structure using X-ray FZRET employing as a ruler the distance-dependent shift of the acceptor core ionization potential induced by the Coulomb field of the core-ionized donor.

Gradual collapse of nuclear wave functions regulated by frequency tuned X-ray scattering.

As is well established, the symmetry breaking by isotope substitution in the water molecule results in localisation of the vibrations along one of the two bonds in the ground state. In this study we find that this localisation may be broken in excited electronic states. Contrary to the ground state, the stretching vibrations of HDO are delocalised in the bound core-excited state in spite of the mass difference between hydrogen and deuterium. The reason for this effect can be traced to the narrow "canyon-like" shape of the potential of the state along the symmetric stretching mode, which dominates over the localisation mass-difference effect. In contrast, the localisation of nuclear motion to one of the HDO bonds is preserved in the dissociative core-excited state . The dynamics of the delocalisation of nuclear motion in these core-excited states is studied using resonant inelastic X-ray scattering of the vibrationally excited HDO molecule. The results shed light on the process of a wave function collapse. After core-excitation into the state of HDO the initial wave packet collapses gradually, rather than instantaneously, to a single vibrational eigenstate.

A study of the water molecule using frequency control over nuclear dynamics in resonant X-ray scattering.

In this combined theoretical and experimental study we report a full analysis of the resonant inelastic X-ray scattering (RIXS) spectra of H2O, D2O and HDO. We demonstrate that electronically-elastic RIXS has an inherent capability to map the potential energy surface and to perform vibrational analysis of the electronic ground state in multimode systems. We show that the control and selection of vibrational excitation can be performed by tuning the X-ray frequency across core-excited molecular bands and that this is clearly reflected in the RIXS spectra. Using high level ab initio electronic structure and quantum nuclear wave packet calculations together with high resolution RIXS measurements, we discuss in detail the mode coupling, mode localization and anharmonicity in the studied systems.

Selective gating to vibrational modes through resonant X-ray scattering.

The dynamics of fragmentation and vibration of molecular systems with a large number of coupled degrees of freedom are key aspects for understanding chemical reactivity and properties. Here we present a resonant inelastic X-ray scattering (RIXS) study to show how it is possible to break down such a complex multidimensional problem into elementary components. Local multimode nuclear wave packets created by X-ray excitation to different core-excited potential energy surfaces (PESs) will act as spatial gates to selectively probe the particular ground-state vibrational modes and, hence, the PES along these modes. We demonstrate this principle by combining ultra-high resolution RIXS measurements for gas-phase water with state-of-the-art simulations.

Anomalously strong two-electron one-photon X-ray decay transitions in CO caused by avoided crossing.

The unique opportunity to study and control electron-nuclear quantum dynamics in coupled potentials offered by the resonant inelastic X-ray scattering (RIXS) technique is utilized to unravel an anomalously strong two-electron one-photon transition from core-excited to Rydberg final states in the CO molecule. High-resolution RIXS measurements of CO in the energy region of 12-14 eV are presented and analyzed by means of quantum simulations using the wave packet propagation formalism and ab initio calculations of potential energy curves and transition dipole moments. The very good overall agreement between the experimental results and the theoretical predictions allows an in-depth interpretation of the salient spectral features in terms of Coulomb mixing of "dark" with "bright" final states leading to an effective two-electron one-photon transition. The present work illustrates that the improved spectral resolution of RIXS spectra achievable today may call for more advanced theories than what has been used in the past.

Rotational Doppler Effect: A Probe for Molecular Orbitals Anisotropy.

The vibrationally resolved X-ray photoelectron spectra of X2Σg+(3σg−1) and B2Σu+(2σu−1) states of N2+ were recorded for different photon energies and orientations of the polarization vector. Clear dependencies of the spectral line widths on the X-ray polarization as well as on the symmetry of the final electronic states are observed. Contrary to the translational Doppler, the rotational Doppler broadening is sensitive to the photoelectron emission anisotropy. On the basis of theoretical modeling, we suggest that the different rotational Doppler broadenings observed for gerade and ungerade final states result from a Young's double-slit interference phenomenon.

Toward fully nonempirical simulations of optical band shapes of molecules in solution: a case study of heterocyclic ketoimine difluoroborates.

This study demonstrates that a hybrid density functional theory/molecular mechanics approach can be successfully combined with time-dependent wavepacket approach to predict the shape of optical bands for molecules in solutions, including vibrational fine structure. A key step in this treatment is the estimation of the inhomogeneous broadening based on the hybrid approach, where the polarization between solute and atomically decomposed solvent is taken into account in a self-consistent manner. The potential of this approach is shown by predicting optical absorption bands for three heterocyclic ketoimine difluoroborates in solution.

Site-selective photoemission from delocalized valence shells induced by molecular rotation.

Due to the generally delocalized nature of molecular valence orbitals, valence-shell spectroscopies do not usually allow to specifically target a selected atom in a molecule. However, in X-ray electron spectroscopy, the photoelectron momentum is large and the recoil angular momentum transferred to the molecule is larger when the photoelectron is ejected from a light atom compared with a heavy one. This confers an extreme sensitivity of the rotational excitation to the ionization site. Here we show that, indeed, the use of high-energy photons to photoionize valence-shell electrons of hydrogen chloride offers an unexpected way to decrypt the atomic composition of the molecular orbitals due to the rotational dependence of the photoionization profiles. The analysis of the site-specific rotational envelopes allows us to disentangle the effects of the two main mechanisms of rotational excitation, based on angular momentum exchange between the molecule and either the incoming photon or the emitted electron.