Auger-Meitner and X-ray Absorption Spectra of Ethylene Cation: Insight into Conical Intersection Dynamics.

We present a theoretical investigation of the near-edge X-ray absorption fine structure and the Auger-Meitner decay spectra of ethylene and its cation. Herein, we demonstrate that our method, coupled with the nuclear ensemble approach, successfully reproduces the natural bandwidth structure of the experimental resonant Auger-Meitner decay spectra of ethylene, which is not very well reproduced within the Franck-Condon approximation. Furthermore, we analyze the Auger-Meitner decay spectra of the ethylene cation in light of minimum energy conical intersection structures involving the two lowest cationic states (D1 and D0), providing valuable insights into the ultrafast D1/D0 relaxation dynamics. Our results suggest that Auger-Meitner electron spectroscopy can help elucidate the mechanism behind the initial 20 fs of the relaxation dynamics.

Description of the KLL Auger-Meitner decay spectra of argon following primary and satellite core-ionized states.

The K-edge photoelectron and KLL Auger-Meitner decay spectra of Argon have been investigated computationally at the restricted active space perturbation theory to the second order level using biorthonormally transformed orbital sets. Binding energies were computed for the Ar 1s primary ionization, as well as for satellite states originated from shake-up and shake-off processes. Based on our calculations, the contributions of shake-up and shake-off states to the KLL Auger-Meitner spectra of Argon have been completely elucidated. Our results are compared with recent state-of-the-art experimental measurements on Argon.

Photochemical Ring-Opening Reaction of 1,3-Cyclohexadiene: Identifying the True Reactive State.

The photochemically induced ring-opening isomerization reaction of 1,3-cyclohexadiene to 1,3,5-hexatriene is a textbook example of a pericyclic reaction and has been amply investigated with advanced spectroscopic techniques. The main open question has been the identification of the single reactive state which drives the process. The generally accepted description of the isomerization pathway starts with a valence excitation to the lowest lying bright state, followed by a passage through a conical intersection to the lowest lying doubly excited state, and finally a branching between either the return to the ground state of the cyclic molecule or the actual ring-opening reaction leading to the open-chain isomer. Here, in a joint experimental and computational effort, we demonstrate that the evolution of the excitation-deexcitation process is much more complex than that usually described. In particular, we show that an initially high-lying electronic state smoothly decreasing in energy along the reaction path plays a key role in the ring-opening reaction.

Strong chiral response in non-collinear high harmonic generation driven by purely electric-dipole interactions.

High harmonic generation (HHG) records the ultrafast electronic response of matter to light, encoding key properties of the interrogated quantum system, such as chirality. The first implementation of chiral HHG [Cireasa et al, Nat. Phys.11, 654 (2015)10.1038/nphys3369] relied on the weak electronic response of a medium of randomly oriented chiral molecules to the magnetic component of an elliptically polarized wave, yielding relatively weak chiro-optical signals. Here we apply state-of-the-art semi-analytical modelling to show that elliptically polarized light can drive a strong chiral response in chiral molecules via purely electric-dipole interactions - the magnetic component of the wave does not participate at all. This strong chiro-optical response, which remains hidden in standard HHG experiments, can be mapped into the macroscopic far-field signal using a non-collinear configuration, creating new opportunities for imaging chiral matter and chiral dynamics on ultrafast time scales.

Trends in angle-resolved molecular photoelectron spectroscopy.

The field of angle-resolved molecular photoelectron spectroscopy is reviewed, with emphasis on foundations and most recent applications in different regimes of light-matter interaction. The basic formalism underlying one-photon electron angular distributions is presented, from the primary molecular frame (MF) photoemission i.e. emission from fully oriented molecules to laboratory frame (LF) observables produced from randomly oriented targets, extensions to multiphoton and strong field processes being briefly described, followed by a survey of current quantum mechanical computational approaches. The description of experimental developments is focused on the advancements in two major instrumentation fields for angle-resolved PES of molecules in the last two decades, namely charged-particle imaging spectrometers and adiabatically or impulsively laser-induced molecular alignment, together with their interplay with the remarkable characteristics achieved nowadays by the ionizing light sources and the challenging control of complex molecules in the gas phase. Aspects and applications of LF angular observables from unoriented targets are presented, with contemporary applications, especially as probes of the target electronic structure, including higher angular observables, in particular photoelectron circular dichroism (PECD) from chiral molecules, which is confirmed as a powerful chiral technique, and higher terms arising from multiphoton or non-dipole terms. Molecular frame photoelectron angular distributions (MFPADs), which stand out as the most complete observables of molecular photoionization stereodynamics in different excitation regimes, now broadly extended to characterize molecular structure and dynamics, are then discussed stemming from fully oriented molecules tackled by electron-ion momentum coincidence techniques, or from laser aligned samples. Finally, novel developments and challenging perspectives, notably the implementation of PAD in time-resolved schemes at ultrashort time scales, high energy, and high intensity regimes are drawn.

Disentangling the resonant Auger spectra of ozone: overlapping core-hole states and core-excited state dynamics.

We investigate the resonant and non-resonant Auger spectra of ozone with a newly implemented multi-reference protocol based on the one-center approximation [Tenorio et al., J. Chem. Theory Comput. 2022, 18, 4387-4407]. The results of our calculations are compared to existing experimental data, where we elucidate the resonant Auger spectrum measured at 530.8 and 536.7 eV, that correspond to the 1sOT → π*(2b1) and 1sOT → σ*(7a1) resonances, and at 542.3 eV, which lies near the 1sOC → σ*(7a1) excited state and above the 1sOT-1 ionization threshold. Using molecular dynamics simulations, we demonstrate the relevance of few-femtoseconds nuclear dynamics in the resonant Auger spectrum of ozone following the 1sOT → π*(2b1) core-excitation.

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 description of the electronic continuum via a time-dependent density functional approach using a multicentric B-spline basis, this yields highly accurate photoionization dynamical parameters (cross-sections, branching ratios, asymmetry parameters and dichroic coefficients) for primary (1h) states as well as satellite states of (2h1p) character. Illustrative results are presented for the molecular systems H2O, H2S, CS, CS2 and (S)-propylene oxide (a.k.a. methyloxirane).

Vibrationally resolved photoelectron angular distributions of ammonia.

We present a theoretical study of vibrationally resolved photoelectron angular distributions for ammonia in both laboratory and molecular frames, in the photon energy range up to 70 eV, where only valence and inner-valence ionization is possible. We focus on the band resulting from ionization of the 3a1 HOMO orbital leading to NH3+ in the electronic ground state, , for which the dominant vibrational progression corresponds to the activation of the umbrella inversion mode. We show that, at room temperature, the photoelectron angular distributions for randomly oriented molecules or molecules whose principal C3 symmetry axis is aligned along the light polarization direction are perfectly symmetric with respect to the plane that contains the intermediate D3h conformation connecting the pyramidal structures associated with the double-well potential of the umbrella inversion mode. These distributions exhibit symmetric, nearly perfect two-lobe shapes in the whole range of investigated photon energies. In contrast, for molecules where the initial vibrational state is localized in one of the two wells, a situation that can experimentally be achieved by introducing an external electric field, the molecular-frame photoelectron angular distributions (MFPADs) are in general asymmetric, but the degree of asymmetry of the two lobes dramatically changes and oscillates with photoelectron energy. We also show that, at ultracold temperatures, where all aligned molecules initially lie in the delocalized ground vibrational state, the photoelectron angular distributions are perfectly symmetric, but the two-lobe shape is only observed when the final vibrational state of the resulting NH3+ cation has even parity. When the latter vibrational state has odd parity, the angular distributions are much more involved and, at photoelectron energies of ∼10 eV, they directly reflect the bi-pyramidal geometry of the molecule in its ground vibrational state. These results suggest that, in order to obtain structural information from MFPADs in ammonia and likely in other molecules containing a similar double-well potential, one could preferably work at ultracold temperatures, which is not the case for most molecules.

Core spectroscopy of oxazole.

We have measured, analyzed, and simulated the ground state valence photoelectron spectrum, x-ray absorption (XA) spectrum, x-ray photoelectron (XP) spectrum as well as normal and resonant Auger-Meitner electron (AE) spectrum of oxazole at the carbon, oxygen, and nitrogen K-edge in order to understand its electronic structure. Experimental data are compared to theoretical calculations performed at the coupled cluster, restricted active space perturbation theory to second-order and time-dependent density functional levels of theory. We demonstrate (1) that both N and O K-edge XA spectra are sensitive to the amount of dynamical electron correlation included in the theoretical description and (2) that for a complete description of XP spectra, additional orbital correlation and orbital relaxation effects need to be considered. The normal AE spectra are dominated by a singlet excitation channel and well described by theory. The resonant AE spectra, however, are more complicated. While the participator decay channels, dominating at higher kinetic energies, are well described by coupled cluster theory, spectator channels can only be described satisfactorily using a method that combines restricted active space perturbation theory to second order for the bound part and a one-center approximation for the continuum.

Discrimination of Excited States of Acetylacetone through Theoretical Molecular-Frame Photoelectron Angular Distributions.

Photoelectron angular distribution (PAD) in the laboratory frame for randomly oriented molecules is typically described by a single anisotropy parameter, the so-called asymmetry parameter. However, especially from a theoretical perspective, it is more natural to consider molecular photoionization by using a molecular frame. The molecular frame PADs (MFPADs) may be used to extract information about the electronic structure of the system studied. In the last decade, significant experimental efforts have been directed to MFPAD measurements. MFPADs are highly characterizing signatures of the final ionic states. In particular, they are very sensitive to the nature of the final state, which is embodied in the corresponding Dyson orbital. In our previous work on acetylacetone, a prototype system for studying intra-molecular hydrogen bond interactions, we followed the dynamics of the excited states involved in the photoexcitation-deexcitation process of this molecule. It remains to be explored the possibility of discriminating between different excited states through the MFPAD profiles. The calculation of MFPADs to differentiate excited states can pave the way to the possibility of a clear discrimination for all the cases where the recognition of excited states is otherwise intricate.

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.

Photoionization Observables from Multi-Reference Dyson Orbitals Coupled to B-Spline DFT and TD-DFT Continuum.

We present a theoretical model to compute the accurate photoionization dynamical parameters (cross-sections, asymmetry parameters and orbital, or cross-section, ratios) from Dyson orbitals obtained with the multi-state complete active space perturbation theory to the second order (MS-CASPT2) method. Our new implementation of Dyson orbitals in OpenMolcas takes advantage of the full Abelian symmetry point group and has the corrected normalization. The Dyson orbitals are coupled to an accurate description of the electronic continuum obtained with a multicentric B-spline basis at the DFT and TD-DFT levels. Two prototype diatomic molecules, i.e., CS and SiS, have been chosen due to their smallness, which hides important correlation effects. These effects manifest themselves in the appearance of well-characterized isolated satellite bands in the middle of the valence region. The rich satellite structures make CS and SiS the perfect candidates for a computational study based on our highly accurate MS-CASPT2/B-spline TD-DFT protocol.

Molecular fragmentation as a way to reveal early electron dynamics induced by attosecond pulses.

We present a theoretical study of the electron and nuclear dynamics that would arise in an attosecond two-color XUV-pump/XUV-probe experiment in glycine. In this scheme, the broadband pump pulse suddenly ionizes the molecule and creates an electronic wave packet that subsequently evolves under the influence of the nuclear motion until it is finally probed by the second XUV pulse. To describe the different steps of such an experiment, we have combined a multi-reference static-exchange scattering method with a trajectory surface hopping approach. We show that by changing the central frequency of the pump pulse, i.e., by engineering the initial electronic wave packet with the pump pulse, one can drive the cation dynamics into a specific fragmentation pathway. Reminiscence of this early electron dynamics can be observed in specific fragmentation channels (not all of them) as a function of the pump-probe delay and in time-resolved photoelectron spectra at specific photoelectron energies. The optimum conditions to visualize the initial electronic coherence in photoelectron and photo-ion spectra depend very much on the characteristics of the pump pulse as well as on the electronic structure of the molecule under study.

Valence-shell photoelectron circular dichroism of ruthenium(III)-tris-(acetylacetonato) gas-phase enantiomers.

Chiral transition-metal complexes are of interest in many fields ranging from asymmetric catalysis and molecular materials science to optoelectronic applications or fundamental physics including parity violation effects. We present here a combined theoretical and experimental investigation of gas-phase valence-shell photoelectron circular dichroism (PECD) on the challenging open-shell ruthenium(III)-tris-(acetylacetonato) complex, Ru(acac)3. Enantiomerically pure Δ- or Λ-Ru(acac)3, characterized by electronic circular dichroism (ECD), were vaporized and adiabatically expanded to produce a supersonic beam and photoionized by circularly-polarized VUV light from the DESIRS beamline at Synchrotron SOLEIL. Photoelectron spectroscopy (PES) and PECD experiments were conducted using a double imaging electron/ion coincidence spectrometer, and compared to density functional theory (DFT) and time-dependent DFT (TDDFT) calculations. The open-shell character of Ru(acac)3, which is not taken into account in our DFT approach, is expected to give rise to a wide multiplet structure, which is not resolved in our PES signals but whose presence might be inferred from the additional striking features observed in the PECD curves. Nevertheless, the DFT-based assignment of the electronic bands leads to the characterisation of the ionized orbitals. In line with other recent works, the results confirm that PECD persists independently on the localization and/or on the achiral or chiral nature of the initial orbital, but is rather a probe of the molecular potential as a whole. Overall, the measured PECD signals on Ru(acac)3, a system exhibiting D3 propeller-type chirality, are of similar magnitude compared to those on asymmetric-carbon-based chiral organic molecules which constitute the vast majority of species investigated so far, thus suggesting that PECD is a universal mechanism, inherent to any type of chirality.

Multi-reference approach to the computation of double core-hole spectra.

Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K-2) are obtained for H2O, N2, CO, and C2H2n (n = 1-3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K-2 shake-up spectra of H2O and C2H2n molecules are here completely characterized for the first time.

Photoionization Dynamics of the Tetraoxo Complexes OsO4 and RuO4.

The photoionization dynamics of OsO4 and RuO4, chosen as model systems of small-size mononuclear heavy-metal complexes, has been theoretically studied by the time-dependent density functional theory (TDDFT). Accurate experimental measurements of photoionization dynamics as a benchmarking test for the theory are reported for the photoelectron asymmetry parameters of outer valence ionizations of OsO4, measured in the 17-90 eV photon energy range. The theoretical results are in good agreement with the available experimental data. The observed dynamical behavior of partial cross sections and asymmetry parameters has been related to both the coupling to the continuum of discrete excited states, giving strong modulations in the photon energy dependency, and the atomic composition of the initial ionized states, which determines the rate of decay of ionization probability for increasing excitation energies. Overall, an extensive analysis of the photoionization dynamics for valence and core orbitals is presented, showing good agreement with all the available experimental data. This provides confidence for the validity of the TDDFT approach in describing photoionization of heavy transition element compounds, with the perspective of being used for larger systems. Further experimental work is suggested for RuO4 to gather evidence of the sensitivity of the theoretical method to the nature of the metal atom.

Attosecond Electron Dynamics in Molecules.

Advances in attosecond science have led to a wealth of important discoveries in atomic, molecular, and solid-state physics and are progressively directing their footsteps toward problems of chemical interest. Relevant technical achievements in the generation and application of extreme-ultraviolet subfemtosecond pulses, the introduction of experimental techniques able to follow in time the electron dynamics in quantum systems, and the development of sophisticated theoretical methods for the interpretation of the outcomes of such experiments have raised a continuous growing interest in attosecond phenomena, as demonstrated by the vast literature on the subject. In this review, after introducing the physical mechanisms at the basis of attosecond pulse generation and attosecond technology and describing the theoretical tools that complement experimental research in this field, we will concentrate on the application of attosecond methods to the investigation of ultrafast processes in molecules, with emphasis in molecules of chemical and biological interest. The measurement and control of electronic motion in complex molecular structures is a formidable challenge, for both theory and experiment, but will indubitably have a tremendous impact on chemistry in the years to come.

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.

Resonant Photoelectron Confinement in the SF6 Molecule.

Recent thorough experimental activity aiming to generate high harmonics in the SF6 molecules requires the knowledge of, on one hand, accurate valence-shell photoionization cross sections and phases, from a threshold up to a few tens of eV, where resonances are likely to appear, and, on the other hand, the effect of the nuclear vibrational dynamics on the process. In this work, we have experimentally determined and theoretically evaluated vibrationally resolved photoionization cross sections of SF6 up to 80 eV photon energies, with an emphasis on the E2T1u channel, for which vibrational progressions are fully resolved in the experiment. Our results reveal the presence of shape resonances due to excitation to SF6 virtual states lying just above the ionization threshold, in agreement with previous synchrotron radiation work and theoretical calculations. More interestingly, our calculations also disclose resonance features at photoelectron energies as high as 40-50 eV, which are due to the transient confinement of the ejected electron in the octahedral cage formed by the peripheral F atoms. In the vicinity of all resonances, including those due to confinement, the calculated ionization phases experience an excursion of about π or π/2 and significantly depend on the final vibrational state of the remaining cation. Both effects should be taken into account to correctly interpret ongoing high-harmonic generation work in SF6. A similar behavior is expected for other symmetric molecules containing a central atom, such as BF3, CF4, and the like.

Energy-Dependent Relative Cross Sections in Carbon 1s Photoionization: Separation of Direct Shake and Inelastic Scattering Effects in Single Molecules.

We demonstrate that the possibility of monitoring relative photoionization cross sections over a large photon energy range allows us to study and disentangle shake processes and intramolecular inelastic scattering effects. In this gas-phase study, relative intensities of the carbon 1s photoelectron lines from chemically inequivalent carbon atoms in the same molecule have been measured as a function of the incident photon energy in the range of 300-6000 eV. We present relative cross sections for the chemically shifted carbon 1s lines in the photoelectron spectra of ethyl trifluoroacetate (the "ESCA" molecule). The results are compared with those of methyl trifluoroacetate and S-ethyl trifluorothioacetate as well as a series of chloro-substituted ethanes and 2-butyne. In the soft X-ray energy range, the cross sections show an extended X-ray absorption fine structure type of wiggles, as was previously observed for a series of chloroethanes. The oscillations are damped in the hard X-ray energy range, but deviations of cross-section ratios from stoichiometry persist, even at high energies. The current findings are supported by theoretical calculations based on a multiple scattering model. The use of soft and tender X-rays provides a more complete picture of the dominant processes accompanying photoionization. Such processes reduce the main photoelectron line intensities by 20-60%. Using both energy ranges enabled us to discern the process of intramolecular inelastic scattering of the outgoing electron, whose significance is otherwise difficult to assess for isolated molecules. This effect relates to the notion of the inelastic mean free path commonly used in photoemission studies of clusters and condensed matter.