Charge Migration in Propiolic Acid: A Full Quantum Dynamical Study

Electronic Coherences in Molecules: The Projected Nuclear Quantum Momentum as a Hidden Agent

Electronic coherences are key to understanding and controlling photoinduced molecular transformations. We identify a crucial quantum-mechanical feature of electron-nuclear correlation, the projected nuclear quantum momenta, essential to capture the correct coherence behavior. For simulations, we show that, unlike traditional trajectory-based schemes, exact-factorization-based methods approximate these correlation terms and correctly capture electronic coherences in a range of situations, including their spatial dependence, an important aspect that influences subsequent electron dynamics and that is becoming accessible in more experiments.

Spatio-Temporal Symmetries of Electronic Chirality Flips in Oriented RbCs Induced by two Coincident Laser Pulses with Circular ++, +-, -+, -- Polarizations

Recently it has been shown that two coincident well designed laser pulses with two different combinations of circular polarizations (+ + ${ + + }$ or- + ${ - + }$ ) can create chiral electronic densities in an oriented heteronuclear diatomic molecule. Subsequently, the chirality flips from the electronic Ra to Sa to Ra to Sa etc. enantiomers, with periods in the femtosecond (fs) and attosecond (as) time domains. The results were obtained by means of quantum dynamics simulations for oriented NaK. Here we investigate the electronic chirality flips in oriented RbCs induced by all possible (+ + ${ + + }$ ,- + ${ - + }$ ,+ - ${ + - }$ ,- - ${ - - }$ ) combinations of circular polarizations of two coincident well-designed laser pulses. Accordingly, the+ + ${ + + }$ and- - ${ - - }$ as well as the+ - ${ + - }$ and- + ${ - + }$ combinations generate opposite electronic enantiomers, e. g. Ra versus Sa, followed by opposite periodic chirality flips, e. g. from Ra to Sa to Ra to Sa etc. versus from Sa to Ra to Sa to Ra etc, with periods in the fs and as time domains, respectively. The laser induced spatio-temporal symmetries are derived from first principles and illustrated by quantum dynamics simulations.

Time Resolved Quantum Tomography in Molecular Spectroscopy by the Maximal Entropy Approach

Attosecond science offers unprecedented precision in probing the initial moments of chemical reactions, revealing the dynamics of molecular electrons that shape reaction pathways. A fundamental question emerges: what role, if any, do quantum coherences between molecular electron states play in photochemical reactions? Answering this question necessitates quantum tomography─the determination of the electronic density matrix from experimental data, where the off-diagonal elements represent these coherences. The Maximal Entropy (MaxEnt) based Quantum State Tomography (QST) approach offers unique advantages in studying molecular dynamics, particularly with partial tomographic data. Here, we explore the application of MaxEnt-based QST on photoexcited ammonia, necessitating the operator form of observables specific to the performed measurements. We present two methodologies for constructing these operators: one leveraging Molecular Angular Distribution Moments (MADMs) which accurately capture the orientation-dependent vibronic dynamics of molecules and another utilizing Angular Momentum Coherence Operators to construct measurement operators for the full rovibronic density matrix in the symmetric top basis. A key revelation of our study is the direct link between Lagrange multipliers in the MaxEnt formalism and the unique set of MADMs. Additionally, we visualize the electron density within the molecular frame, demonstrating charge migration across the molecule. Furthermore, we achieve a groundbreaking milestone by constructing, for the first time, the entanglement entropy of the electronic subsystem─a metric that was previously inaccessible. The entropy vividly reveals and quantifies the effects of coupling between the excited electron and nuclear degrees of freedom. Consequently, our findings open new avenues for research in ultrafast molecular spectroscopy within the broader domain of quantum information science, offering profound implications for the study of molecular systems under excitation using quantum tomographic schemes.

Reducing the Cost of TD-CI Simulations of Strong Field Ionization

Strong field ionization of molecules by intense laser pulses can be simulated by time-dependent configuration interaction (TD-CI) with a complex absorbing potential (CAP). Standard molecular basis sets need to be augmented with several sets of diffuse functions for effective interaction with the CAP. This dramatically increases the number of configurations and the cost of the TD-CI simulations as the size of the molecules increases. The cost can be reduced by making use of spin symmetry and by employing an orbital energy cutoff to limit the number of virtual orbitals used to construct the excited configurations. Greater reductions in the number of virtual orbitals can be obtained by examining their interaction with the absorbing potential during simulations and their contributions to the strong field ionization rate. This can be determined from the matrix elements of the absorbing potential and the TD-CI coefficients from test simulations. Compared to a simple 3 hartree cutoff in the orbital energies, these approaches reduce the number of virtual orbitals by 20-35% for neutral molecules and 5-10% for cations. As a result, the cost of simulations is reduced by 35-60% for neutral molecules. The number of virtual orbitals needed can also be estimated by second-order perturbation theory without the need for test simulations. The number of virtual orbitals can be reduced further by adapting orbitals to the laser field using natural orbitals derived from test simulations. This is particularly effective for cations, yielding reductions of more than 20%.

Condensed Matter Systems Exposed to Radiation: Multiscale Theory, Simulations, and Experiment

This roadmap reviews the new, highly interdisciplinary research field studying the behavior of condensed matter systems exposed to radiation. The Review highlights several recent advances in the field and provides a roadmap for the development of the field over the next decade. Condensed matter systems exposed to radiation can be inorganic, organic, or biological, finite or infinite, composed of different molecular species or materials, exist in different phases, and operate under different thermodynamic conditions. Many of the key phenomena related to the behavior of irradiated systems are very similar and can be understood based on the same fundamental theoretical principles and computational approaches. The multiscale nature of such phenomena requires the quantitative description of the radiation-induced effects occurring at different spatial and temporal scales, ranging from the atomic to the macroscopic, and the interlinks between such descriptions. The multiscale nature of the effects and the similarity of their manifestation in systems of different origins necessarily bring together different disciplines, such as physics, chemistry, biology, materials science, nanoscience, and biomedical research, demonstrating the numerous interlinks and commonalities between them. This research field is highly relevant to many novel and emerging technologies and medical applications.

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.

Simulating Attochemistry: Which Dynamics Method to Use?

Attochemistry aims to exploit the properties of coherent electronic wavepackets excited via attosecond pulses to control the formation of photoproducts. Such molecular processes can, in principle, be simulated with various nonadiabatic dynamics methods, yet the impact of the approximations underlying the methods is rarely assessed. The performances of widely used mixed quantum-classical approaches, Tully surface hopping, and classical Ehrenfest methods are evaluated against the high-accuracy DD-vMCG quantum dynamics. This comparison is conducted for the valence ionization of fluorobenzene. Analyzing the nuclear motion induced in the branching space of the nearby conical intersection, the results show that the mixed quantum-classical methods reproduce quantitatively the average motion of a quantum wavepacket when initiated on a single electronic state. However, they fail to properly capture the nuclear motion induced by an electronic wavepacket along the derivative coupling, the latter originating from the quantum electronic coherence property, key to attochemistry.

From chiral laser pulses to femto- and attosecond electronic chirality flips in achiral molecules

Chirality is an important topic in biology, chemistry and physics. Here we show that ultrashort circularly polarized laser pulses, which are chiral, can be fired on achiral oriented molecules to induce chirality in their electronic densities, with chirality flips within femtoseconds or even attoseconds. Our results, obtained by quantum dynamics simulations, use the fact that laser pulses can break electronic symmetry while conserving nuclear symmetry. Here two laser pulses generate a superposition of three electronic eigenstates. This breaks all symmetry elements of the electronic density, making it chiral except at the periodic rare events of the chirality flips. As possible applications, we propose the combination of the electronic chirality flips with Chiral Induced Spin Selectivity.

Size Effect in Correlation-Driven Charge Migration in Correlation Bands of Alkyne Chains

Correlation-driven charge migration initiated by inner-valence ionization leading to the population of the correlation bands of alkyne chains containing between 4 and 12 carbon atoms is explored through ab initio simulations. Scaling laws are observed, both for the time scale of the charge migration and for the slope of the density of states of the correlation bands. These can be used for predicting the relaxation time scale in much larger systems from the same molecular family and for finding promising candidates for the development of an attochemistry scheme taking advantages of the specificity of the dynamics in the correlation bands of molecules.

Long-Lived Electronic Coherences in Molecules

We demonstrate long-lived electronic coherences in molecules using a combination of measurements with shaped octave spanning ultrafast laser pulses and calculations of the light matter interaction. Our pump-probe measurements prepare and interrogate entangled nuclear-electronic wave packets whose electronic phase remains well defined despite vibrational motion along many degrees of freedom. The experiments and calculations illustrate how coherences between excited states can survive, even when coherence with the ground state is lost, and may have important implications for many areas of attosecond science and photochemistry.

Ultrafast Molecular Frame Quantum Tomography

We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH_{3}). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH_{3}, we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.

Manipulating Attosecond Charge Migration in Molecules by Optical Cavities

The ultrafast electronic charge dynamics in molecules upon photoionization while the nuclear motions are frozen is known as charge migration. In a theoretical study of the quantum dynamics of photoionized 5-bromo-1-pentene, we show that the charge migration process can be induced and enhanced by placing the molecule in an optical cavity, and can be monitored by time-resolved photoelectron spectroscopy. The collective nature of the polaritonic charge migration process is investigated. We find that, unlike spectroscopy, molecular charge dynamics in a cavity is local and does not show many-molecule collective effects. The same conclusion applies to cavity polaritonic chemistry.

The role of symmetric vibrational modes in the decoherence of correlation-driven charge migration

Due to the electron correlation, the fast removal of an electron from a molecule may create a coherent superposition of cationic states and in this way initiate pure electronic dynamics in which the hole-charge left by the ionization migrates throughout the system on an ultrashort time scale. The coupling to the nuclear motion introduces a decoherence that eventually traps the charge, and crucial questions in the field of attochemistry include how long the electronic coherence lasts and which nuclear degrees of freedom are mostly responsible for the decoherence. Here, we report full-dimensional quantum calculations of the concerted electron-nuclear dynamics following outer-valence ionization of propynamide, which reveal that the pure electronic coherences last only 2-3 fs before being destroyed by the nuclear motion. Our analysis shows that the normal modes that are mostly responsible for the fast electronic decoherence are the symmetric in-plane modes. All other modes have little or no effect on the charge migration. This information can be useful to guide the development of reduced dimensionality models for larger systems or the search for molecules with long coherence times.

Photo-ionization initiated differential ultrafast charge migration: impacts of molecular symmetries and tautomeric forms

Photo-ionization induced ultrafast electron dynamics is considered as a precursor for the slower nuclear dynamics associated with molecular dissociation. Here, using the ab initio multielectron wave-packet propagation method, we study the overall many-electron dynamics, triggered by ionizing the outer-valence orbitals of different tautomers for a prototype molecule with more than one symmetry element. From the time evolution of the initially created averaged hole density of each system, we identify distinctly different charge dynamics responses in the tautomers. We observe that the keto form shows a charge migration direction away from the nitrogen bonded with hydrogen, while in enol-U - away from oxygen bonded to hydrogen. Additionally, the dynamics following the ionization of molecular orbitals with different symmetries reveals that a' orbitals show a fast and highly delocalized charge density in comparison to a'' symmetry. These observations indicate why different tautomers respond differently to an XUV ionization, and might explain the subsequent different fragmentation pathways. An experimental schematics allowing the detection and reconstruction of such charge dynamics is also proposed. Although the present study uses a simple, prototypical bio-relevant molecule, it reveals the explicit role of molecular symmetry and tautomerism in the ionization-triggered charge migration that controls many ultrafast physical, chemical, and biological processes, making tautomeric forms a promising tool of molecular design for desired charge migration.

Probing Electronic Symmetry Reduction during Charge Migration via Time-Resolved X-Ray Diffraction

The present work focuses on probing ultrafast charge migration after symmetry-breaking excitation using ultrashort laser pulses. LiCN is chosen as prototypical system because it can be oriented in the laboratory frame and it possesses optically-accessible charge transfer states at low energies. The charge migration is simulated within the hybrid time-dependent density functional theory/configuration interaction framework. Time-resolved electronic current densities and simulated time-resolved x-ray diffraction signals are used to unravel the mechanism of charge migration. Our simulations demonstrate that specific choices of laser polarization lead to a control over the symmetry of the induced charge migration. Moreover, time-resolved x-ray diffraction signals are shown to encode transient symmetry reduction at intermediate times.

Characterizing coherences in chemical dynamics with attosecond time-resolved x-ray absorption spectroscopy

Coherence can drive wave-like motion of electrons and nuclei in photoexcited systems, which can yield fast and efficient ways to exert materials’ functionalities beyond the thermodynamic limit. The search for coherent phenomena has been a central topic in chemical physics although their direct characterization is often elusive. Here, we highlight recent advances in time-resolved x-ray absorption spectroscopy (tr-XAS) to investigate coherent phenomena, especially those that utilize the eminent light source of isolated attosecond pulses. The unparalleled time and state sensitivities of tr-XAS in tandem with the unique element specificity render the method suitable to study valence electronic dynamics in a wide variety of materials. The latest studies have demonstrated the capabilities of tr-XAS to characterize coupled electronic–structural coherence in small molecules and coherent light–matter interactions of core-excited excitons in solids. We address current opportunities and challenges in the exploration of coherent phenomena, with potential applications for energy- and bio-related systems, potential crossings, strongly driven solids, and quantum materials. With the ongoing developments in both theory and light sources, tr-XAS holds great promise for revealing the role of coherences in chemical dynamics.

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.

A posteriori localization of many-body excited states through simultaneous diagonalization

In this paper we propose a numerical method to localize many-electron excited states. To characterize the electronic structure of the electronic excited states of a system, quantum chemistry methods typically yield a delocalized description of the excitations. Some a priori localization methods have been developed to provide an intuitive local picture of the excited states. They typically require a good strategy to separate the system of interest from its environment, or a set of a priori localized orbitals, that may reduce their computational accuracy. Here, we introduce an a posteriori method to localize delocalized many-body excited states directly obtained from quantum chemistry calculations. A localization metric for the excited states is defined from their representation as electron-hole pairs, which is encoded in the transition density matrix. This novel a posteriori strategy thus allows to localize excitons within a volume around selected fragments of a complex molecular system without tempering with its quantum chemical treatment. The method is tested on π-stacked oligomers of phenanthrenes and pyrenes. It is found to efficiently localize and separate the excitons according to their character while preserving the information about delocalized many-body states at a low computational cost.

Decoherence and Revival in Attosecond Charge Migration Driven by Non-adiabatic Dynamics

Attosecond charge migration is a periodic evolution of the charge density at specific sites of a molecule on a time scale defined by the energy intervals between the electronic states involved. Here, we report the observation of charge migration in neutral silane (SiH₄) in 690 as, its decoherence within 15 fs, and its revival after 40-50 fs, using X-ray attosecond transient absorption spectroscopy. We observe the migration of charge as pairs of quantum beats with a characteristic spectral phase in the transient spectrum, in agreement with theory. The decay and revival of the degree of electronic coherence is found to be a result of both adiabatic and non-adiabatic dynamics in the populated Rydberg and valence states. The experimental results are supported by fully quantum-mechanical ab-initio calculations that include both electronic and nuclear dynamics, which additionally support the experimental evidence that conical intersections can mediate the transfer of electronic coherence from an initial superposition state to another one involving a different lower-lying state.

Theoretical analysis of the role of complex transition dipole phase in XUV transient-absorption probing of charge migration

We theoretically investigate the role of complex dipole phase in the attosecond probing of charge migration. The iodobromoacetylene ion (ICCBr⁺) is considered as an example, in which one can probe charge migration by accessing both the iodine and bromine ends of the molecule with different spectral windows of an extreme-ultraviolet (XUV) pulse. The analytical expression for transient absorption shows that the site-specific information of charge migration is encoded in the complex phase of cross dipole products for XUV transitions between the I-4d and Br-3d spectral windows. Ab-initio quantum chemistry calculations on ICCBr⁺ reveal that there is a constant π phase difference between the I-4d and Br-3d transient-absorption spectral windows, irrespective of the fine-structure energy splittings. Transient absorption spectra are simulated with a multistate model including the complex dipole phase, and the results correctly reconstruct the charge-migration dynamics via the quantum beats in the two element spectral windows, exhibiting out-of-phase oscillations.

Attosecond coherent electron motion in Auger-Meitner decay

In quantum systems, coherent superpositions of electronic states evolve on ultrafast time scales (few femtoseconds to attoseconds; 1 attosecond = 0.001 femtoseconds = 10^-18 seconds), leading to a time-dependent charge density. Here we performed time-resolved measurements using attosecond soft x-ray pulses produced by a free-electron laser, to track the evolution of a coherent core-hole excitation in nitric oxide. Using an additional circularly polarized infrared laser pulse, we created a clock to time-resolve the electron dynamics and demonstrated control of the coherent electron motion by tuning the photon energy of the x-ray pulse. Core-excited states offer a fundamental test bed for studying coherent electron dynamics in highly excited and strongly correlated matter.

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.

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.

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.

Core-Valence Attosecond Transient Absorption Spectroscopy of Polyatomic Molecules

Tracing ultrafast processes induced by interaction of light with matter is often very challenging. In molecular systems, the initially created electronic coherence becomes damped by the slow nuclear rearrangement on a femtosecond timescale which makes real-time observations of electron dynamics in molecules particularly difficult. In this work, we report an extension of the theory underlying the attosecond transient absorption spectroscopy (ATAS) for the case of molecules, including a full account for the coupled electron-nuclear dynamics in the initially created wave packet, and apply it to probe the oscillations of the positive charge created after outer-valence ionization of the propiolic acid molecule. By taking advantage of element-specific core-to-valence transitions induced by x-ray radiation, we show that the resolution of ATAS makes it possible to trace the dynamics of electron density with atomic spatial resolution.

Attochemistry: Is Controlling Electrons the Future of Photochemistry?

Controlling matter with light has always been a great challenge, leading to the ever-expanding field of photochemistry. In addition, since the first generation of light pulses of attosecond (1 as = 10^-18 s) duration, a great deal of effort has been devoted to observing and controlling electrons on their intrinsic time scale. Because of their short duration, attosecond pulses have a large spectral bandwidth populating several electronically excited states in a coherent manner, i.e., an electronic wavepacket. Because of interference, such a wavepacket has a new electronic distribution implying a potentially different and totally new reactivity as compared to traditional photochemistry, leading to the novel concept of "attochemistry". This nascent field requires the support of theory right from the start. In this Perspective, we discuss the opportunities offered by attochemistry, the related challenges, and the current and future state-of-the-art developments in theoretical chemistry needed to model it accurately.

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.

Quantum electronic coherences by attosecond transient absorption spectroscopy: ab initio B-spline RCS-ADC study

Here I present a fully ab initio time-resolved study of X-ray attosecond transient absorption spectroscopy (ATAS) in a prototypical polyatomic molecule, pyrazine, and demonstrate the possibility of retrieving the many-electron quantum ionic coherences arising in attosecond molecular photoionisation and pre-determining the subsequent charge-directed photochemical reactivity. Advanced first-principles many-electron simulations are performed, within a hybrid XUV pump/X-ray probe setup, to describe the interaction of pyrazine with both XUV pump and X-ray probe pulses, and study the triggered correlated many-electron dynamics. The calculations are carried out by means of the recently-developed ab initio method for many-electron dynamics in polyatomic molecules, the time-dependent (TD) B-spline Restricted Correlation Space-Algebraic Diagrammatic Construction (RCS-ADC). RCS-ADC simulates molecular ionisation from first principles, combining the accurate description of electron correlation of quantum chemistry with the full account of the continuum dynamics of the photoelectron. Complete theoretical characterisation of the atto-ionised many-electron state and photo-induced attosecond charge dynamics is achieved by calculating the reduced ionic density matrix (R-IDM) of the bipartite ion-photoelectron system, with full inclusion of the correlated shakeup states. Deviations from the sudden approximation picture of photoionisation, in the low-photon-energy limit, are presented. The effect of the multi-channel interaction between the parent-ion and the emitted photoelectron on the onset of the quantum electronic coherences is analysed. Moreover, I show how the Schmidt decomposition of the R-IDM unravels the many-electron dynamics triggered by the pump, allowing for the identification of the key channels involved. Finally, I calculate the X-ray attosecond transient absorption spectra of XUV-ionised pyrazine. The results unveil the mapping of the ATAS measurement onto the quantum electronic coherences, and related non-zero R-IDM matrix elements, produced upon ionisation by the XUV pump laser pulse.

On-the-Fly Ab Initio Semiclassical Evaluation of Electronic Coherences in Polyatomic Molecules Reveals a Simple Mechanism of Decoherence

Irradiation of a molecular system by an intense laser field can trigger dynamics of both electronic and nuclear subsystems. The lighter electrons usually move on much faster, attosecond timescale but the slow nuclear rearrangement damps ultrafast electronic oscillations, leading to the decoherence of the electronic dynamics within a few femtoseconds. We show that a simple, single-trajectory semiclassical scheme can evaluate the electronic coherence time in polyatomic molecules accurately by demonstrating an excellent agreement with full-dimensional quantum calculations. In contrast to numerical quantum methods, the semiclassical one reveals the physical mechanism of decoherence beyond the general blame on nuclear motion. In the propiolic acid, the rate of decoherence and the large deviation from the static frequency of electronic oscillations are quantitatively described with just two semiclassical parameters-the phase space distance and signed area between the trajectories moving on two electronic surfaces. Because it evaluates the electronic structure on the fly, the semiclassical technique avoids the "curse of dimensionality" and should be useful for preselecting molecules for experimental studies.

Attosecond science based on high harmonic generation from gases and solids

Recent progress in high power ultrafast short-wave and mid-wave infrared lasers has enabled gas-phase high harmonic generation (HHG) in the water window and beyond, as well as the demonstration of HHG in condensed matter. In this Perspective, we discuss the recent advancements and future trends in generating and characterizing soft X-ray pulses from gas-phase HHG and extreme ultraviolet (XUV) pulses from solid-state HHG. Then, we discuss their current and potential usage in time-resolved study of electron and nuclear dynamics in atomic, molecular and condensed matters.

Different methods are demonstrated in recent years to produce attosecond pulses. Here, the authors discuss recent development and future prospects of the generation of such pulses from gases and solids and their potential applications in spectroscopy and ultrafast dynamics in atoms, molecules and other complex systems.

Ultrafast Quantum Interference in the Charge Migration of Tryptophan

Extreme-ultraviolet-induced charge migration in biorelevant molecules is a fundamental step in the complex path leading to photodamage. In this work we propose a simple interpretation of the charge migration recently observed in an attosecond pump-probe experiment on the amino acid tryptophan. We find that the decay of the prominent low-frequency spectral structure with increasing pump-probe delay is due to a quantum beating between two geometrically distinct, almost degenerate charge oscillations. Quantum beating is ubiquitous in these systems, and at least on the few-to-tens of femtosecond time scales, it may dominate over decoherence the line intensities of time-resolved spectra. We also address the experimentally observed phase shift in the charge oscillations of two different amino acids, tryptophan and phenylalanine. Our results indicate that a beyond mean-field treatment of the electron dynamics is necessary to reproduce the correct behavior.

Timing the recoherences of attosecond electronic charge migration by quantum control of femtosecond nuclear dynamics: A case study for HCCI. J Chem Phys 2019;151:244306. [PMID: 31893866 DOI: 10.1063/1.5134665]

This work suggests an approach to a new target of laser control of charge migration in molecules or molecular ions. The target is motivated by the fact that nuclear motions can not only cause decoherence of charge migration, typically within few femtoseconds, but they may also enable the reappearance of charge migration after much longer times, typically several tens or even hundreds of femtoseconds. This phenomenon is called recoherence of charge migration, opposite to its decoherence. The details depend on the initiation of the original charge migration by an ultrashort strong intense pump laser pulse. It may reappear quasiperiodically, with reference period T_r. We show that a well-designed pump-dump laser pulse can enforce recoherences of charge migration at different target times T_c, for example, at T_c ≈ T_r/2. The approach is demonstrated by quantum dynamics simulations of the laser driven electronic and nuclear motions in the oriented linear cation HCCI⁺. First, the concept is explained in terms of a didactic one-dimensional (1D) model that accounts for the decisive CI stretch. The 1D results are then confirmed by a three-dimensional model for the complete set of the CH, CC, and CI stretches.

Competition between charge migration and charge transfer induced by nuclear motion following core ionization: Model systems and application to Li2. J Chem Phys 2019;151:124108. [PMID: 31575213 DOI: 10.1063/1.5117246]

Attosecond and femtosecond spectroscopies present opportunities for the control of chemical reaction dynamics and products, as well as for quantum information processing; we address the somewhat unique situation of core-ionization spectroscopy which, for dimeric chromophores, leads to strong valence charge localization and hence tightly paired potential-energy surfaces of very similar shape. Application is made to the quantum dynamics of core-ionized Li₂ ⁺. This system is chosen as Li₂ is the simplest stable molecule facilitating both core ionization and valence ionization. First, the quantum dynamics of some model surfaces are considered, with the surprising result that subtle differences in shape between core-ionization paired surfaces can lead to dramatic differences in the interplay between electronic charge migration and charge transfer induced by nuclear motion. Then, equation-of-motion coupled-cluster calculations are applied to determine potential-energy surfaces for 8 core-excited state pairs, calculations believed to be the first of their type for other than the lowest-energy core-ionized molecular pair. While known results for the lowest-energy pair suggest that Li₂ ⁺ is unsuitable for studying charge migration, higher-energy pairs are predicted to yield results showing competition between charge migration and charge transfer. Central is a focus on the application of Hush's 1975 theory for core-ionized X-ray photoelectron spectroscopy to understand the shapes of the potential-energy surfaces and hence predict key features of charge migration.

Onset of ionic coherence and ultrafast charge dynamics in attosecond molecular ionisation

Here is presented a fully ab initio theoretical framework for simulating the correlated many-electron dynamics occurring during and emerging from molecular ionisation by attosecond laser pulses. This is based on the time-dependent (TD) version of the B-spline restricted correlation space (RCS)-algebraic diagrammatic construction (ADC) method, with the full description of the photoelectron and inclusion of electron correlation effects, such as shakeup processes and inter-channel couplings. The nature of the ultrafast charge dynamics in the molecular ion is elucidated by quantitatively predicting the degree of electronic coherence and eigenstate content of the prepared molecular cationic state, beyond the commonly used sudden approximation. The results presented here for the acetylene and ethylene molecules show that even in the high photon energy regime the simulated hole dynamics is quantitatively different from the prediction of the sudden approximation. Moreover, for high-bandwidth ionising pulse, the residual interaction between the cation, in highly-excited shake-up states, and the emitted slow photoelectron gives rise to a loss of coherence in the ionic system which can persist for the first few femtoseconds after ionisation.

De- and Recoherence of Charge Migration in Ionized Iodoacetylene

During charge migration, electrons flow rapidly from one site of a molecule to another, perhaps inducing subsequent processes (e.g., selective breaking of chemical bonds). The first joint experimental and theoretical preparation and measurement of the initial state and subsequent quantum dynamics simulation of charge migration for fixed nuclei was demonstrated recently for oriented, ionized iodoacetylene. Here, we present new quantum dynamics simulations for the same system with moving nuclei. They reveal the decisive role of the nuclei, i.e. they switch charge migration off (decoherence) and on (recoherence). This is a new finding in attosecond-to-femtosecond chemistry and physics which opens new prospects for laser control over electronic dynamics via nuclear motions.