Isotope-induced partial localization of core electrons in the homonuclear molecule N2

Double-Slit Interference in the Ion Dynamics of Dissociative Photoionization

The ion momentum distribution in the x-ray-induced dissociative photoionization of molecules is investigated, treating the ionization analytically under the Born-Oppenheimer approximation and simulating numerically the ion motion via the Schrödinger equation. The ion-photoelectron entanglement transfers information of the electronic interference to the ion dynamics. As a consequence, the ion momentum distributions of dissociative molecular photoionization present Young's double-slit interference when the photoelectron emission angle is fixed. We demonstrate that double-slit interference signatures persist in the ion longitudinal momentum shift even when the information of the correlated photoelectron is lost, which is the case for heteronuclear molecules when an additional photoelectron recoil momentum arises due to the different ion masses. For the case of sequential double ionization, we show that double-slit interference in the ion dynamics can be utilized for coherent control of the molecular dynamics.

Trends in angle-resolved molecular photoelectron spectroscopy

In this perspective article, main trends of angle-resolved molecular photoelectron spectroscopy in the laboratory up to the molecular frame, in different regimes of light-matter interactions, are highlighted with emphasis on foundations and most recent applications.

Transient Valence Charge Localization in Strong-Field Dissociative Ionization of HCl Molecules

Probing transient charge localization in the innershell orbital of atoms and molecules has been made possible by the recent progress of advanced light sources. Here, we demonstrate that the ultrafast electron tunneling ionization by an intense femtosecond laser pulse could induce an asymmetric transient charge localization in the valence shell of the HCl molecule during the dissociative ionization process. The transient charge localization is encoded in the laser impulse acquired by the outgoing ionic fragments, and the asymmetry is revealed by carefully examining the electron tunneling-site distinguished momentum angular distribution of the ejected H^{+} fragments. Our work proposes a way to visualize the transient valence charge motion and will stimulate further investigations of the tunneling-site-sensitive ultrafast dynamics of molecules in strong laser fields.

Breaking inversion symmetry by protonation: experimental and theoretical NEXAFS study of the diazynium ion, N2H. Phys Chem Chem Phys 2021;23:17166-17176. [PMID: 34346432 DOI: 10.1039/d1cp02002a]

As an example of symmetry breaking in NEXAFS spectra of protonated species we present a high resolution NEXAFS spectrum of protonated dinitrogen, the diazynium ion N₂H⁺. By ab initio calculations we show that the spectrum consists of a superposition of two nitrogen 1s absorption spectra, each including a π* band, and a nitrogen 1s to H⁺ charge transfer band followed by a weak irregular progression of high energy excitations. Calculations also show that, as an effect of symmetry breaking by protonation, the π* transitions are separated by 0.23 eV, only slightly exceeding the difference in the corresponding dark (symmetry forbidden) and bright (symmetry allowed) core excitations of neutral N₂. By DFT and calculations and vibrational analysis, the complex π* excitation band of N₂H⁺ is understood as due to the superposition of the significantly different vibrational progressions of excitations from terminal and central nitrogen atoms, both leading to bent final state geometries. We also show computationally that the electronic structure of the charge transfer excitation smoothly depends on the nitrogen-proton distance and that there is a clear extension of the spectra going from infinity to close nitrogen-proton distance where fine structures show some, although not fully detailed, similarities. An interesting feature of partial localization of the nitrogen core orbitals, with a strong, non-monotonous, variation with nitrogen-proton distance could be highlighted. Specific effects could be unraveled when comparing molecular cation NEXAFS spectra, as represented by recently recorded spectra of N₂⁺ and CO⁺, and spectra of protonated molecules as represented here by the N₂H⁺ ion. Both types containing rich physical effects not represented in NEXAFS of neutral molecules because of the positive charge, whereas protonation also breaks the symmetry. The effect of the protonation on dinitrogen can be separated in charge, which extends the high-energy part of the spectrum, and symmetry-breaking, which is most clearly seen in the low-energy π* transition.

Electron-ion coincidence measurements of molecular dynamics with intense X-ray pulses

Molecules can sequentially absorb multiple photons when irradiated by an intense X-ray pulse from a free-electron laser. If the time delay between two photoabsorption events can be determined, this enables pump-probe experiments with a single X-ray pulse, where the absorption of the first photon induces electronic and nuclear dynamics that are probed by the absorption of the second photon. Here we show a realization of such a single-pulse X-ray pump-probe scheme on N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2 molecules, using the X-ray induced dissociation process as an internal clock that is read out via coincident detection of photoelectrons and fragment ions. By coincidence analysis of the kinetic energies of the ionic fragments and photoelectrons, the transition from a bound molecular dication to two isolated atomic ions is observed through the energy shift of the inner-shell electrons. Via ab-initio simulations, we are able to map characteristic features in the kinetic energy release and photoelectron spectrum to specific delay times between photoabsorptions. In contrast to previous studies where nuclear motions were typically revealed by measuring ion kinetics, our work shows that inner-shell photoelectron energies can also be sensitive probes of nuclear dynamics, which adds one more dimension to the study of light-matter interactions with X-ray pulses.

Double Core-Hole Generation in O_{2} Molecules Using an X-Ray Free-Electron Laser: Molecular-Frame Photoelectron Angular Distributions

We report on a multiparticle coincidence experiment performed at the European X-ray Free-Electron Laser at the Small Quantum Systems instrument using a COLTRIMS reaction microscope. By measuring two ions and two electrons in coincidence, we investigate double core-hole generation in O_{2} molecules in the gas phase. Single-site and two-site double core holes have been identified and their molecular-frame electron angular distributions have been obtained for a breakup of the oxygen molecule into two doubly charged ions. The measured distributions are compared to results of calculations performed within the frozen- and relaxed-core Hartree-Fock approximations.

Young's Double-Slit Interference in a Hydrogen Atom

We demonstrate the possibility of realizing Young's double-slit interference in a hydrogen atom via ab initio simulations. By exposing the hydrogen atom to a high-frequency intensive laser pulse, the bound state distorts into a dichotomic Kramers-Henneberger state whose photoelectron momentum distribution imprints a double-slit interference structure. The dichotomic hydrogen atom presents molecular peculiarities, such as charge-resonance enhanced ionization, electron spin flipping due to the non-Abelian Berry phase. In return, the photoelectron momentum distribution carrying the double-slit interference structure provides unambiguous evidence on the existence of Kramers-Henneberger states, and thus the adiabatic stabilization.

Multi-slit-type interference in carbon 2s photoionization of polyatomic molecules: from a fundamental effect to structural parameters

In molecular photoemission, the analogue of the celebrated Young's double slit experiment is coherent electron emission from two equivalent atomic centers, giving rise to an interference pattern. Here multi-slit interference is investigated in inner-valence photoionization of propane, n-butane, isobutane and methyl peroxide. A more complex pattern is observed due to molecular orbital delocalization in polyatomic molecules, blurring the distinction between interference and diffraction. The potential to extract geometrical information is emphasized, as a more powerful extension of the EXAFS technique. Accurate reproduction of experimental features is obtained by simulations at the static Density Functional Theory level.

Double-slit photoelectron interference in strong-field ionization of the neon dimer

Wave-particle duality is an inherent peculiarity of the quantum world. The double-slit experiment has been frequently used for understanding different aspects of this fundamental concept. The occurrence of interference rests on the lack of which-way information and on the absence of decoherence mechanisms, which could scramble the wave fronts. Here, we report on the observation of two-center interference in the molecular-frame photoelectron momentum distribution upon ionization of the neon dimer by a strong laser field. Postselection of ions, which are measured in coincidence with electrons, allows choosing the symmetry of the residual ion, leading to observation of both, gerade and ungerade, types of interference.

Imaging molecular geometry with electron momentum spectroscopy

Electron momentum spectroscopy is a unique tool for imaging orbital-specific electron density of molecule in momentum space. However, the molecular geometry information is usually veiled due to the single-centered character of momentum space wavefunction of molecular orbital (MO). Here we demonstrate the retrieval of interatomic distances from the multicenter interference effect revealed in the ratios of electron momentum profiles between two MOs with symmetric and anti-symmetric characters. A very sensitive dependence of the oscillation period on interatomic distance is observed, which is used to determine F-F distance in CF₄ and O-O distance in CO₂ with sub-Ångström precision. Thus, using one spectrometer, and in one measurement, the electron density distributions of MOs and the molecular geometry information can be obtained simultaneously. Our approach provides a new robust tool for imaging molecules with high precision and has potential to apply to ultrafast imaging of molecular dynamics if combined with ultrashort electron pulses in the future.

Selecting core-hole localization or delocalization in CS2 by photofragmentation dynamics

Electronic core levels in molecules are highly localized around one atomic site. However, in single-photon ionization of symmetric molecules, the question of core-hole localization versus delocalization over two equivalent atoms has long been debated as the answer lies at the heart of quantum mechanics. Here, using a joint experimental and theoretical study of core-ionized carbon disulfide (CS2), we demonstrate that it is possible to experimentally select distinct molecular-fragmentation pathways in which the core hole can be considered as either localized on one sulfur atom or delocalized between two indistinguishable sulfur atoms. This feat is accomplished by measuring photoelectron angular distributions within the frame of the molecule, directly probing entanglement or disentanglement of quantum pathways as a function of how the molecule dissociates.

Imaging molecular structure through femtosecond photoelectron diffraction on aligned and oriented gas-phase molecules

This paper gives an account of our progress towards performing femtosecond time-resolved photoelectron diffraction on gas-phase molecules in a pump-probe setup combining optical lasers and an X-ray free-electron laser. We present results of two experiments aimed at measuring photoelectron angular distributions of laser-aligned 1-ethynyl-4-fluorobenzene (C(8)H(5)F) and dissociating, laser-aligned 1,4-dibromobenzene (C(6)H(4)Br(2)) molecules and discuss them in the larger context of photoelectron diffraction on gas-phase molecules. We also show how the strong nanosecond laser pulse used for adiabatically laser-aligning the molecules influences the measured electron and ion spectra and angular distributions, and discuss how this may affect the outcome of future time-resolved photoelectron diffraction experiments.

Angular momentum sensitive two-center interference

In quantum mechanics the Young-type double-slit experiment can be performed with electrons either traveling through a double slit or being coherently emitted from two inversion symmetric molecular sites. In the latter one the valence photoionization cross sections of homonuclear diatomic molecules were predicted to oscillate over kinetic energy almost 50 years ago. Beyond the direct proof of the oscillatory behavior of these photoionization cross sections σ, we show that the angular distribution of the emitted electrons reveals hitherto unexplored information on the relative phase shift between the corresponding partial waves through two-center interference patterns.

Observation of the interference effect in vibrationally resolved electron momentum spectroscopy of H2

We report the first measurement on vibrationally resolved electron momentum spectroscopy of H2 by using a high-resolution (e, 2e) spectrometer. The vibrational-specific experimental momentum profiles have been obtained and shown to be in agreement with calculations of (e, 2e) ionization cross sections taking into account the vibrational wave functions. Distinct deviations from Franck-Condon predictions have been observed in vibrational ratios of cross sections, which can readily be ascribed to the Young-type two-center interference. Unlike previous (e, 2e) work, the present observation of an interference effect does not rely on the comparison with the one-center atomic cross section.

Double momentum spectrometer for ion-electron vector correlations in dissociative photoionization

We have developed a new momentum spectrometer dedicated to momentum vector correlations in the context of deep core photoionization of atomic and molecular species in the gas phase. In this article, we describe the design and operation of the experimental setup. The capabilities of the apparatus are illustrated with a set of measurements done on the sulphur core 1s photoionization of gas-phase CS2.

From double-slit interference to structural information in simple hydrocarbons

Interferences in coherent emission of photoelectrons from two equivalent atomic centers in a molecule are the microscopic analogies of the celebrated Young's double-slit experiment. By considering inner-valence shell ionization in the series of simple hydrocarbons C2H2, C2H4, and C2H6, we show that double-slit interference is widespread and has built-in quantitative information on geometry, orbital composition, and many-body effects. A theoretical and experimental study is presented over the photon energy range of 70-700 eV. A strong dependence of the oscillation period on the C-C distance is observed, which can be used to determine bond lengths between selected pairs of equivalent atoms with an accuracy of at least 0.01 Å. Furthermore, we show that the observed oscillations are directly informative of the nature and atomic composition of the inner-valence molecular orbitals and that observed ratios are quantitative measures of elusive many-body effects. The technique and analysis can be immediately extended to a large class of compounds.

Core hole-electron correlation in coherently coupled molecules

We study the core hole-electron correlation in coherently coupled molecules by energy dispersive near edge x-ray absorption fine-structure spectroscopy. In a transient phase, which exists during the transition between two bulk arrangements, 1,4,5,8-naphthalene-tetracarboxylicacid-dianhydride multilayer films exhibit peculiar changes of the line shape and energy position of the x-ray absorption signal at the C K-edge with respect to the bulk and gas phase spectra. By a comparison to a theoretical model based on a coupling of transition dipoles, which is established for optical absorption, we demonstrate that the observed spectroscopic differences can be explained by an intermolecular delocalized core hole-electron pair. By applying this model we can furthermore quantify the coherence length of the delocalized core exciton.

Ultrafast charge rearrangement and nuclear dynamics upon inner-shell multiple ionization of small polyatomic molecules

Ionization and fragmentation of methylselenol (CH(3)SeH) molecules by intense (>10(17) W/cm(2)) 5 fs x-ray pulses (ħω=2 keV) are studied by coincident ion momentum spectroscopy. We contrast the measured charge state distribution with data on atomic Kr, determine kinetic energies of resulting ionic fragments, and compare them to the outcome of a Coulomb explosion model. We find signatures of ultrafast charge redistribution from the inner-shell ionized Se atom to its molecular partners, and observe significant displacement of the atomic constituents in the course of multiple ionization.

Direct observation of Young’s double-slit interferences in vibrationally resolved photoionization of diatomic molecules

Vibrationally resolved valence-shell photoionization spectra of H₂, N₂ and CO have been measured in the photon energy range 20–300 eV using third-generation synchrotron radiation. Young’s double-slit interferences lead to oscillations in the corresponding vibrational ratios, showing that the molecules behave as two-center electron-wave emitters and that the associated interferences leave their trace in the angle-integrated photoionization cross section. In contrast to previous work, the oscillations are directly observable in the experiment, thereby removing any possible ambiguity related to the introduction of external parameters or fitting functions. A straightforward extension of an original idea proposed by Cohen and Fano [Cohen HD, Fano U (1966) Phys Rev 150:30] confirms this interpretation and shows that it is also valid for diatomic heteronuclear molecules. Results of accurate theoretical calculations are in excellent agreement with the experimental findings.

Exploring dynamical electron theory beyond the Born-Oppenheimer framework: from chemical reactivity to non-adiabatically coupled electronic and nuclear wavepackets on-the-fly under laser field

Chemical theory and its application to dynamical electrons in molecules under intense electromagnetic fields is explored, in which we take an explicit account of nuclear nonadiabatic (kinematic) interactions along with simultaneous coupling with intense optical interactions. All the electronic wavefunctions studied here are necessarily time-dependent, and thereby beyond stationary state quantum chemistry based on the Born-Oppenheimer framework. As a general and tractable alternative framework with which to track the electronic and nuclear simultaneous dynamics, we propose an on-the-fly method to calculate the electron and nuclear wavepackets coupled along the branching non-Born-Oppenheimer paths, through which their bifurcations, strong quantum entanglement between nuclear electronic motions, and coherence and decoherence among the phases associated with them are properly represented. Some illustrative numerical examples are also reported, which are aimed at our final goals; real time tracking of nonadiabatic electronic states, chemical dynamics in densely degenerate electronic states coupled with nuclear motions and manipulation and/or creation of new electronic states in terms of intense lasers, and so on. Other examples are also presented as to how the electron wavepacket dynamics can be used to analyze chemical reactions, shedding a new light on some typical and conventional chemical reactions such as proton transfer followed by tautomerization.

Circular dichroism in photoionization of H2

Circular dichroism is a consequence of chirality. However, nonchiral molecules can also exhibit it when the measurement itself introduces chirality, e.g., when measuring molecular-frame photoelectron angular distributions. The few such experiments performed on homonuclear diatomic molecules show that, as expected, circular dichroism vanishes when the molecular-frame photoelectron angular distributions are integrated over the polar electron emission angle. Here we show that this is not the case in resonant dissociative ionization of H2 for photons of 30-35 eV, which is the consequence of the delayed ionization from molecular doubly excited states into ionic states of different inversion symmetry.

Two-source double-slit interference in angle-resolved high-energy above-threshold ionization spectra of diatoms

When an electron from a diatomic molecule undergoes tunneling-rescattering ionization, a novel form of destructive interference can be realized that involves all four geometric orbits that are available to the electron when it is freed, because both ionization and rescattering may take place at the same or at different centers. We find experimentally and confirm theoretically that in orientation-averaged angle-resolved high-order above-threshold ionization spectra the corresponding destructive interference is visible for O_{2} but not for N_{2}. This effect is different from the suppression of ionization that is well known to occur for O_{2}.

Probing molecular frame photoionization via laser generated high-order harmonics from aligned molecules

Present experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) for ionization from the outermost valence orbitals of molecules. We show that the details of MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides the needed theoretical basis for ultrafast dynamic chemical imaging using infrared laser pulses.

Two-center double-capture interference in fast He2+ + H2 collisions

We report the first observation of Young-type interference effects in a two-electron transfer process. These effects change strongly as the projectile velocity changes in fast (1.2 and 2.0 MeV) He(2+) + H(2) collisions as manifested in strong variations of the double-electron capture rates with the H(2) orientation. This is consistent with fully quantum mechanical calculations, which ignore sequential electron transfer, and a simple projectile de Broglie wave picture assuming that two-electron transfer probabilities are higher in collisions where the projectile passes close to either one of the H(2) nuclei.

Molecular-frame angular distributions of resonant CO:C(1s) Auger electrons

The molecular-frame angular distributions of resonantly excited CO:C(1s) --> pi* Auger electrons were determined using angle-resolved electron-ion coincidence spectroscopy in combination with a novel transformation procedure. Our new methodology yields full three-dimensional electron angular distributions with high energy resolution from the measurement of electrons at only two angles. The experimentally determined distributions are well reproduced by calculations performed in a simple one-center approximation, allowing an unambiguous identification of several overlapping Auger lines.

Classical two-slit interference effects in double photoionization of molecular hydrogen at high energies

Recent experiments on double photoionization of H2 with photon energies between 160 and 240 eV have revealed body-frame angular distributions that suggest classical two-slit interference effects may be present when one electron carries most of the available energy and the second electron is not observed. We report precise quantum mechanical calculations that reproduce the experimental findings. They reveal that the interpretation in terms of classical diffraction is only appropriate at substantially higher photon energies. At the energies considered in the experiment we offer an alternative explanation based on the mixing of two nondiffractive contributions by circularly polarized light.

Ultrafast probing of core hole localization in N2

Although valence electrons are clearly delocalized in molecular bonding frameworks, chemists and physicists have long debated the question of whether the core vacancy created in a homonuclear diatomic molecule by absorption of a single x-ray photon is localized on one atom or delocalized over both. We have been able to clarify this question with an experiment that uses Auger electron angular emission patterns from molecular nitrogen after inner-shell ionization as an ultrafast probe of hole localization. The experiment, along with the accompanying theory, shows that observation of symmetry breaking (localization) or preservation (delocalization) depends on how the quantum entangled Bell state created by Auger decay is detected by the measurement.

Interference in the collective electron momentum in double photoionization of H2

We investigate single-photon double ionization of H(2) by 130 to 240 eV circularly polarized photons. We find a double slitlike interference pattern in the sum momentum of both electrons in the molecular frame which survives integration over all other degrees of freedom. The difference momentum and the individual electron momentum distributions do not show such a robust interference pattern. We show that this interference results from a non-Heitler-London fraction of the H(2) ground state where both electrons are at the same atomic center.

Numerical experiments on quantum chaotic billiards

A recently proposed numerical technique for generation of high-quality unstructured meshes is combined with a finite-element method to solve the Helmholtz equation that describes the quantum mechanics of a particle confined in two-dimensional cavities. Different shapes are treated on equal footing, including Sinai, stadium, annular, threefold symmetric, mushroom, cardioid, triangle, and coupled billiards. The results are shown to be in excellent agreement with available measurements in flat microwave resonator counterparts with nonintegrable geometries.

Molecular frame and recoil frame photoelectron angular distributions from dissociative photoionization of NO2

The authors report measured and computed molecular frame photoelectron angular distributions (MFPADs) and recoil frame photoelectron angular distributions (RFPADs) for the single photon ionization of the nonlinear molecule NO2 leading to the (1a2)-1 b 3A2 and (4a1)-1 3A1 states of NO2+. Experimentally, the RFPADs were obtained using the vector correlation approach applied to the dissociative photoionization (DPI) involving these molecular ionic states. The polar and azimuthal angle dependences of the photoelectron angular distributions are measured relative to the reference frame provided by the ion recoil axis and direction of polarization of the linearly polarized light. Experimental results are reported for the photon excitation energies hnu=14.4 and 22.0 eV. Theoretically the authors give expressions for both the MFPAD and the RFPAD. They show that the functional form in the recoil frame, where an average over the azimuthal dependence of the molecular fragments about the recoil direction is made, is identical to that they have earlier found for the DPI experiments performed on linear molecules. MFPADs were then computed using single-center expansion techniques within the fixed-nuclei frozen-core Hartree-Fock approximation. The computed cross sections for ionization to the (1a2)-1 b 3A2 state show a strong propensity for ionization with the polarization of the light perpendicular to the plane of the molecule, whereas the ionization to the (4a1)-1 3A1 state of the ion is of similar intensity for all orientations of the polarization of the light in the molecular frame. These qualitative features of the MFPAD are also evident in the RFPAD. The RFPAD for ionization leading to the (1a2)-1 b 3A2 state is strongly peaked in the perpendicular orientation, whereas the RFPAD for ionization leading to the (4a2)-1 3A1 state is much more nearly isotropic. Comparison between experimental and theoretical RFPADs indicates that the recoil angle for NO+ fragments is approximately 50 degrees relative to the symmetry axis of the initial C2v symmetry of the NO2 molecule in the ionization leading to the (1a2)-1 b 3A2 state and the recoil angle is approximately 120 degrees for the O+ fragment for ionization leading to the (4a1)-1 3A1 state.

Single Photon-Induced Symmetry Breaking of H2 Dissociation

H2, the smallest and most abundant molecule in the universe, has a perfectly symmetric ground state. What does it take to break this symmetry? We found that the inversion symmetry can be broken by absorption of a linearly polarized photon, which itself has inversion symmetry. In particular, the emission of a photoelectron with subsequent dissociation of the remaining H+2 fragment shows no symmetry with respect to the ionic H+ and neutral H atomic fragments. This lack of symmetry results from the entanglement between symmetric and antisymmetric H+2 states that is caused by autoionization. The mechanisms behind this symmetry breaking are general for all molecules.

Interferences from fast electron emission in molecular photoionization

We present a theoretical study of fast-electron emission produced in H2 and H2+ photoionization. We show that, when the electron wave length is comparable to the molecular size, the electron angular distributions arising from fixed-in-space molecules exhibit pronounced interference effects that critically depend on orientation and energy sharing between electrons and nuclei. In particular, for molecules oriented parallel to the polarization direction, the angular patterns reveal a complex nodal structure, while for molecules oriented perpendicularly, typical Young's double-slit interferences are observed. These patterns change dramatically as the molecule vibrates.