Single center method: A computational tool for ionization and electronic excitation studies of molecules

Core-Hole Coherent Spectroscopy in Molecules

We study the ultrafast dynamics initiated by a coherent superposition of core-excited states of nitrous oxide molecule. Using high-level ab initio methods, we show that the decoherence caused by the electronic decay and the nuclear dynamics is substantially slower than the induced ultrafast quantum beatings, allowing the system to undergo several oscillations before it dephases. We propose a proof-of-concept experiment using the harmonic up-conversion scheme available at x-ray free-electron laser facilities to trace the evolution of the created core-excited-state coherence through a time-resolved x-ray photoelectron spectroscopy.

Role of the Binding Energy on Nondipole Effects in Single-Photon Ionization

We experimentally study the influence of the binding energy on nondipole effects in K-shell single-photon ionization of atoms at high photon energies. We find that for each ionization event, as expected by momentum conservation, the photon momentum is transferred almost fully to the recoiling ion. The momentum distribution of the electrons becomes asymmetrically deformed along the photon propagation direction with a mean value of 8/(5c)(E_{γ}-I_{P}) confirming an almost 100 year old prediction by Sommerfeld and Schur [Ann. Phys. (N.Y.) 396, 409 (1930)10.1002/andp.19303960402]. The emission direction of the photoions results from competition between the forward-directed photon momentum and the backward-directed recoil imparted by the photoelectron. Which of the two counteracting effects prevails depends on the binding energy of the emitted electron. As an example, we show that at 20 keV photon energy, Ne^{+} and Ar^{+} photoions are pushed backward towards the radiation source, while Kr^{+} photoions are emitted forward along the light propagation direction.

Implementation of the Time-Dependent Complete-Active-Space Self-Consistent-Field Method for Diatomic Molecules

We present a computational approach that implements the time-dependent complete-active-space self-consistent-field method, as introduced in [Phys. Rev. A 88, 023402 (2013)]. Our implementation addresses the challenge of diatomic molecules subjected to an intense laser pulse by considering the full dimensionality of the problem using prolate spheroidal coordinates. The method incorporates the gauge-invariant frozen-core approximation, boosts the evaluation of the electron-electron interaction term using finite-element discrete-variable representation with Neumann expansion, and utilizes an exponential time differencing scheme tailored for the stable propagation of the stiff nonlinear orbital functions. We have successfully applied this methodology to study high-harmonic generation in diatomic molecules such as H2, LiH, and N2, shedding light on the impact of electron correlations in these systems.

Observation of Nondipole-Induced Asymmetry in the Angular Emission Distribution of Photoelectrons from Fixed-in-Space CO Molecules

We investigate experimentally and theoretically the C and O 1s photoionization of fixed-in-space CO molecules at a photon energy of 905 eV. We find a significant dependence of the photoelectron angular distributions on the direction of propagation of the ionizing radiation. It results from an interplay of nondipole effects, on one hand, and molecular effects, on the other. The nondipole effects lead to an increase of the emission probability in the forward direction along the light propagation, and the photoelectron wave being scattered by the molecular potential gives rise to a strong peak in the direction of the atom neighboring the emitter site. These effects can either conspire or extenuate each other, depending on the photoelectron emission direction and molecular orientation in space.

Influence of the emission site on the photoelectron circular dichroism in trifluoromethyloxirane

We report a joint experimental and theoretical study of the differential photoelectron circular dichroism (PECD) in inner-shell photoionization of uniaxially oriented trifluoromethyloxirane. By adjusting the photon energy of the circularly polarized synchrotron radiation, we address 1s-photoionization of the oxygen, different carbon, and all fluorine atoms. The photon energies were chosen such that in all cases electrons with a similar kinetic energy of about 11 eV are emitted. Employing coincident detection of electrons and fragment ions, we concentrate on identical molecular fragmentation channels for all of the electron-emitter scenarios. Thereby, we systematically examine the influence of the emission site of the photoelectron wave on the differential PECD. We observe large differences in the PECD signals. The present experimental results are supported by corresponding relaxed-core Hartree-Fock calculations.

Continuum Electronic States: The Tiresia Code

A multicenter (LCAO) B-spline basis is described in detail, and its capabilities concerning affording convergent solutions for electronic continuum states and wavepacket propagation are presented. It forms the core of the Tiresia code, which implements static-DFT and TDDFT hamiltonians, as well as single channel Dyson-DFT and Dyson-TDDFT descriptions to include correlation in the bound states. Together they afford accurate and computationally efficient descriptions of photoionization properties of complex systems, both in the single photon and strong field environments. A number of examples are provided.

Multi-electron excitation contributions towards primary and satellite states in the photoelectron spectrum

The computation of Dyson orbitals and corresponding ionization energies has been implemented within the Equation of Motion Coupled Cluster Singles, Doubles and Perturbative Triples (EOM-CC3) method. Coupled to an accurate...

Investigating charge-up and fragmentation dynamics of oxygen molecules after interaction with strong X-ray free-electron laser pulses

The X-ray-induced charge-up and fragmentation process of a small molecule is examined in great detail by measuring the molecular-frame photoelectron interference pattern in conjunction with other observables in coincidence.

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.

A new route for enantio-sensitive structure determination by photoelectron scattering on molecules in the gas phase

Combination of Coulomb explosion imaging, molecular frame diffraction imaging, and ab initio computations provide a route for enantio-sensitive structure determination.

Measuring the photoelectron emission delay in the molecular frame

How long does it take to emit an electron from an atom? This question has intrigued scientists for decades. As such emission times are in the attosecond regime, the advent of attosecond metrology using ultrashort and intense lasers has re-triggered strong interest on the topic from an experimental standpoint. Here, we present an approach to measure such emission delays, which does not require attosecond light pulses, and works without the presence of superimposed infrared laser fields. We instead extract the emission delay from the interference pattern generated as the emitted photoelectron is diffracted by the parent ion's potential. Targeting core electrons in CO, we measured a 2d map of photoelectron emission delays in the molecular frame over a wide range of electron energies. The emission times depend drastically on the photoelectrons' emission directions in the molecular frame and exhibit characteristic changes along the shape resonance of the molecule.

Fourfold Differential Photoelectron Circular Dichroism

We report on a joint experimental and theoretical study of photoelectron circular dichroism (PECD) in methyloxirane. By detecting O 1s photoelectrons in coincidence with fragment ions, we deduce the molecule's orientation and photoelectron emission direction in the laboratory frame. Thereby, we retrieve a fourfold differential PECD clearly beyond 50%. This strong chiral asymmetry is reproduced by ab initio electronic structure calculations. Providing such a pronounced contrast makes PECD of fixed-in-space chiral molecules an even more sensitive tool for chiral recognition in the gas phase.

Site-specific interrogation of an ionic chiral fragment during photolysis using an X-ray free-electron laser

Short-wavelength free-electron lasers with their ultrashort pulses at high intensities have originated new approaches for tracking molecular dynamics from the vista of specific sites. X-ray pump X-ray probe schemes even allow to address individual atomic constituents with a 'trigger'-event that preludes the subsequent molecular dynamics while being able to selectively probe the evolving structure with a time-delayed second X-ray pulse. Here, we use a linearly polarized X-ray photon to trigger the photolysis of a prototypical chiral molecule, namely trifluoromethyloxirane (C₃H₃F₃O), at the fluorine K-edge at around 700 eV. The created fluorine-containing fragments are then probed by a second, circularly polarized X-ray pulse of higher photon energy in order to investigate the chemically shifted inner-shell electrons of the ionic mother-fragment for their stereochemical sensitivity. We experimentally demonstrate and theoretically support how two-color X-ray pump X-ray probe experiments with polarization control enable XFELs as tools for chiral recognition.

Photoelectron circular dichroism of O 1s-photoelectrons of uniaxially oriented trifluoromethyloxirane: energy dependence and sensitivity to molecular configuration

The photoelectron circular dichroism (PECD) of the O 1s-photoelectrons of trifluoromethyloxirane (TFMOx) is studied experimentally and theoretically for different photoelectron kinetic energies. The experiments were performed employing circularly polarized synchrotron radiation and coincident electron and fragment ion detection using cold target recoil ion momentum spectroscopy. The corresponding calculations were performed by means of the single center method within the relaxed-core Hartree-Fock approximation. We concentrate on the energy dependence of the differential PECD of uniaxially oriented TFMOx molecules, which is accessible through the employed coincident detection. We also compare the results for the differential PECD of TFMOx to those obtained for the equivalent fragmentation channel and similar photoelectron kinetic energy of methyloxirane (MOx), studied in our previous work. Thereby, we investigate the influence of the substitution of the methyl group by the trifluoromethyl group at the chiral center on the molecular chiral response. Finally, the presently obtained angular distribution parameters are compared to those available in the literature.

Feshbach-Fano approach for calculation of Auger decay rates using equation-of-motion coupled-cluster wave functions. I. Theory and implementation

X-ray absorption creates electron vacancies in the core shell. These highly excited states often relax by Auger decay-an autoionization process in which one valence electron fills the core hole and another valence electron is ejected into the ionization continuum. Despite the important role of Auger processes in many experimental settings, their first-principles modeling is challenging, even for small systems. The difficulty stems from the need to describe many-electron continuum (unbound) states, which cannot be tackled with standard quantum-chemistry methods. We present a novel approach to calculate Auger decay rates by combining Feshbach-Fano resonance theory with the equation-of-motion coupled-cluster single double (EOM-CCSD) framework. We use the core-valence separation scheme to define projectors into the bound (square-integrable) and unbound (continuum) subspaces of the full function space. The continuum many-body decay states are represented by products of an appropriate EOM-CCSD state and a free-electron state, described by a continuum orbital. The Auger rates are expressed in terms of reduced quantities, two-body Dyson amplitudes (objects analogous to the two-particle transition density matrix), contracted with two-electron bound-continuum integrals. Here, we consider two approximate treatments of the free electron: a plane wave and a Coulomb wave with an effective charge, which allow us to evaluate all requisite integrals analytically; however, the theory can be extended to incorporate a more sophisticated description of the continuum orbital.

Interatomic and Intermolecular Coulombic Decay

Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed.

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.

Photoelectron circular dichroism in the multiphoton ionization by short laser pulses. III. Photoionization of fenchone in different regimes

Photoelectron circular dichroism (PECD) in different regimes of multiphoton ionization of fenchone is studied theoretically using the time-dependent single center method. In particular, we investigate the chiral response to the one-color multiphoton or strong-field ionization by circularly polarized 400 nm and 814 nm optical laser pulses or 1850 nm infrared pulse. In addition, the broadband ionization by short coherent circularly polarized 413-1240 nm spanning pulse is considered. Finally, the two-color ionization by the phase-locked 400 nm and 800 nm pulses, which are linearly polarized in mutually orthogonal directions, is investigated. The present computational results on the one-color multiphoton ionization of fenchone are in agreement with the available experimental data. For the ionization of fenchone by broadband and bichromatic pulses, the present theoretical study predicts substantial multiphoton PECDs.

Recoil-Induced Asymmetry of Nondipole Molecular Frame Photoelectron Angular Distributions in the Hard X-ray Regime

We investigate angular emission distributions of the 1s photoelectrons of N_{2} ionized by linearly polarized synchrotron radiation at hν=40  keV. As expected, nondipole contributions cause a very strong forward-backward asymmetry in the measured emission distributions. In addition, we observe an unexpected asymmetry with respect to the polarization direction, which depends on the direction of the molecular fragmentation. In particular, photoelectrons are predominantly emitted in the direction of the forward nitrogen atom. This observation cannot be explained via asymmetries introduced by the initial bound and final continuum electronic states of the oriented molecule. The present simulations assign this asymmetry to a novel nontrivial effect of the recoil imposed to the nuclei by the fast photoelectrons and high-energy photons, which results in a propensity for the ions to break up along the axis of the recoil momentum. The results are of particular importance for the interpretation of future experiments at x-ray free electron lasers operating in the few tens of keV regime, where such nondipole and recoil effects will be essential.

Recovery of High-Energy Photoelectron Circular Dichroism through Fano Interference

It is commonly accepted that the magnitude of a photoelectron circular dichroism (PECD) is governed by the ability of an outgoing photoelectron wave packet to probe the chiral asymmetry of a molecule. To be able to accumulate this characteristic asymmetry while escaping the chiral ion, photoelectrons need to have relatively small kinetic energies of up to a few tens of electron volts. Here, we demonstrate a substantial PECD for very fast photoelectrons above 500 eV kinetic energy released from methyloxirane by a participator resonant Auger decay of its lowermost O 1s excitation. This effect emerges as a result of the Fano interference between the direct and resonant photoionization pathways, notwithstanding that their individual effects are negligibly small. The resulting dichroic parameter has an anomalous dispersion: It changes its sign across the resonance, which can be considered as an analogue of the Cotton effect in the x-ray regime.

Photoelectron Circular Dichroism with Two Overlapping Laser Pulses of Carrier Frequencies ω and 2ω Linearly Polarized in Two Mutually Orthogonal Directions

Using a model methanelike chiral system, we theoretically demonstrate a possibility to access photoelectron circular dichroism (PECD) by a single experiment with two overlapping laser pulses of carrier frequencies ω and 2ω, which are linearly polarized in two mutually orthogonal directions. Depending on the relative phase, the resulting electric field can be tailored to have two different rotational directions in the upper and lower hemispheres along the polarization of the ω pulse. We predict a strong forward-backward asymmetry in the emission of photoelectrons from randomly oriented samples, which has an opposite sign in the upper and lower hemispheres. The predicted PECD effect is phase and enantiomer sensitive, providing new insight in this fascinating fundamental phenomenon. The effect can be optimized by varying relative intensities of the pulses.

Breakdown of the Spectator Concept in Low-Electron-Energy Resonant Decay Processes

We suggest that low-energy electrons, released by resonant decay processes, experience substantial scattering on the electron density of excited electrons, which remain a spectator during the decay. As a result, the angular emission distribution is altered significantly. This effect is expected to be a common feature of low-energy secondary electron emission. In this Letter, we exemplify our idea by examining the spectator resonant interatomic Coulombic decay of Ne dimers. Our theoretical predictions are confirmed by a corresponding coincidence experiment.

Circular Dichroism in Fluorescence Emission Following the C 1s→π* Excitation and Resonant Auger Decay of Carbon Monoxide

Dichroism in angle-resolved spectra of circularly polarized fluorescence from freely-rotating CO molecules was studied experimentally and theoretically. For this purpose, carbon monoxide in the gas phase was exposed to circularly polarized soft X-ray synchrotron radiation. The photon energy was tuned across the C 1s→π* resonant excitation, which decayed via the participator Auger transition into the CO⁺ A ²Π state. The dichroic parameter β1 of the subsequent CO⁺ (A ²Π → X ²Σ⁺) visible fluorescence was measured by photon-induced fluorescence spectroscopy. Present experimental results are explained with the ab initio electronic structure and dynamics calculations performed by the single center method. Our results confirm the possibility to perform partial wave analysis of the emitted photoelectrons in closed-shell molecules.

Observation of Enhanced Chiral Asymmetries in the Inner-Shell Photoionization of Uniaxially Oriented Methyloxirane Enantiomers

Most large molecules are chiral in their structure: they exist as two enantiomers, which are mirror images of each other. Whereas the rovibronic sublevels of two enantiomers are almost identical (neglecting a minuscular effect of the weak interaction), it turns out that the photoelectric effect is sensitive to the absolute configuration of the ionized enantiomer. Indeed, photoionization of randomly oriented enantiomers by left or right circularly polarized light results in a slightly different electron flux parallel or antiparallel with respect to the photon propagation direction-an effect termed photoelectron circular dichroism (PECD). Our comprehensive study demonstrates that the origin of PECD can be found in the molecular frame electron emission pattern connecting PECD to other fundamental photophysical effects such as the circular dichroism in angular distributions (CDAD). Accordingly, distinct spatial orientations of a chiral molecule enhance the PECD by a factor of about 10.

Interaction of molecular nitrogen with free-electron-laser radiation

Molecular double core hole contribution to the final atomic ion fragments of N₂ when driven by an FEL pulse.

Delocalization of a Vacancy across Two Neon Atoms Bound by the van der Waals Force

We experimentally study 2p photoionization of neon dimers (Ne_{2}) at a photon energy of hν=36.56  eV. By postselection of ionization events which lead to a dissociation into Ne^{+}+Ne we obtain the photoelectron angular emission distribution in the molecular frame. This distribution is symmetric with respect to the direction of the charged vs neutral fragment. It shows an inverted Cohen-Fano double slit interference pattern of two spherical waves emitted coherently but with opposite phases from the two atoms of the dimer.

Angle-Resolved Auger Spectroscopy as a Sensitive Access to Vibronic Coupling

In the angle-averaged excitation and decay spectra of molecules, vibronic coupling may induce the usually weak dipole-forbidden transitions by the excitation intensity borrowing mechanism. The present complementary theoretical and experimental study of the resonant Auger decay of core-to-Rydberg excited CH_{4} and Ne demonstrates that vibronic coupling plays a decisive role in the formation of the angle-resolved spectra by additionally involving the decay rate borrowing mechanism. Thereby, we propose that the angle-resolved Auger spectroscopy can in general provide very insightful information on the strength of the vibronic coupling.

Photoelectron wave function in photoionization: plane wave or Coulomb wave?

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

Inner-shell photoionization and core-hole decay of Xe and XeF2

Photoionization cross sections and partial ion yields of Xe and XeF2 from Xe 3d(5/2), Xe 3d(3/2), and F 1s subshells in the 660-740 eV range are compared to explore effects of the F ligands. The Xe 3d-ϵf continuum shape resonances dominate the photoionization cross sections of both the atom and molecule, but prominent resonances appear in the XeF2 cross section due to nominal excitation of Xe 3d and F 1s electrons to the lowest unoccupied molecular orbital (LUMO), a delocalized anti-bonding MO. Comparisons of the ion products from the atom and molecule following Xe 3d photoionization show that the charge-state distribution of Xe ions is shifted to lower charge states in the molecule along with production of energetic F(+) and F(2+) ions. This suggests that, in decay of a Xe 3d core hole, charge is redistributed to the F ligands and the system dissociates due to Coulomb repulsion. The ion products from excitation of the F 1s-LUMO resonance are different and show strong increases in the yields of Xe(+) and F(+) ions. The subshell ionization thresholds, the LUMO resonance energies, and their oscillator strengths are calculated by relativistic coupled-cluster methods and agree well with measurements.

Core hole screening and decay rates of double core ionized first row hydrides

Because of the high intensity, X-ray free electron lasers allow one to create and probe double core ionized states in molecules. The decay of these multiple core ionized states crucially determines the evolution of radiation damage in single molecule diffractive imaging experiments. Here we have studied the Auger decay in hydrides of first row elements after single and double core ionization by quantum mechanical ab initio calculations. In our approach the continuum wave function of the emitted Auger electron is expanded into spherical harmonics on a radial grid. The obtained decay rates of double K-shell vacancies were found to be systematically larger than those for the respective single K-shell vacancies, markedly exceeding the expected factor of two. This enhancement is attributed to the screening effects induced by the core hole. We propose a simple model, which is able to predict core hole decay rates in molecules with low Z elements based on the electron density in the vicinity of the core hole.