Attosecond Electron Dynamics in Molecules

Bond breaking of furan-maleimide adducts via a diradical sequential mechanism under an external mechanical force

Substituted furan-maleimide Diels-Alder adducts are bound by dynamic covalent bonds that make them particularly attractive mechanophores. Thermally activated [4 + 2] retro-Diels-Alder (DA) reactions predominantly proceed via a concerted mechanism in the ground electronic state. We show that an asymmetric mechanical force along the anchoring bonds in both the endo and exo isomers of proximal dimethyl furan-maleimide adducts favors a sequential pathway. The switching from a concerted to a sequential mechanism occurs at external forces of ≈1 nN. The first bond rupture occurs for a projection of the pulling force on the scissile bond at ≈4.3 nN for the exo adduct and ≈3.8 nN for the endo one. The reaction is inhibited for external forces up to ≈3.4 nN for the endo adduct and 3.6 nN for the exo one after which it is activated. In the activated region, at 4 nN, the rupture rate of the first bond for the endo adduct is computed to be ≈3 orders of magnitude larger than for the exo one in qualitative agreement with recent sonication experiments [Z. Wang and S. L. Craig, Chem. Commun., 2019, 55, 12263-12266]. In the intermediate region of the path between the rupture of the first and the second bond, the lowest singlet state exhibits a diradical character for both adducts and is close in energy to a diradical triplet state. The computed values of spin-orbit coupling along the path are too small for inducing intersystem crossings. These findings open the way for the rational design of DA mechanophores for polymer science and photochemistry.

Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 - δ while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: Θ‖H‖|t|+ln(1/ϵ)+ln(1/δ). Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H₂ molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

Controlling Fragmentation of the Acetylene Cation in the Vacuum Ultraviolet via Transient Molecular Alignment

An open-loop control scheme of molecular fragmentation based on transient molecular alignment combined with single-photon ionization induced by a short-wavelength free electron laser (FEL) is demonstrated for the acetylene cation. Photoelectron spectra are recorded, complementing the ion yield measurements, to demonstrate that such control is the consequence of changes in the electronic response with molecular orientation relative to the ionizing field. We show that stable C2H2+ cations are mainly produced when the molecules are parallel or nearly parallel to the FEL polarization, while the hydrogen fragmentation channel (C2H2+ → C2H+ + H) predominates when the molecule is perpendicular to that direction, thus allowing one to distinguish between the two photochemical processes. The experimental findings are supported by state-of-the art theoretical calculations.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Few-Femtosecond C2H4+ Internal Relaxation Dynamics Accessed by Selective Excitation

Dissociation of the ethylene cation is a prototypical multistep pathway in which the exact mechanisms leading to internal energy conversions are not fully known. For example, it is still unclear how the energy is exactly redistributed among the internal modes and which step is rate-determining. Here we use few-femtosecond extreme-ultraviolet pulses of tunable energy to excite a different superposition of the four lowest states of C₂H₄⁺ and probe the subsequent fast relaxation with a short infrared pulse. Our results demonstrate that the infrared pulse photoexcites the cationic ground state (GS) to higher excited states, producing a hot GS upon relaxation, which enhances the fragmentation yield. As the photoexcitation probability of the GS strongly depends on the molecular geometry, the probing by the IR pulse provides information about the ultrafast excited-state dynamics and the type of conical intersection (planar or twisted) involved in the first 20 fs of the nonradiative relaxation.

Ultrafast light-induced dynamics in the microsolvated biomolecular indole chromophore with water

Interactions between proteins and their solvent environment can be studied in a bottom-up approach using hydrogen-bonded chromophore-solvent clusters. The ultrafast dynamics following UV-light-induced electronic excitation of the chromophores, potential radiation damage, and their dependence on solvation are important open questions. The microsolvation effect is challenging to study due to the inherent mix of the produced gas-phase aggregates. We use the electrostatic deflector to spatially separate different molecular species in combination with pump-probe velocity-map-imaging experiments. We demonstrate that this powerful experimental approach reveals intimate details of the UV-induced dynamics in the near-UV-absorbing prototypical biomolecular indole-water system. We determine the time-dependent appearance of the different reaction products and disentangle the occurring ultrafast processes. This approach ensures that the reactants are well-known and that detailed characteristics of the specific reaction products are accessible - paving the way for the complete chemical-reactivity experiment.

Photoelectron tomography with an intra-cavity velocity-map imaging spectrometer at 100 MHz repetition rate

We present a compact velocity-map imaging (VMI) spectrometer for photoelectron imaging at 100 MHz repetition rate. Ultrashort pulses from a near-infrared frequency comb laser are amplified in a polarization-insensitive passive femtosecond enhancement cavity. In the focus, multi-photon ionization (MPI) of gas-phase atoms is studied tomographically by rotating the laser polarization. We demonstrate the functioning of the VMI spectrometer by reconstructing photoelectron angular momentum distributions from xenon MPI. Our intra-cavity VMI setup collects electron energy spectra at high rates, with the advantage of transferring the coherence of the cavity-stabilized femtosecond pulses to the electrons. In addition, the setup will allow studies of strong-field effects in nanometric tips.

Ultrafast chirality: the road to efficient chiral measurements

Today we are witnessing the electric-dipole revolution in chiral measurements. Here we reflect on its lessons and outcomes, such as the perspective on chiral measurements using the complementary principles of "chiral reagent" and "chiral observer", the hierarchy of scalar, vectorial and tensorial enantio-sensitive observables, the new properties of the chiro-optical response in the ultrafast and non-linear domains, and the geometrical magnetism associated with the chiral response in photoionization. The electric-dipole revolution is a landmark event. It has opened routes to extremely efficient enantio-discrimination with a family of new methods. These methods are governed by the same principles but work in vastly different regimes - from microwaves to optical light; they address all molecular degrees of freedom - electronic, vibrational and rotational, and use flexible detection schemes, i.e. detecting photons or electrons, making them applicable to different chiral phases, from gases to liquids to amorphous solids. The electric-dipole revolution has also enabled enantio-sensitive manipulation of chiral molecules with light. This manipulation includes exciting and controlling ultrafast helical currents in vibronic states of chiral molecules, enantio-sensitive control of populations in electronic, vibronic and rotational molecular states, and opens the way to efficient enantio-separation and enantio-sensitive trapping of chiral molecules. The word "perspective" has two meanings: an "outlook" and a "point of view". In this perspective article, we have tried to cover both meanings.

A laboratory frame density matrix for ultrafast quantum molecular dynamics

In most cases, the ultrafast dynamics of resonantly excited molecules are considered and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here, we provide a formalism in terms of a lab frame density matrix, which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences, which are potentially experimentally accessible, are rejected by the orientation-averaged reduced vibronic density matrix. Instead, molecular angular distribution moments are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.

Quantum Interference Paves the Way for Long-Lived Electronic Coherences

The creation and dynamical fate of a coherent superposition of electronic states generated in a polyatomic molecule by broadband ionization with extreme ultraviolet pulses is studied using the multiconfiguration time-dependent Hartree method together with an ionization continuum model Hamiltonian. The electronic coherence between the hole states usually lasts until the nuclear dynamics leads to decoherence. A key goal of attosecond science is to control the electronic motion and design laser control schemes to retain this coherence for longer timescales. Here, we investigate this possibility using time-delayed pulses and show how this opens up the prospect of coherent control of charge migration phenomenon.

Stimulated-Raman-scattering amplification of attosecond XUV pulses with pulse-train pumps and application to local in-depth plasma-density measurement

We present a scheme for amplifying an extreme-ultraviolet (XUV) seed isolated attosecond pulse via stimulated Raman scattering of a pulse-train pump. At sufficient seed and pump intensity, the amplification is nonlinear, and the amplitude of the seed pulse can reach that of the pump, one order of magnitude higher than the initial seed amplitude. In the linear amplification regime, we find that the spectral signature of the pump pulse train is imprinted on the spectrum of the amplified seed pulse. Since the spectral signature is imprinted with its frequency downshifted by the plasma frequency, it is possible to deduce the electron density in the region of interaction. This region can be of micrometer length scale longitudinally. By varying the delay between the seed and the pump, this scheme provides a local electron-density measurement inside solid-density plasmas that cannot be probed with optical frequencies, with micrometer resolution.

Atomic partial wave meter by attosecond coincidence metrology

Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics in matter from gas to the condensed phase with attosecond temporal resolution. It has, however, not yet been possible to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attosecond chronoscopy serving as a partial wave meter to reveal the role of each partial wave from the angle-resolved photoionization phase shifts in rare gas atoms. We steer the relative ratio between different partial waves and realize a magnetic-sublevel-resolved atomic phase shift measurement. Our experimental observations are well supported by time-dependent R-matrix numerical simulations and analytical soft-photon approximation analysis. The symmetry-resolved, partial-wave analysis identifies the transition rate and phase shift property in the attosecond photoelectron emission dynamics. Our findings provide critical insights into the ubiquitous attosecond optical timer and the underlying attosecond photoionization dynamics.

Understanding the photoelectron emission time after the interaction of photon with atoms and molecules is of fundamental interest. Here the authors examine the role of partial waves to the photoionization phase shift of atoms using an attosecond clock and electron-ion coincidence spectroscopy.

Quantum coherence in molecular photoionization

The study of onset and decay, as well as control of ultrafast quantum coherence in many-electron systems is in the focus of interest of attosecond physics. Interpretation of attosecond experiments detecting the ultrafast quantum coherence requires application of advanced theoretical and computational tools combining many-electron theory, description of the electronic continuum, including in the strong laser field scenario, as well as nuclear dynamics theory. This perspective reviews the recent theoretical advances in understanding the attosecond dynamics of quantum coherence in photoionized molecular systems and outlines possible future directions of theoretical and experimental study of coherence and entanglement in the attosecond regime.

Few-Femtosecond Isotope Effect in Polyatomic Molecules Ionized by Extreme Ultraviolet Attosecond Pulse Trains

Following ionization by an extreme ultraviolet (XUV) attosecond pulse train, a polyatomic molecule can be promoted to more-than-one excited states of the residual ion. The ensuing relaxation dynamics is often facilitated by several reaction coordinates, making them difficult to disentangle by the usual spectroscopic means. Here, we show that in atto-chemistry isotope labeling can be an efficient tool for unraveling the relaxation pathways in highly excited photoionized molecules. Employing an XUV pump pulse and a near-infrared probe pulse, we found the nuclear as well as coupled electron-nuclear dynamics in ethylene to be almost 40% faster compared to that of its deuterated counterpart. The findings, which are supported by advanced nonadiabatic dynamics calculations, led to the identification of the relevant nuclear coordinates controlling the relaxation. Our experiment highlights the relevance of ultrashort XUV pulses to capture the isotopic effect in few-femtosecond molecular photodynamics.

Nuclear–Electron Correlation Effects and Their Photoelectron Imprint in Molecular XUV Ionisation

The ionisation of molecules by attosecond XUV pulses is accompanied by complex correlated dynamics, such as the creation of coherent electron wave packets in the parent ion, their interplay with nuclear wave packets, and a correlated photoelectron moving in a multi-centred potential. Additionally, these processes are influenced by the dynamics prior to and during the ionisation. To fully understand and subsequently control the ionisation process on different time scales, a profound understanding of electron and nuclear correlation is needed. Here, we investigate the effect of nuclear–electron correlation in a correlated two-electron and one-nucleus quantum model system. Solving the time-dependent Schrödinger equation allows to monitor the correlation impact pre, during, and post-XUV ionisation. We show how an initial nuclear wave packet displaced from equilibrium influences the post-ionisation dynamics by means of momentum conservation between the target and parent ion, whilst the attosecond electron population remains largely unaffected. We calculate time-resolved photoelectron spectra and their asymmetries and demonstrate how the coupled electron–nuclear dynamics are imprinted on top of electron–electron correlation on the photoelectron properties. Finally, our findings give guidelines towards when correlation resulting effects have to be incorporated and in which instances the exact correlation treatment can be neglected.

On-the-fly investigation of XUV excited large molecular ions using a high harmonic generation light source

We present experiments where extreme ultraviolet femtosecond light pulses are used to photoexcite large molecular ions at high internal energy. This is done by combining an electrospray ionization source and a mass spectrometer with a pulsed light source based on high harmonic generation. This allows one to study the interaction between high energy photons and mass selected ions in conditions that are accessible on large-scale facilities. We show that even without an ion trapping device, systems as large as a protein can be studied. We observe light induced dissociative ionization and proton migration in model systems such as reserpine, insulin and cytochrome c. These results offer new perspectives to perform time-resolved experiments with ultrashort pulses at the heart of the emerging field of attosecond chemistry.

Time evolution of entanglement of electrons and nuclei and partial traces in ultrafast photochemistry

Broad in energy optical pulses induce ultrafast molecular dynamics where nuclear degrees of freedom are entangled with electronic ones. We discuss a matrix representation of wave functions of such entangled systems. Singular Value Decomposition (SVD) of this matrix provides a representation as a sum of separable terms. Their weights can be arranged in decreasing order. The representation provided by the SVD is equivalent to a Schmidt decomposition. If there is only one term or if one term is already a good approximation, the system is not entangled. The SVD also provides either an exact or a few term approximation for the partial traces. A simple example, the dynamics of LiH upon ultrafast excitation to several non-adiabatically coupled electronic states, is provided. The major contribution to the entanglement is created during the exit from the Franck Condon region. An additional contribution is the entanglement due to the nuclear motion induced non-adiabatic transitions.

Laser-Dressed Molecular Point Groups in the Kramers-Henneberger Oscillating Frame-of-Reference: Selection Rules for Higher Harmonic Generation

Point groups of molecules in a laser, within the Kramers-Henneberger (KH) oscillating frame for laser-dressed states, is given in this work. In a Fourier series of the time-dependent potential, the zeroth-order time-average yields the point group of the laser-dressed molecule. Various laser polarizations and relative molecular orientation induce a new point group or retain the original point group. The dynamical Fourier components (KH potentials) classify as irreducibles of this new laser-dressed point group. Recurrence of unique irreducibles in the Fourier expansion dictates the dynamical symmetry of the Floquet Hamiltonian. Hence, selection rules for harmonic generation spectra are Nk ± 1 in harmonic order, where N is the number of unique irreducibles and k∈N.

Steady State Photoisomerization Quantum Yield of Model Rhodopsin: Insights from Wavepacket Dynamics?

We simulate the nonequilibrium steady state cis-trans photoisomerization of retinal chromophore in rhodopsin on the basis of a two-state, two-mode model coupled to a thermal environment. By analyzing the systematic trends within an inhomogeneously broadened ensemble of systems, we find that the steady state reaction quantum yield (QY) correlates strongly with the excess energy above the crossing point of the system, in agreement with the prediction of the short-time dynamical wavepacket picture. However, the nontrivial dependence of the QY on the system-environment interaction indicates that a pure dynamical picture is insufficient and that environment-induced partial internal energy redistribution takes place before the reaction concludes. These results imply that a proper treatment of the photoisomerization reaction, particularly its high QY, must account for the redistribution and dissipation of energy beyond the dynamical wavepacket motion that is typically employed in the literature and that is appropriate only in the transient regime.

Molecular Free Electron Vortices in Photoionization by Polarization-Tailored Ultrashort Laser Pulses

Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.

High harmonic spectra computed using time-dependent Kohn-Sham theory with Gaussian orbitals and a complex absorbing potential

High harmonic spectra for H₂ and H₂ ⁺ are simulated by solving the time-dependent Kohn-Sham equation in the presence of a strong laser field using an atom-centered Gaussian representation of the density and a complex absorbing potential. The latter serves to mitigate artifacts associated with the finite extent of the basis functions, including spurious reflection of the outgoing electronic wave packet. Interference between the outgoing and reflected waves manifests as peak broadening in the spectrum as well as the appearance of spurious high-energy peaks after the harmonic progression has terminated. We demonstrate that well-resolved spectra can be obtained through the use of an atom-centered absorbing potential. As compared to grid-based algorithms, the present approach is more readily extensible to larger molecules.

Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics

Since the first demonstration of the generation of attosecond pulses (1 as = 10^-18s) in the extreme-ultraviolet spectral region, several measurement techniques have been introduced, at the beginning for the temporal characterization of the pulses, and immediately after for the investigation of electronic and nuclear ultrafast dynamics in atoms, molecules and solids with unprecedented temporal resolution. The attosecond spectroscopic tools established in the last two decades, together with the development of sophisticated theoretical methods for the interpretation of the experimental outcomes, allowed to unravel and investigate physical processes never observed before, such as the delay in photoemission from atoms and solids, the motion of electrons in molecules after prompt ionization which precede any notable nuclear motion, the temporal evolution of the tunneling process in dielectrics, and many others. This review focused on applications of attosecond techniques to the investigation of ultrafast processes in atoms, molecules and solids. Thanks to the introduction and ongoing developments of new spectroscopic techniques, the attosecond science is rapidly moving towards the investigation, understanding and control of coupled electron-nuclear dynamics in increasingly complex systems, with ever more accurate and complete investigation techniques. Here we will review the most common techniques presenting the latest results in atoms, molecules and solids.

Ionization of HCCI Neutral and Cations by Strong Laser Fields Simulated With Time Dependent Configuration Interaction

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations. This superposition results in charge migration between the CC π orbital and the iodine π-type lone pair which can be monitored by strong field ionization with short, intense probe pulses. Strong field ionization of the X and A states of HCCI cation was simulated with time-dependent configuration interaction using singly ionized configurations and singly excited, singly ionized configurations (TD-CISD-IP) and an absorbing boundary. Studies with static fields were used to obtain the 3-dimensional angular dependence of instantaneous ionization rates by strong fields and the orbitals involved in producing the cations and dications. The frequency of charge oscillation is determined by the energy separation of the X and A states; this separation can change depending on the direction and strength of the field. Furthermore, fields along the molecular axis can cause extensive mixing between the field-free X and A configurations. For coherent superpositions of the X and A states, the charge oscillations are characterized by two frequencies-the driving frequency of the laser field of the probe pulse and the intrinsic frequency due to the energy separation between the X and A states. For linear and circularly polarized pulses, the ionization rates show marked differences that depend on the polarization direction of the pulse, the carrier envelope phase and initial phase of the superposition. Varying the initial phase of the superposition at the beginning of the probe pulse is analogous to changing the delay between the pump and probe pulses. The charge oscillation in the coherent superposition of the X and A states results in maxima and minima in the ionization yield as a function of the superposition phase.

Effects of electronic correlation on the high harmonic generation in helium: a time-dependent configuration interaction singles vs time-dependent full configuration interaction study

In this paper, we investigate the effects of full electronic correlation on the high harmonic generation in the helium atom subjected to laser pulses of extremely high intensity. To do this, we perform real-time propagations of the helium atom wavefunction using quantum chemistry methods coupled to Gaussian basis sets. The calculations are done within the real-time time-dependent configuration interaction framework, at two levels of theory: time-dependent configuration interation with single excitations (TD-CIS, uncorrelated method) and time-dependent full configuration interaction (TD-FCI, fully correlated method). The electronic wavefunction is expanded in Dunning basis sets supplemented with functions adapted to describing highly excited and continuum states. We also compare the TD-CI results with grid-based propagations of the helium atom within the single-active-electron approximation. Our results show that when including the dynamical electron correlation, a noticeable improvement to the description of HHG can be achieved, in terms of e.g. a more constant intensity in the lower energy part of the harmonic plateau. However, such effects can be captured only if the basis set used suffices to reproduce the most basic features, such as the HHG cutoff position, at the uncorrelated level of theory.

A quantum-chemical perspective on the laser-induced alignment and orientation dynamics of the CH3 X (X = F, Cl, Br, I) molecules

Motivated by recent experiments, the laser-induced alignment-and-orientation (A&O) dynamics of the prolate symmetric top CH3 X (X = F, Cl, Br, I) molecules is investigated, with particular emphasis on the effect of halogen substitution on the rotational constants, dipole moments, and polarizabilities of these species, as these quantities determine the A&O dynamics. Insight into possible control schemes for preferred A&O dynamics of halogenated molecules and best practices for A&O simulations are provided, as well. It is shown that for accurate A&O -dynamics simulations it is necessary to employ large basis sets and high levels of electron correlation when computing the rotational constants, dipole moments, and polarizabilities. The benchmark-quality values of these molecular parameters, corresponding to the equilibrium, as well as the vibrationally averaged structures are obtained with the help of the focal-point analysis (FPA) technique and explicit electronic-structure computations utilizing the gold-standard CCSD(T) approach, basis sets up to quintuple-zeta quality, core-correlation contributions and, in particular, relativistic effects for CH3 Br and CH3 I. It is shown that the different A&O behavior of the CH3 X molecules in the optical regime is mostly caused by the differences in their polarizability anisotropy, in other terms, the size of the halogen atom. In contrast, the A&O dynamics of the CH3 X series induced by an intense few-cycle THz pulse is mostly governed by changes in the rotational constants, due to the similar dipole moments of the CH3 X molecules. The A&O dynamics is most sensitive to the B rotational constant: even the difference between its equilibrium and vibrationally-averaged values results in noticeably different A&O dynamics. The contribution of rotational states having different symmetry, weighted by nuclear-spin statistics, to the A&O dynamics is also studied.

Attosecond photoionisation time delays reveal the anisotropy of the molecular potential in the recoil frame

Photoionisation time delays carry structural and dynamical information on the target system, including electronic correlation effects in atoms and molecules and electron transport properties at interfaces. In molecules, the electrostatic potential experienced by an outgoing electron depends on the emission direction, which should thus lead to anisotropic time delays. To isolate this effect, information on the orientation of the molecule at the photoionisation instant is required. Here we show how attosecond time delays reflect the anisotropic molecular potential landscape in CF₄ molecules. The variations in the measured delays can be directly related to the different heights of the potential barriers that the outgoing electrons see in the vicinity of shape resonances. Our results indicate the possibility to investigate the spatial characteristics of the molecular potential by mapping attosecond photoionisation time delays in the recoil-frame.

Photoionization time delays provide insights on the interaction of photon with the electrons. Here the authors explore the role of the molecular potential to the attosecond time delays in the photoionization of CF4 molecule.

Experimental Control of Quantum-Mechanical Entanglement in an Attosecond Pump-Probe Experiment

Entanglement is one of the most intriguing aspects of quantum mechanics and lies at the heart of the ongoing second quantum revolution, where it is a resource that is used in quantum key distribution, quantum computing, and quantum teleportation. We report experiments demonstrating the crucial role that entanglement plays in pump-probe experiments involving ionization, which are a hallmark of the novel research field of attosecond science. We demonstrate that the degree of entanglement in a bipartite ion + photoelectron system, and, as a consequence, the degree of vibrational coherence in the ion, can be controlled by tailoring the spectral properties of the attosecond extreme ultraviolet laser pulses that are used to create them.

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...

Spiers Memorial Lecture: Prospects for photoelectron spectroscopy

An overview is presented of recent advances in photoelectron spectroscopy, focussing on advances in in situ and time-resolved measurements, and in extending the sampling depth of the technique. The future...

RhoDyn: A ρ-TD-RASCI Framework to Study Ultrafast Electron Dynamics in Molecules

This article presents the program module RhoDyn as part of the OpenMOLCAS project intended to study ultrafast electron dynamics within the density-matrix-based time-dependent restricted active space configuration interaction framework (ρ-TD-RASCI). The formalism allows for the treatment of spin-orbit coupling effects, accounts for nuclear vibrations in the form of a vibrational heat bath, and naturally incorporates (auto)ionization effects. Apart from describing the theory behind and the program workflow, the paper also contains examples of its application to the simulations of the linear L_2,3 absorption spectra of a titanium complex, high harmonic generation in the hydrogen molecule, ultrafast charge migration in benzene and iodoacetylene, and spin-flip dynamics in the core excited states of iron complexes.

Theoretical Calculation of Core-Excited States along Dissociative Pathways beyond Second-Order Perturbation Theory

We extend the multireference driven similarity renormalization (MR-DSRG) method to compute core-excited states by combining it with a GASSCF treatment of orbital relaxation and static electron correlation effects. We consider MR-DSRG treatments of dynamical correlation truncated at the level of perturbation theory (DSRG-MRPT2/3) and iterative linearized approximations with one- and two-body operators [MR-LDSRG(2)] in combination with a spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects. This approach is calibrated and tested on a series of 16 core-excited states of five closed- and open-shell diatomic molecules containing first-row elements (C, N, and O). All GASSCF-MR-DSRG theories show excellent agreement with experimental adiabatic transitions energies, with mean absolute errors ranging between 0.17 and 0.35 eV, even for the challenging partially doubly excited states of the N₂⁺ molecule. The vibrational structure of all these transitions, obtained from using a full potential energy scan, shows a mean absolute error as low as 25 meV for DSRG-MRPT2 and 12/13 meV for DSRG-MRPT3 and MR-LDSRG(2). We generally find that a treatment of dynamical correlation that goes beyond the second-order level in perturbation theory improves the accuracy of the potential energy surface, especially in the bond-dissociation region.

Influence of shape resonances on the angular dependence of molecular photoionization delays

Characterizing time delays in molecular photoionization as a function of the ejected electron emission direction relative to the orientation of the molecule and the light polarization axis provides unprecedented insights into the attosecond dynamics induced by extreme ultraviolet or X-ray one-photon absorption, including the role of electronic correlation and continuum resonant states. Here, we report completely resolved experimental and computational angular dependence of single-photon ionization delays in NO molecules across a shape resonance, relying on synchrotron radiation and time-independent ab initio calculations. The angle-dependent time delay variations of few hundreds of attoseconds, resulting from the interference of the resonant and non-resonant contributions to the dynamics of the ejected electron, are well described using a multichannel Fano model where the time delay of the resonant component is angle-independent. Comparing these results with the same resonance computed in e-NO⁺ scattering highlights the connection of photoionization delays with Wigner scattering time delays.

Conditional Wave Function Theory: A Unified Treatment of Molecular Structure and Nonadiabatic Dynamics

We demonstrate that a conditional wave function theory enables a unified and efficient treatment of the equilibrium structure and nonadiabatic dynamics of correlated electron-ion systems. The conditional decomposition of the many-body wave function formally recasts the full interacting wave function of a closed system as a set of lower-dimensional (conditional) coupled "slices". We formulate a variational wave function ansatz based on a set of conditional wave function slices and demonstrate its accuracy by determining the structural and time-dependent response properties of the hydrogen molecule. We then extend this approach to include time-dependent conditional wave functions and address paradigmatic nonequilibrium processes including strong-field molecular ionization, laser-driven proton transfer, and nuclear quantum effects induced by a conical intersection. This work paves the road for the application of conditional wave function theory in equilibrium and out-of-equilibrium ab initio molecular simulations of finite and extended systems.

A systematic study of the valence electronic structure of cyclo(Gly-Phe), cyclo(Trp-Tyr) and cyclo(Trp-Trp) dipeptides in the gas phase

The electronic energy levels of cyclo(glycine-phenylalanine), cyclo(tryptophan-tyrosine) and cyclo(tryptophan-tryptophan) dipeptides are investigated with a joint experimental and theoretical approach. Experimentally, valence photoelectron spectra in the gas phase are measured using VUV radiation. Theoretically, we first obtain low-energy conformers through an automated conformer-rotamer ensemble sampling scheme based on tight-binding simulations. Then, different first principles computational schemes are considered to simulate the spectra: Hartree-Fock (HF), density functional theory (DFT) within the B3LYP approximation, the quasi-particle GW correction, and the quantum-chemistry CCSD method. Theory allows assignment of the main features of the spectra. A discussion on the role of electronic correlation is provided, by comparing computationally cheaper DFT scheme (and GW) results with the accurate CCSD method.

Synchronized beamline at FLASH2 based on high-order harmonic generation for two-color dynamics studies

We present the design, integration, and operation of the novel vacuum ultraviolet (VUV) beamline installed at the free-electron laser (FEL) FLASH. The VUV source is based on high-order harmonic generation (HHG) in gas and is driven by an optical laser system synchronized with the timing structure of the FEL. Ultrashort pulses in the spectral range from 10 to 40 eV are coupled with the FEL in the beamline FL26, which features a reaction microscope (REMI) permanent endstation for time-resolved studies of ultrafast dynamics in atomic and molecular targets. The connection of the high-pressure gas HHG source to the ultra-high vacuum FEL beamline requires a compact and reliable system, able to encounter the challenging vacuum requirements and coupling conditions. First commissioning results show the successful operation of the beamline, reaching a VUV focused beam size of about 20 µm at the REMI endstation. Proof-of-principle photo-electron momentum measurements in argon indicate the source capabilities for future two-color pump-probe experiments.

Time-dependentab initioapproaches for high-harmonic generation spectroscopy

High-harmonic generation (HHG) is a nonlinear physical process used for the production of ultrashort pulses in XUV region, which are then used for investigating ultrafast phenomena in time-resolved spectroscopies. Moreover, HHG signal itself encodes information on electronic structure and dynamics of the target, possibly coupled to the nuclear degrees of freedom. Investigating HHG signal leads to HHG spectroscopy, which is applied to atoms, molecules, solids and recently also to liquids. Analysing the number of generated harmonics, their intensity and shape gives a detailed insight of, e.g., ionisation and recombination channels occurring in the strong-field dynamics. A number of valuable theoretical models has been developed over the years to explain and interpret HHG features, with the three-step model being the most known one. Originally, these models neglect the complexity of the propagating electronic wavefunction, by only using an approximated formulation of ground and continuum states. Many effects unravelled by HHG spectroscopy are instead due to electron correlation effects, quantum interference, and Rydberg-state contributions, which are all properly captured by anab initioelectronic-structure approach. In this review we have collected recent advances in modelling HHG by means ofab initiotime-dependent approaches relying on the propagation of the time-dependent Schrödinger equation (or derived equations) in presence of a very intense electromagnetic field. We limit ourselves to gas-phase atomic and molecular targets, and to solids. We focus on the various levels of theory employed for describing the electronic structure of the target, coupled with strong-field dynamics and ionisation approaches, and on the basis used to represent electronic states. Selected applications and perspectives for future developments are also given.

Coherence in macroscopic high harmonic generation for spatial focal phase distributions of monochromatic and broadband Gaussian laser pulses

Efficient application of ultrafast laser sources from high harmonic generation requires an understanding of how the spectrum can be controlled - the extent of the highest harmonics and the strength and cleanness of the harmonic lines. We study one important aspect in the coherent build-up of macroscopic high-order harmonic generation, namely the impact of different phase distributions in the focal area on the features of the generated radiation. Specifically, we compare the high harmonic signals for the commonly-used Gouy distribution of a monochromatic beam with those for the phase distribution of a short broadband Gaussian pulse. To this end, we apply a theoretical model in which the microscopic yields are obtained via interpolation of results of the time-dependent Schrödinger equation, which are then used in an individual-emitter approach to determine the macroscopic signals. Regions of poor and good coherent build-up as a function of the position of the gas jet are identified using measures for the strength of the harmonic lines and for the impact of off-harmonic radiation. While the largest extent of the spectra as well as the strongest contribution of off-harmonic radiation is found for positioning the gas jet after the focus for both distributions, the relative strength of the harmonics is overall weaker for the short Gaussian pulse distribution and the spectra differ for a gas jet positioned at the focus. These differences are mainly caused by the additional dependence of the focal phase in the transverse direction for the short Gaussian pulse distribution.

Strong-field coherent control of isolated attosecond pulse generation

Attosecond science promises to reveal the most fundamental electronic dynamics occurring in matter and it can develop further by meeting two linked technological goals related to high-order harmonic sources: improved spectral tunability (allowing selectivity in addressing electronic transitions) and higher photon flux (permitting to measure low cross-section processes). New developments come through parametric waveform synthesis, which provides control over the shape of field transients, enabling the creation of highly-tunable isolated attosecond pulses via high-harmonic generation. Here we demonstrate that the first goal is fulfilled since central energy, spectral bandwidth/shape and temporal duration of isolated attosecond pulses can be controlled by shaping the laser waveform via two key parameters: the relative-phase between two halves of the multi-octave spanning spectrum, and the overall carrier-envelope phase. These results not only promise to expand the experimental possibilities in attosecond science, but also demonstrate coherent strong-field control of free-electron trajectories using tailored optical waveforms.

Attosecond pulse generation needs improvements both in terms of tunability and photon flux for next level attosecond experiments. Here the authors show how to control the HHG emission and its spectral-temporal characteristics by driving the IAP generation with synthesized sub-cycle optical pulses.

Attosecond Intramolecular Scattering and Vibronic Delays

We study the temporal and vibrational signature of the universal nuclear recoil associated with the electron emission and intramolecular scattering that accompanies the photoelectric effect. We illustrate these phenomena in the photoionization of the CO molecule from the C-1s orbital using an analytical model that reproduces the entangled character of the nuclear and electronic motion in this process. We show that the photoelectron emission delay can be decomposed into its localization and resonant-confinement components. Photoionization by a broadband x-ray pulse results in a coherent vibrational ionic state delayed compared to the classical sudden-photoemission limit.

Electronic Coherences Steer the Strong Isotope Effect in the Ultrafast Jahn-Teller Structural Rearrangement of Methane Cation upon Tunnel Ionization

We report on fully quantum electronic-nuclear dynamics following sudden ionization from the neutral in the three lowest electronic states of the CH₄⁺ and CD₄⁺ cations. There is a strong Jahn-Teller effect in the Franck-Condon region, and we employ two nuclear degrees of freedom that span the internal coordinates involved in the Jahn-Teller coupling. The initial state results from tunneling ionization by a strong IR field which coherently pumps the three lowest states of the cation, D₀, D₁, and D₂. The quantum dynamical simulations show that a strong isotope effect occurs when the ionization significantly accesses the D₂ state of the cation in the Franck-Condon region. The computed isotope effect is larger than expected on the basis of the effective mass ratio. The strong effect is due to fast oscillations of the electronic coherences between the D₂ and the D₁ and D₀ electronic states and their modulation by the nonadiabatic couplings before a significant onset of nuclear motion. The magnitude of the effect is similar to the one that we previously reported for a sudden photoionization process. A strong isotope effect has been observed in high harmonic spectroscopy studies of the very short time dynamics Jahn-Teller structural rearrangement of the methane cation upon sudden ionization.

Attosecond charge migration following oxygen K-shell ionization in DNA bases and base pairs

Core ionization of DNA begins a cascade of events which could lead to cellular inactivation or death. The created core-hole following an impulse inner-shell ionization of molecules naturally decays in the auger timescale. We simulated charge migration (CM) phenomena following an impulsive core ionization of individual DNA bases at the oxygen K-edge which occurs before Auger decay of the oxygen. Our approach is based on real-time time dependent density functional theory (RT-TDDFT). It is shown that the pronounced hole fluctuation observed around bonds of the initial core-hole results in various valence orbital migrations. Also, the same photo-core-ionized dynamics is studied for the related base pairs. We investigate the role of base pairing and H-bonding interactions in the attosecond CM dynamics. In particular, the creation of a core-hole in the oxygen involved in H-bonding leads to an enhancement of charge migration relative to the respective single bases. Importantly, the hole oscillation of the adenine-thymine base pair upon creation of a core-hole at the oxygen, which does not contribute to the donor-acceptor interactions (not H-bonded), decreases compared to the single thymine base. Understanding the detailed dynamics of the localized core-hole initiating CM process would open the way for chemically controlling DNA damage/repair in the future.