We report on a computational study of resonant inelastic x-ray scattering (RIXS), at different fluorine K-edge resonances of the SF6 molecule, and corresponding nonresonant x-ray emission. Previously measured polarization dependence in RIXS is reproduced and traced back to the local σ and π symmetry of the molecular orbitals and corresponding states involved in the RIXS process. Also electron-hole coupling energies are calculated and related to experimentally observed spectator shifts. The role of dissociative S-F bond dynamics is explored to model detuning of RIXS spectra at the |F1s-16a1g1) resonance, which shows challenges to accurately reproduce the required steepness for core-excited potential energy surface. We show that the RIXS spectra can only be properly described by considering breaking of the global inversion symmetry of the electronic wave function and core-hole localization, induced by vibronic coupling. Due to the core-hole localization we have symmetry forbidden transitions, which lead to additional resonances and changing width of the RIXS profile.
In this study, we investigate the nuclear dynamics in nitrogen monoxide after valence ionization by a pump pulse and subsequent probing with a time-delayed x-ray pulse. We calculate the development of the resulting vibrational wave packet, taking into account three different ionization mechanisms: one-photon, multiphoton, and tunneling ionization. Using a two-time propagation method, we solve the nonstationary nuclear Schrödinger equation to obtain time-resolved x-ray absorption spectra (TRXAS), considering the finite duration of the probe pulse. Our simulations show that the TRXAS profile accurately reflects the vibrational wave packets' trajectory in the cationic ground state. Additionally, we find that the TRXAS evolution is highly sensitive to small changes in the probed potential energy curve, making it a useful tool for reconstructing molecular potentials and determining anharmonicity and equilibrium bond length. This method can be applied to other polyatomic molecules and pump mechanisms.
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.
We experimentally observed interference effects in elastic x-ray scattering from gas-phase HCl in the vicinity of the Cl Kedge. Comparison to theory identifies these effects as interference effects between non-resonant elastic Thomson scattering and resonant Raman scattering. The results indicate the non-resonant Thomson and resonant Raman contributions are of comparable strength. The measurements also exhibit strong polarization dependence, allowing an easy identification of the resonant and non-resonant contributions.
Resonant X-ray Raman scattering is a powerful tool to study molecular dynamics and subtle chemical effects like the molecular field beyond vibrational and lifetime limitations. Using this technique in the tender X-ray region, gas phase HCl is studied as a benchmark molecule for other compounds like freons, which play an important role in physical-chemical properties of the ozone layer of atmosphere.
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 tau, 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.
We present a detailed experimental-theoretical analysis of O K-edge resonant 1 sigma-2 pi inelastic x-ray scattering (RIXS) from carbon monoxide with unprecedented energy resolution. We employ high-level ab initio calculations to compute the potential energy curves of the states involved in the RIXS process and simulate the measured RIXS spectra using the wave-packet-propagation formalism, including Coulomb coupling in the final-state manifold. The theoretical analysis allows us to explain all the key features of the experimental spectra, including some that were not seen before. First, we clearly show the interference effect between different RIXS channels corresponding to the transition via orthogonal (1)Pi(x) and (1)Pi(y) core-excited states of CO. Second, the RIXS region of 13 eV energy loss presents a triple structure, revealed only by the high-resolution measurement. In previous studies, this region was attributed solely to a valence state. Here we show a strong Coulomb mixing of the Rydberg and valence final states, which opens the forbidden RIXS channels to the "dark" final Rydberg states and drastically changes the RIXS profile. Third, using a combination of high-resolution experiment and high-level theory, we improve the vertical bar 4 sigma(-1)2 pi(1)> final-state potential-energy curve by fitting its bottom part with the experiment. Also, the coupling constants between Rydberg and valence states were refined via comparison with the experiment. Our results illustrate the large potential of the RIXS technique for advanced studies of highly excited states of neutral molecules.
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.
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.
It is well established that different electronic channels, in resonant inelastic x-ray scattering (RIXS), display different polarization dependences due to different orientations of their corresponding transition dipole moments in the molecular frame. However, this effect does not influence the vibrational progression in the Franck-Condon approximation. We have found that the transition dipole moments of core excitation and deexcitation experience ultrafast rotation during dissociation in the intermediate core-excited state. This rotation makes the vibrational progression in RIXS sensitive to the polarization of the x-ray photons. We study the water molecule, in which the effect is expressed in RIXS through the dissociative core-excited state where the vibrational scattering anisotropy is accompanied also by violation of parity selection rules for the vibrations.
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.
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.
The concept of the potential-energy surface (PES) and directional reaction coordinates is the backbone of our description of chemical reaction mechanisms. Although the eigenenergies of the nuclear Hamiltonian uniquely link a PES to its spectrum, this information is in general experimentally inaccessible in large polyatomic systems. This is due to (near) degenerate rovibrational levels across the parameter space of all degrees of freedom, which effectively forms a pseudospectrum given by the centers of gravity of groups of close-lying vibrational levels. We show here that resonant inelastic x-ray scattering (RIXS) constitutes an ideal probe for revealing one-dimensional cuts through the ground-state PES of molecular systems, even far away from the equilibrium geometry, where the independent-mode picture is broken. We strictly link the center of gravity of close-lying vibrational peaks in RIXS to a pseudospectrum which is shown to coincide with the eigenvalues of an effective one-dimensional Hamiltonian along the propagation coordinate of the core-excited wave packet. This concept, combined with directional and site selectivity of the core-excited states, allows us to experimentally extract cuts through the ground-state PES along three complementary directions for the showcase H2O molecule.
The concept of the potential-energy surface (PES) and directional reaction coordinates is the backbone of ourdescription of chemical reaction mechanisms. Although the eigenenergies of the nuclear Hamiltonian uniquely link a PES to its spectrum, this information is in general experimentally inaccessible in large polyatomic systems. This is due to (near) degenerate rovibrational levels across the parameter space of all degrees of freedom, which effectively forms a pseudospectrum given by the centers of gravity of groups of close-lying vibrational levels. We show here that resonant inelastic x-ray scattering (RIXS) constitutes an ideal probe for revealing one-dimensional cuts through the ground-state PES of molecular systems, even far away from the equilibrium geometry, where the independent-mode picture is broken. We strictly link the center of gravity of close-lying vibrational peaks in RIXS to a pseudospectrum which is shown to coincide with the eigenvalues of an effective one-dimensional Hamiltonian along the propagation coordinate of the core-excited wave packet. This concept, combined with directional and site selectivity of the core-excited states, allows us to experimentally extract cuts through the ground-state PES along three complementary directions for the showcase H2O molecule.
Resonant inelastic x-ray scattering spectra excited at the fluorine K resonances of SF(6)have been recorded. While a small but significant propensity for electronically parity-allowed transitions is found, the observation of parity-forbidden electronic transitions is attributed to vibronic coupling that breaks the global inversion symmetry of the electronic wavefunction and localizes the core hole. The dependence of the scattering cross section on the polarization of the incident radiation and the scattering angle is interpreted in terms of local pi/sigma symmetry around the S-F bond. This symmetry selectivity prevails during the dissociation that occurs during the scattering process.
Near-edge x-ray absorption fine structure (NEXAFS) and resonant inelastic x-ray scattering (RIXS) measurements at the oxygen K edge were combined with theoretical spectrum simulations, based on periodic density functional theory and nuclear quantum dynamics, to investigate the electronic structure and chemical bonding in kaolinite Al2Si2O5(OH)(4). We simulated NEXAFS spectra of all crystallographically inequivalent oxygen atoms in the crystal and RIXS spectra of the hydroxyl groups. Detailed insight into the ground-state potential energy surface of the electronic states involved in the RIXS process were accessed by analyzing the vibrational excitations, induced by the core excitation, in quasielastic scattering back to the electronic ground state. In particular, we find that the NEXAFS pre-edge is dominated by features related to OH groups within the silica and alumina sheets, and that the vibrational progression in RIXS can be used to selectively probe vibrational modes of this subclass of OH groups. The signal is dominated by the OH stretching mode, but also other lower vibrational degrees of freedom, mainly hindered rotational modes, contribute to the RIXS signal.
In this combined theoretical and experimental study we report on an analysis of the resonant inelastic X-ray scattering spectra (RIXS) of gas phase water via the lowest dissociative core-excited state |1sO-14a11〉. 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 |1b1-14a11〉 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 the isotope substituted water (HDO and D2O) where the nuclear dynamics is significantly affected by the heavier fragments' mass.
We show that the anisotropy of the recoil velocity distribution of x-ray-ionized atoms or molecules leads to observable splittings in subsequent optical fluorescence or absorption when the polarization vector of the x rays is parallel to the momentum of the fluorescent photons. The order of the magnitude of the recoil-induced splitting is about 10 mu eV, which can be observed using Fourier or laser-absorption spectroscopic techniques.
In the description of resonant inelastic x-ray scattering (RIXS) from inversion-symmetric molecules the small core-level splitting is typically neglected. However, the spacing Δ between gerade and ungerade core levels in homonuclear diatomic molecules can be comparable with the lifetime broadening of the intermediate core-excited state Γ. We show that when Δ∼Γ the scattering becomes nonlocal in the sense that x-ray absorption at one atomic site is followed by emission at the other one. This is manifested in an unusual dependence of the RIXS cross section on the sum of the momenta of incoming and outgoing x-ray photons k+k′, contrary to the normal k-k′ dependence in the conventional local RIXS theory. The nonlocality of the scattering influences strongly the scattering angle and excitation energy dependence of the intensity ratio between parity forbidden and allowed RIXS channels. Numerical simulations for N2 show that this effect can readily be measured at present-day x-ray radiation facilities.
Anoverview of both experimental and theoretical results in the field of resonant scattering of tunable soft and hard x-ray radiation is presented, with a main focus on the closely related processes of resonant inelastic x-ray scattering (RIXS) and resonant Auger scattering (RAS). The review starts with an overview of fundamental dynamical aspects of RIXS illustrated for different systems. A detailed analysis of case studies with increasing complexity, considering both gas-phase and condensed matter (liquids and solids) applications, is given. In the review, the most important achievements in investigations of coupled electron-nuclear dynamics and structural aspects in studies of liquids and solids over the last two decades are outlined. To give a perspective on the insights from RIXS and RAS, the x-ray results are discussed against the background of complementary experimental techniques like vibrational infrared absorption and Raman spectroscopy, as well as small-angle x-ray and neutron scattering. Finally, recent achievements in time-resolved studies based on x-ray free-electron lasers are described.
We develop a theory of infrared (IR)-pump–x-ray-probe spectroscopy for molecular studies. We illustrate advantages of the proposed scheme by means of numerical simulations employing a vibrational wave packet technique applied to x-ray absorption and resonant inelastic x-ray scattering (RIXS) spectra of the water molecule vibrationally excited by a preceding IR field. The promotion of the vibrationally excited molecule to the dissociative 1a−114a1 and bound 1a−112b2 core-excited states with qualitatively different shapes of the potential energy surfaces creates nuclear wave packets localized along and between the OH bonds, respectively. The projection of these wave packets on the final vibrational states, governed by selection and propensity rules, results in spatial selectivity of RIXS sensitive to the initial vibrationally excited state, which makes it possible to probe selectively the ground state properties along different modes. In addition, we propose to use RIXS as a tool to study x-ray absorption from a selected vibrational level of the ground state when the spectral resolution is sufficiently high to resolve vibrational overtones. The proposed technique has potential applications for advanced mapping of multidimensional potential energy surfaces of ground and core-excited molecular states, for symmetry-resolved spectroscopy, and for steering chemical reactions.
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.
This paper reports an advanced study of the excited ionic states of the gas-phase nitrogen molecule in the binding-energy region of 22-34 eV, combining ultrahigh-resolution resonant photoemission (RPE) and ab initio configuration-interaction calculations. The RPE spectra are recorded for nine photon energies within the N 1s -> pi* absorption resonance of N-2 by using a photon bandwidth that is considerably smaller than lifetime broadening, and the dependence on excitation energy of the decay spectra is analyzed and used for the first assignment of 12 highly overlapped molecular states. The effect on the RPE profile of avoided curve crossings between the final N-2(+) ionic states is discussed, based on theoretical simulations that account for vibronic coupling, and compared with the experimental data. By use of synchrotron radiation with high spectral brightness, it is possible to selectively promote the molecule to highly excited vibrational sublevels of a core-excited electronic state, thereby controlling the spatial distribution of the vibrational wave packets, and to accurately image the ionic molecular potentials. In addition, the mapping of the vibrational wave functions of the core-excited states using the bound final states with far-from-equilibrium bond lengths has been achieved experimentally for the first time. Theoretical analysis has revealed the rich femtosecond nuclear dynamics underlying the mapping phenomenon. DOI: 10.1103/PhysRevX.3.011017
Born–Oppenheimer and Franck–Condon approximations are two major concepts in the interpretation of electronic excitations and modeling of spectroscopic data in the gas and condensed phases. We report large variations of the anisotropy parameter (β) for the fully resolved vibrational sub-states of the X2Πg electronic ground state of O+2 populated by participator resonant Auger decay following excitations of K-shell electrons into the σ☆ resonance by monochromatic x-rays. Decay spectra for light polarization directions parallel and perpendicular to the electron detection axis recorded at four different excitation energies in the vicinity of the O 1s → σ☆ transition are presented. Breakdown of the Born–Oppenheimer approximation is for the first time selectively observed for the lower vibrational sub-states, where two quantum paths—resonant and direct—leading to the same final cationic state exist. The higher vibrational sub-states can only be populated by resonant photoemission; hence no interference between these channels can occur.
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.
Different types of Young's double-slit experiments contain a significant amount of both particle and wave information running from full-particle to full-wave knowledge depending on the experimental conditions. We study the Young's double-slit interference in resonant Auger scattering from homonuclear diatomic molecules where opposite Doppler shifts for the dissociating atomic slits provide path information. Different quantitative formulation of Bohr's complementarity principle - path information vs interference - is applied to two types of resonant Auger scattering experiments, with fixed-in-space and randomly oriented molecules. Special attention is paid to the orientational dephasing in conventional Auger experiments with randomly oriented molecules. Our quantitative formulation of the complementarity is compared with the formulation made earlier by Greenberger and Yasin [D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988)0375-960110.1016/0375-9601(88)90114-4].
We predict the recoil-induced molecular dissociation in hard-x-ray photoionization. The recoil effect is caused by electronic and photon momentum exchange with the molecule. We show the strong role of relativistic effects for the studied molecular fragmentation. The recoil-induced fragmentation of the molecule is caused by elongation of the bond due to the vibrational recoil effect and because of the centrifugal force caused by the rotational recoil. The calculations of the x-ray photoelectron spectra of the H-2 and NO molecules show that the predicted effects can be observed in high-energy synchrotrons like SOLEIL, SPring-8, PETRA, and XFEL SACLA. The relativistic effect enhances the recoil momentum transfer and makes it strongly sensitive to the direction of ejection of the fast photoelectron with respect to the photon momentum.
We explore the x-ray second-harmonic generation process induced by resonant two-photon absorption in systems with inversion symmetry. We show that this process becomes allowed in the x-ray region due to nondipole contributions. It is found that, although a plane-wave pump field generates only a longitudinal second-harmonic field, a Gaussian pump beam creates also a radially polarized transverse second-harmonic field which is stronger than the longitudinal one. Contrary to the longitudinal component, the transverse second-harmonic field with zero intensity on the axis of the pump beam can run in free space. Our theory is applied to Ar and Ne atomic vapors and predicts an energy conversion efficiency of x-ray second-harmonic generation of 3.2 x 10(-11) and 1.3 x 10(-12), respectively.
Resonant Auger spectra of ethene molecule have been measured with vibrational resolution at several excitation energies in the region of the C1s(-1)1b(2g)(π*) resonance. The main features observed in the experiment have been assigned and are accurately interpreted on the basis of ab initio multimode calculations. Theory explains the extended vibrational distribution of the resonant Auger spectra and its evolution as a function of the excitation energy by multimode excitation during the scattering process. As a result, the resonant Auger spectra display two qualitatively different spectral features following the Raman and non-Raman dispersion laws, respectively. Calculations show that two observed thresholds of formation of non-Raman spectral bands are related to the "double-edge" structure of the X-ray absorption spectrum.
In theoretical simulations of a UV + x-ray pump-probe (UVX-PP) setup, we show that frequency detuning of the pump UV pulse acts as a camera shutter by regulating the duration of the UVX-PP process. This two-photon absorption with long overlapping UV and x-ray pulses, allowing for high spectral resolution, thereby provides information about ultrafast dynamics of the nuclear wave packet without the requirement of ultrashort pulses and controlled delay times. In a case study of carbon monoxide, the calculated UVX-PP spectra of the O1s (-1)2 pi (1) and C1s (-1)2 pi (1) core-excited states show different vibrational profiles. The interference of intermediate vibrational states reveals details of nuclear dynamics in the UVX-PP process related to a variable duration time controlled by the UV detuning. Both O1s (-1)2 pi (1) and C1s (-1)2 pi (1) pump-probe channels display a splitting of the spectral profile, which however is associated with different physical mechanisms. At the O1s (-1)2 pi (1) resonance, the observed dispersive and non-dispersive spectral bands intersect and result in destructive interference.
X-ray absorption and core-ionization spectra of molecules pumped by two coherent infrared pulses with different polarizations are studied theoretically. We have found a sensitivity of the vibrational profile of x-ray probe spectra to polarizations of the IR and x-ray pulses. This polarization dependence is qualitatively different for x-ray absorption and x-ray photoelectron spectra. Measurements of this polarization dependence allow to select the difference in Franck-Condon distributions from the lowest and pumped vibrational levels of the electronic ground state. The proposed technique is exemplified numerically using x-ray absorption spectra of the pumped CO molecule. We also show that this kind of pump-probe spectroscopy can enable studies of the dynamics of molecular rotation.
We study the role of propagation of strong x-ray free-electron laser pulses on the Auger effect. When the system is exposed to a strong x-ray pulse the stimulated emission starts to compete with the Auger decay. As an illustration we present numerical results for Ar gas with the frequency of the incident x-ray pulse tuned in the 2p(3/2)-4s resonance. It is shown that the pulse propagation is accompanied by two channels of amplified spontaneous emission, 4s-2p(3/2) and 3s-2p(3/2), which reshape the pulse when the system is inverted. The population inversion is quenched for longer propagation distances where lasing without inversion enhances the Stokes component. The results of simulations show that the propagation of the strong x-ray pulses affect intensively the Auger branching ratio.
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 N-2 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.
Double-slit experiments illustrate proof for wave-particle complementarity. The essence of Einstein-Bohr's debate about wave-particle duality was whether the momentum transfer between a particle and a recoiling slit could mark the path, thus destroying the interference. We realized this recoiling double-slit gedanken experiment by resonant X-ray photoemission from molecular oxygen for geometries near equilibrium (coupled slits) and in a dissociative state far away from equilibrium (decoupled slits). Interference is observed in the former case, while the electron momentum transfer quenches the interference in the latter case.
Double-slit experiments illustrate the quintessential proof for wave-particle complementarity. If information is missing about which slit the particle has traversed, the particle, behaving as a wave, passes simultaneously through both slits. This wave-like behaviour and corresponding interference is absent if 'which-slit' information exists. The essence of Einstein-Bohr's debate about wave-particle duality was whether the momentum transfer between a particle and a recoiling slit could mark the path, thus destroying the interference. To measure the recoil of a slit, the slits should move independently. We showcase a materialization of this recoiling double-slit gedanken experiment by resonant X-ray photoemission from molecular oxygen for geometries near equilibrium (coupled slits) and in a dissociative state far away from equilibrium (decoupled slits). Interference is observed in the former case, while the electron momentum transfer quenches the interference in the latter case owing to Doppler labelling of the counter-propagating atomic slits, in full agreement with Bohr's complementarity.
We present an experimental and theoretical study of resonant inelastic x-ray scattering (RIXS) in the carbon disulphide CS 2 molecule near the sulfur K-absorption edge. We observe a strong evolution of the RIXS spectral profile with the excitation energy tuned below the lowest unoccupied molecular orbital (LUMO) absorption resonance. The reason for this is twofold. Reducing the photon energy in the vicinity of the LUMO absorption resonance leads to a relative suppression of the LUMO contribution with respect to the emission signal from the higher unoccupied molecular orbitals, which results in the modulation of the total RIXS profile. At even larger negative photon-energy detuning from the resonance, the excitation-energy dependence of the RIXS profile is dominated by the onset of electron dynamics triggered by a coherent excitation of multiple electronic states. Furthermore, our study demonstrates that in the hard x-ray regime, localization of the S 1s core hole occurs in CS2 during the RIXS process because of the orientational dephasing of interference between the waves scattering on the two sulfur atoms. Core-hole localization leads to violation of the symmetry selection rules for the electron transitions observed in the spectra.
A combination of resonant inelastic x-ray scattering and resonant Auger spectroscopy provides complementary information on the dynamic response of resonantly excited molecules. This is exemplified for CH3I, for which we reconstruct the potential energy surface of the dissociative I 3d(-2) double-core-hole state and determine its lifetime. The proposed method holds a strong potential for monitoring the hard x-ray induced electron and nuclear dynamic response of core-excited molecules containing heavy elements, where ab initio calculations of potential energy surfaces and lifetimes remain challenging.
We present an experimental and theoretical study of resonant inelastic x-ray scattering (RIXS) in the CS2 molecule near the S 1s edge. We show that localization of the S 1s core-hole occurs in CS2 during the RIXS process due to the orientational dephasing of interference between the waves scattering on the two sulfur atoms. Strong evolution of the RIXS profile with the excitation energy far below the first absorption resonance reflects the onset of electron dynamics triggered by a coherent excitation of multiple electronic states.
The optical limiting properties of a series of peripherally substituted phthalocyanines with different central metals and axial chloride ligand for nanosecond pulses have been studied by solving numerically the two-dimensional paraxial field equation together with the rate equations using the Crank-Nicholson method. It is shown that all of these compounds exhibit good optical limiting behaviour, and phthalocyanines with heavier central metals have better optical limiting performance due to the faster intersystem crossing caused by the enhanced spin-orbit coupling. The major mechanism of optical limiting for long pulses is the sequential (singlet-singlet)x( triplet-triplet) nonlinear absorption. Dynamics of populations is characterized mainly by the effective transfer time of the population from the ground state to the lowest triplet state. The long lifetime of the triplet state is important but not determinant. In addition, the performance of optical limiting strongly depends on the thickness and concentration of the absorber.
X-ray lasing is predicted to ensue when molecules are pumped into dissociative core-excited states by a free-electron-laser pulse. The lasing is due to the population inversion created in the neutral dissociation product, and the process features self-trapping of the x-ray pulse at the gain ridge. Simulations performed for the HCl molecule pumped at the 2p(1/2) -> 6 sigma resonance demonstrate that the scheme can be used to create ultrashort coherent x-ray pulses.
The vibrationally resolved X-ray photoelectron spectra of X-2 Sigma(+)(g)(3 sigma(-1)(g)) and B-2 Sigma(+)(u)(2 sigma(-1)(u)) states of N-2(+) 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.
Based on angularly and vibrationally resolved electron spectroscopy measurements in acetylene, we report the first observation of anomalously strong vibrational anisotropy of resonant Auger scattering through the C 1s --> pi* excited state. We provide a theoretical model explaining the new phenomenon by three coexisting interference effects: (i) interference between resonant and direct photoionization channels, (ii) interference of the scattering channels through the core-excited bending states with orthogonal orientation of the molecular orbitals, (iii) scattering through two wells of the double-well bending mode potential. The interplay of nuclear and electronic motions offers in this case a new type of nuclear wave packet interferometry sensitive to the anisotropy of nuclear dynamics: whether which-path information is available or not depends on the final vibrational state serving for path selection.
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.
Electron-density distributions and potential-energy surfaces are important for predicting the physical properties and chemical reactivity of molecular systems. Whereas angle-resolved photoelectron spectroscopy enables the reconstruction of molecular-orbital densities of condensed species(1), absorption or traditional photoelectron spectroscopy are widely employed to study molecular potentials of isolated species. However, the information they provide is often limited because not all vibrational substates are excited near the vertical electronic transitions from the ground state. Moreover, many electronic states cannot be observed owing to selection rules or low transition probabilities. In many other cases, the extraction of the potentials is impossible owing to the high densities of overlapping electronic states. Here we use resonant photoemission spectroscopy, where the absence of strict dipole selection rules in Auger decay enables access to a larger number of final states as compared with radiative decay. Furthermore, by populating highly excited vibrational substates in the intermediate core-excited state, it is possible to 'pull out' molecular states that were hidden by overlapping spectral regions before.
We investigate the dynamics of resonant Raman scattering in the course of the frequency detuning. The dephasing in the time domain makes the scattering fast when the photon energy is tuned from the absorption resonance. This makes frequency detuning to act as a camera shutter with a regulated scattering duration and provides a practical tool of controlling the scattering time in ordinary stationary measurements. The theory is applied to resonant Raman spectra of a couple of few-mode model systems and to trams-1,3,5-hexatriene and guanine-cytosine (G-C) Watson-Crick base pairs (DNA) molecules. Besides some particular physical effects, the regime of fast scattering leads to a simplification of the spectrum as well as to the scattering theory itself. Strong overtones appear in the Raman spectra when the photon frequency is tuned in the resonant region, while in the mode of fast scattering, the overtones are gradually quenched when the photon frequency is tuned more than one vibrational quantum below the first a,absorption resonance. The detuning front the resonant region thus leads to a strong purification of the Raman spectrum from the contamination by higher overtones and soft modes and purifies the spectrum also in terms of avoidance of dissociation and interfering fluorescence decay of the resonant state. This makes frequency detuning a very useful practical tool in the analysis of the resonant Raman spectra of complex systems and considerably improves the prospects for using the Raman effect for detection of foreign substances at ultra-low concentrations.
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.
The two-photon absorption (TPA) properties of four TPEB [tetrakis(phenylethynyl)benzene] derivatives (TD, para, ortho, and meta) with different donor/acceptor substitution patterns have been investigated experimentally by the femtosecond open-aperture Z-scan method and theoretically by the time-dependent density-functional theory (TDDFT) method. The four compounds show relatively large TPA cross sections, and the all-donor substituted species (TD) displays the largest TPA cross-section sigma((2)) = 520 +/- 30 GM. On the basis of the calculated electronic structure, TD shows no TPA band in the lower energy region of the spectrum because the transition density is concentrated on particular transitions due to the high symmetry of the molecular structure. The centrosymmetric donor-acceptor TPEB para shows excitations resulting from transitions centered on D-pi-D and A-pi-A moieties, as well as transition between the D-pi-D and A-pi-A moieties; this accounts for the broad nature of the TPA bands for this compound. Calculations for two noncentrosymmetric TPEBs (ortho and meta) reveal that the diminished TPA intensities of higher-energy bands result from destructive interference between the dipolar and three-state terms. The molecular orbitals (MOs) of the TPEBs are derivable with linear combinations of the MOs of the two crossing BPEB [bis(phenylethynyl)benzene] derivatives. Overall, the characteristics of the experimental spectra are well-described based on the theoretical analysis.