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.

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.

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.

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.

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.

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.

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.

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.

Two-photon absorption properties of two-dimensional π-conjugated chromophores: combined experimental and theoretical study.

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 σ(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-π-D and A-π-A moieties, as well as transition between the D-π-D and A-π-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.

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.

Vibrational scattering anisotropy generated by multichannel quantum interference.

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→π* 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.

Circularly polarized x rays: another probe of ultrafast molecular decay dynamics.

Dissociative nuclear motion in core-excited molecular states leads to a splitting of the fragment Auger lines: the Auger-Doppler effect. We present here for the first time experimental evidence for an Auger-Doppler effect following F1s → a(1g)* inner-shell excitation by circularly polarized x rays in SF(6). In spite of a uniform distribution of the dissociating S-F bonds near the polarization plane of the light, the intersection between the subpopulation of molecules selected by the core excitation with the cone of dissociation induces a strong anisotropy in the distribution of the S-F bonds that contributes to the scattering profile measured in the polarization plane.

Theoretical studies of angle-resolved ion yield spectra of core-to-valence transitions of acetylene.

Recent experimental results on angle-resolved photoion-yield spectroscopy (ARPIS) spectra near the core-to-valence excitation in acetylene show significant anisotropies in the spectral profile measured at 0 degrees and 90 degrees regarding to the polarization direction of x-ray photons. In the present work, a theoretical model is proposed to simulate the fine structure and anisotropy in ARPIS. This employs two-dimensional potential energy surfaces of the ground and core-excited states, as well as transition dipole moments, including symmetric and antisymmetric bending modes to account for Duschinsky effect. The ARPIS is simulated by evaluation of the ion flux, which is found as a projection of the excited state wave packet on a particular direction in the molecular frame. Numerical simulations explain qualitatively the angular dependence of the experimental spectra of the 1s-->1pi(g) ( *) and 1s-->3sigma(u) ( *) transitions. The effects of the lifetime of the core-excited state, the direction of the ion flux, and the transition dipole moment are discussed.

Optical limiting for microsecond pulses.

We present a dynamical theory of nonlinear absorption and propagation of laser pulses with duration in the microsecond time domain. The general theory is applied to fullerene C(60) because of its good optical limiting properties, namely, a rather low ground state absorption and a strong triplet-triplet absorption. It is shown that sequential absorption involving strong triplet-triplet transitions is the major mechanism of nonlinear absorption. The intrinsic hierarchy of time scales makes an adiabatic solution of the coupled rate equations valid, which therefore can be reduced to a single dynamical equation for the ground state population. The slow evolution of this population is defined by an effective rate of population transfer to the triplet state and by the pulse duration. The propagation effect plays an important role in the optical power limiting performance. The intensity of the field as well as the population of the triplet state decreases during the pulse propagation, and a weakened nonlinear sequential two-photon absorption is followed by a linear one-photon absorption which gradually becomes the dominating process. The competition between these qualitatively different processes depends on the field intensity, the length of the absorber, and the concentration. The pulse propagation is studied by solving numerically the two-dimensional paraxial field equation together with the effective rate equation for the ground state population.

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.

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.