Attosecond Electron Dynamics in Molecules

Evaluation of Diffuse Basis Sets for Simulations of Strong Field Ionization Using Time-Dependent Configuration Interaction with a Complex Absorbing Potential

For simulations of strong field ionization using time-dependent configuration with a complex absorbing potential (TDCI-CAP), standard molecular basis set must be augmented by several sets of diffuse functions to support the wave function as it is distorted by the strong field and interacts with the absorbing potential. Various sets of diffuse functions used in previous studies have been extended and evaluated for their ability to model the angular dependence of the strong field ionization. These sets include diffuse s, p, d, and f Gaussian functions with selected even-tempered exponents of the form 0.0001 × 2n placed on each atom. For single-centered test cases, the largest contribution to the ionization rate is from functions with a maximum in the radial distribution close to the onset of the complex absorbing potential, while functions with smaller exponents also contributed to the rate. For molecules, diffuse functions on adjacent centers overlap strongly, leading to linear dependencies. The transformation to remove these linear dependencies mixes functions of different angular momenta making it difficult to assess the importance of individual s, p, d, and f functions in simulating the rate for molecules. As an alternative, a hierarchy of diffuse basis sets was constructed by starting with a small set and adding one or two functions at a time. These basis sets were evaluated for their ability to reproduce the rate and shape of the angular dependence of strong field ionization. When combined with the aug-cc-pVTZ molecular basis set and an absorbing potential starting at 3.5 times the van der Waals radius for each atom, the most diffuse s, p, d, and f functions need to have exponents of 0.0032, 0.0032, 0.0064, and 0.0064, respectively, or smaller. Strong field ionization from electronegative atoms such as oxygen required additional f functions with tight exponents of 0.0512 and 0.1024. Diffuse basis sets that perform well for the angular dependence of the ionization rate with a static field are equally effective for strong field ionization with a linearly polarized 7-cycle 800 nm pulse.

Isotope Effect on the Few-Femtosecond Relaxation Dynamics of the Ethylene Cation

Few-femtosecond extreme-ultraviolet (EUV) pulses with tunable energy are employed to initiate the Jahn-Teller structural rearrangement in the ethylene cation. We report on a combined experimental and theoretical investigation of an unusual isotope effect on the low-energy competing H/D-loss and H2/D2-loss channels observed in the ultrafast dynamics induced by an EUV-pump pulse and probed by an infrared (IR) pulse. The relative production yields of C2D4+, C2D3+, and C2D2+ exhibit pronounced oscillations with a period of ∼50 fs as a function of the pump-probe delay, while the oscillatory patterns are less pronounced for C2H4+. By using surface hopping to model the nonadiabatic dynamics in the four lowest electronic states of the cation, we show that the enhanced oscillations in deuterated fragment yields arise from a synergy between the isotope effects on the wave packet relaxation through the network of conical intersections and on the vibrational frequencies of the cation.

Generation of isolated attosecond pulses in CdS semiconductor using polarization gating technique and tailored two-color pulse system

This research uses a two-color pulse system and polarization gating technique to generate single attosecond pulses from femtosecond laser interaction with cadmium sulfide semiconductor. The rotating elliptical polarization two-color pulse system is designed to produce attosecond pulses up to 420 as. Also, the intensity of the single attosecond pulse can be improved by using a two-color-polarizing gate technique. In this presented modifications, the isolated attosecond pulse with greater intensity and a shorter time width of about 400 as is generated. Generation of such an intense isolated attosecond pulse is a great achievement that helps for measuring the ultrafast phenomena.

Microscopic time-resolved spectroscopy of organic crystals at the nanometer and micrometer scale

How can the photoexcitation dynamics processes of solid substances be measured at the microscopic level? This is a popular topic in many fields of basic and applied sciences. Organic crystals are one of many materials, and understanding their intrinsic properties at the microscopic level is the focus of this discussion. Microscopic time-resolved spectroscopy can study the morphology-dependent photoexcitation dynamics and energy spatial transport processes in organic crystals. In this tutorial review, we introduce the principles and methods of microscopic time-resolved photoluminescence and microscopic transient absorption techniques, which are currently or potentially used to study organic crystals at the nanometer and micrometer scale. Meanwhile, the research status of organic crystals investigated via microscopic time-resolved spectroscopy is discussed, with several examples provided. We then compare the advantages and disadvantages of different methods in detail, offering insights into potential improvements for instrument performance.

A versatile and transportable endstation for controlled molecule experiments

We report on a new versatile transportable endstation for controlled molecule (eCOMO) experiments providing a combination of molecular beam purification by electrostatic deflection and simultaneous ion and electron detection using velocity-map imaging (VMI). The b-type electrostatic deflector provides spatial dispersion of species based on their effective-dipole-moment-to-mass ratio. This enables selective investigation of molecular rotational quantum states, conformers, and molecular clusters. Furthermore, the double-sided VMI spectrometer equipped with two high-temporal-resolution event-driven Timepix3 cameras provides detection of all generated ions independently of their mass-over-charge ratio and electrons. To demonstrate the potential of this novel apparatus, we present experimental results from our investigation of carbonyl sulfide (OCS) after ionization. In particular, we provide the characterization of the molecular beam, electrostatic deflector, and electron- and ion-VMI spectrometer. The eCOMO endstation delivers a platform for ultrafast dynamics studies using a wide range of light sources from table-top lasers to free-electron-laser and synchrotron-radiation facilities. This makes it suitable for research activities spanning from atomic, molecular, and cluster physics, over energy science and chemistry, to structural biology.

A theoretical prediction for generating isolated attosecond pulse in water window utilizing instantaneous frequency change of two-color driving laser pulse

This work reports on the theoretical generation of isolated soft-X ray 106 attosecond pulse within the water window spectral region, through interacting a chirped two-color femtosecond laser pulse with a hydrogen atom. To construct this pulse, a chirped 3.5 optical cycle (9.33 fs) laser pulse with a wavelength of 800 nm and an intensity of [Formula: see text] is used as the main field. A 37.32 fs laser pulse with a wavelength of 1600 nm and intensity of [Formula: see text], one-quarter of the main field intensity, is employed as the control field. A tangential hyperbolic function is used to impose chirp on the main field. The study simultaneously utilizes the lowest possible intensity and the highest possible pulse duration for both the main and the control field to reach the water window spectral region in high-order harmonic generation up to the 320th harmonic of the driving field.

Coherent Excitation of the CH Stretching Vibrations in C2H4 +: The Role of the Derivative Coupling Studied by the Quantum Ehrenfest Method

We report nonadiabatic dynamics computations on C2H4 + initiated on a coherent superposition of the five lowest cationic states, employing the Quantum Ehrenfest method. In addition to the totally symmetric carbon-carbon double bond stretch and carbon-hydrogen stretches, we see that the three non-totally symmetric modes become stimulated; torsion and three different CH stretching patterns. Thus, a coherent superposition of states, of the type involved in an attochemistry experiment, leads to the stimulation of specific non-totally symmetric motions. The computations were also performed on the specific combination of the A and C states. In each case normal mode 9 (cis-asymmetric H2CCH2 stretch), out of the set of non-totally-symmetric normal modes, dominates. Thus, we can steer the nuclear motion along specific non-totally symmetric normal modes using a defined coherent superposition.

A non-Markovian neural quantum propagator and its application in the simulation of ultrafast nonlinear spectra

The accurate solution of dissipative quantum dynamics plays an important role in the simulation of open quantum systems. Here, we propose a machine learning-based universal solver for the hierarchical equations of motion, one of the most widely used approaches which takes into account non-Markovian effects and nonperturbative system-environment interactions in a numerically exact manner. We develop a neural quantum propagator model by utilizing the neural network architecture, which avoids time-consuming iterations and can be used to evolve any initial quantum state for arbitrarily long times. To demonstrate the efficacy of our model, we apply it to the simulation of population dynamics and linear and two-dimensional spectra of the Fenna-Matthews-Olson complex.

Few-femtosecond electron transfer dynamics in photoionized donor-π-acceptor molecules

The exposure of molecules to attosecond extreme-ultraviolet (XUV) pulses offers a unique opportunity to study the early stages of coupled electron-nuclear dynamics in which the role played by the different degrees of freedom is beyond standard chemical intuition. We investigate, both experimentally and theoretically, the first steps of charge-transfer processes initiated by prompt ionization in prototype donor-π-acceptor molecules, namely nitroanilines. Time-resolved measurement of this process is performed by combining attosecond XUV-pump/few-femtosecond infrared-probe spectroscopy with advanced many-body quantum chemistry calculations. We show that a concerted nuclear and electronic motion drives electron transfer from the donor group on a sub-10-fs timescale. This is followed by a sub-30-fs relaxation process due to the probing of the continuously spreading nuclear wave packet in the excited electronic states of the molecular cation. These findings shed light on the role played by electron-nuclear coupling in donor-π-acceptor systems in response to photoionization.

Time-dependent ab initio molecular-orbital decomposition for high-harmonic generation spectroscopy

We propose a real-time time-dependent ab initio approach within a configuration-interaction-singles ansatz to decompose the high-harmonic generation (HHG) signal of molecules in terms of individual molecular-orbital (MO) contributions. Calculations have been performed by propagating the time-dependent Schrödinger equation with complex energies, in order to account for ionization of the system, and by using tailored Gaussian basis sets for high-energy and continuum states. We have studied the strong-field electron dynamics and the HHG spectra in aligned CO2 and H2O molecules. Contribution from MOs in the strong-field dynamics depends on the interplay between the MO ionization energy and the coupling between the MO and the laser-pulse symmetries. Such contributions characterize different portions of the HHG spectrum, indicating that the orbital decomposition encodes nontrivial information on the modulation of the strong-field dynamics. Our results correctly reproduce the MO contributions to HHG for CO2 as described in the literature experimental and theoretical data and lead to an original analysis of the role of the highest occupied molecular orbitals HOMO, HOMO-1, and HOMO-2 of H2O according to the polarization direction of the laser pulse.

Simulations of photoinduced processes with the exact factorization: state of the art and perspectives

This perspective offers an overview of the applications of the exact factorization of the electron-nuclear wavefunction to the domain of theoretical photochemistry, where the aim is to gain insights into the ultrafast dynamics of molecular systems via simulations of their excited-state dynamics beyond the Born-Oppenheimer approximation. The exact factorization offers an alternative viewpoint to the Born-Huang representation for the interpretation of dynamical processes involving the electronic ground and excited states as well as their coupling through the nuclear motion. Therefore, the formalism has been used to derive algorithms for quantum molecular-dynamics simulations where the nuclear motion is treated using trajectories and the electrons are treated quantum mechanically. These algorithms have the characteristic features of being based on coupled and on auxiliary trajectories, and have shown excellent performance in describing a variety of excited-state processes, as this perspective illustrates. We conclude with a discussion on the authors' point of view on the future of the exact factorization.

Including Photoexcitation Explicitly in Trajectory-Based Nonadiabatic Dynamics at No Cost

Over the last decades, theoretical photochemistry has produced multiple techniques to simulate the nonadiabatic dynamics of molecules. Surprisingly, much less effort has been devoted to adequately describing the first step of a photochemical or photophysical process: photoexcitation. Here, we propose a formalism to include the effect of a laser pulse in trajectory-based nonadiabatic dynamics at the level of the initial conditions, with no additional cost. The promoted density approach (PDA) decouples the excitation from the nonadiabatic dynamics by defining a new set of initial conditions, which include an excitation time. PDA with surface hopping leads to nonadiabatic dynamics simulations in excellent agreement with quantum dynamics using an explicit laser pulse and highlights the strong impact of a laser pulse on the resulting photodynamics and the limits of the (sudden) vertical excitation. Combining PDA with trajectory-based nonadiabatic methods is possible for any arbitrary-sized molecules using a code provided in this work.

Attosecond formation of charge-transfer-to-solvent states of aqueous ions probed using the core-hole-clock technique

Charge transfer between molecules lies at the heart of many chemical processes. Here, we focus on the ultrafast electron dynamics associated with the formation of charge-transfer-to-solvent (CTTS) states following X-ray absorption in aqueous solutions of Na+, Mg2+, and Al3+ ions. To explore the formation of such states in the aqueous phase, liquid-jet photoemission spectroscopy is employed. Using the core-hole-clock method, based on Auger-Meitner (AM) decay upon 1s excitation or ionization of the respective ions, upper limits are estimated for the metal-atom electron delocalization times to the neighboring water molecules. These delocalization processes represent the first steps in the formation of hydrated electrons, which are determined to take place on a timescale ranging from several hundred attoseconds (as) below the 1s ionization threshold to only 20 as far above the 1s ionization threshold. The decrease in the delocalization times as a function of the photon energy is continuous. This indicates that the excited electrons remain in the vicinity of the studied ions even above the ionization threshold, i.e., metal-ion electronic resonances associated with the CTTS state manifolds are formed. The three studied isoelectronic ions exhibit quantitative differences in their electron energetics and delocalization times, which are linked to the character of the respective excited states.

Time-dependent orbital-optimized coupled-cluster methods families for fermion-mixtures dynamics

Five time-dependent orbital optimized coupled-cluster methods, of which four can converge to the time-dependent complete active space self-consistent-field method, are presented for fermion-mixtures with arbitrary fermion kinds and numbers. Truncation schemes maintaining the intragroup orbital rotation invariance, as well as equations of motion of coupled-cluster (CC) amplitudes and orbitals, are derived. Present methods are compact CC-parameterization alternatives to the time-dependent multiconfiguration self-consistent-field method for systems consisting of arbitrarily different kinds and numbers of interacting fermions. Theoretical analysis of applications of present methods to various chemical systems is reported.

Pushing the limits of ultrafast diffraction: Imaging quantum coherences in isolated molecules

Quantum coherence governs the outcome and efficiency of photochemical reactions and ultrafast molecular dynamics. Recent ultrafast gas-phase X-ray scattering and electron diffraction have enabled the observation of femtosecond nuclear dynamics driven by vibrational coherence. However, probing attosecond electron dynamics and coupled electron-nuclear dynamics remains challenging. This article discusses advances in ultrafast X-ray scattering and electron diffraction, highlighting their potential to resolve attosecond charge migration and vibronic coupling at conical intersections. Novel techniques, such as X-ray scattering with orbital angular momentum beams and combined X-ray and electron diffraction, promise to selectively probe coherence contributions and visualize charge migration in real-space. These emerging methods could further our understanding of coherence effects in chemical reactions.

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%.

Self-Heterodyne Diffractive Imaging of Ultrafast Electron Dynamics Monitored by Single-Electron Pulses

The direct imaging of time-evolving molecular charge densities on atomistic scale and at femtosecond resolution has long been an elusive task. In this theoretical study, we propose a self-heterodyne electron diffraction technique based on single electron pulses. The electron is split into two beams, one passes through the sample and its interference with the second beam produces a heterodyne diffraction signal that images the charge density. Application to probing the ultrafast electronic dynamics in Mg-phthalocyanine demonstrates its potential for imaging chemical dynamics.

Time evolution as an optimization problem: The hydrogen atom in strong laser fields in a basis of time-dependent Gaussian wave packets

Recent advances in attosecond science have made it increasingly important to develop stable, reliable, and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of ångström. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schrödinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that thawed, complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50-181 Gaussians for field strengths up to 5 × 1014 W/cm2. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with Gaussian basis sets for strong fields and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer approximation.

Efficient Control of Electron Localization and Probability Modulation with Synthesized Two-Color Intense Laser Pulses

A coupled electron-nuclear dynamical study at attosecond time scale is performed on the HD+ and H2+ molecular ions under the influence of synthesized intense two-color electric fields. We have employed ω - 2ω and also, ω - 3ω two-color fields in the infrared/mid-infrared regime to study the different fragmentation processes originating from the interference of n - (n + i) (i = 1, 2) photon absorption pathways. The branching ratios corresponding to different photofragments are controlled by tuning the relative phase as well as intensity of the two-color pulses, while the effect of the initial nuclear wave function is also studied by taking an individual vibrational eigenstate or a coherent superposition of several eigenstates of HD+ and H2+. By comprehensive analysis, the efficacy of the two different types of synthesized two-color pulses (ω - 2ω and ω - 3ω) are analyzed with respect to one-color intense pulses in terms of controlling the probability modulation and electron localization asymmetry and compared with previous theoretical calculations and experimental findings. Through the detailed investigation, we have addressed which one is the major controlling knob to have better electron localization as well as probability modulation.

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.

Attosecond ionic photoionization spectroscopy

Photoionization is one of the most fundamental processes in light-matter interaction. Advanced attosecond photoelectron spectroscopy provides the possibility to characterize the ultrafast photoemission process in an extremely short attosecond time scale. Following scattering symmetry rules, residual ions encode ultrafast photoionization prints at the instant of electron removal forming an alternative electron emission chronoscope. Here, we experimentally illustrate the attosecond ion reconstruction of attosecond beating by interference of two-photon transition (RABBIT)-like interferometry through the development of high-resolution ion momentum detection in atomic photoionization processes. Our ion interferometry presents identical momentum- and time-dependent scattering phase shift, as we observed in photoelectron spectroscopy, and thus demonstrates that ion interferometry can be a possible alternative attosecond approach to resolve the photoionization process, without the electron homogeneity limitation.

Capturing electron-driven chiral dynamics in UV-excited molecules

Chiral molecules, used in applications such as enantioselective photocatalysis1, circularly polarized light detection2 and emission3 and molecular switches4,5, exist in two geometrical configurations that are non-superimposable mirror images of each other. These so-called (R) and (S) enantiomers exhibit different physical and chemical properties when interacting with other chiral entities. Attosecond technology might enable influence over such interactions, given that it can probe and even direct electron motion within molecules on the intrinsic electronic timescale6 and thereby control reactivity7-9. Electron currents in photoexcited chiral molecules have indeed been predicted to enable enantiosensitive molecular orientation10, but electron-driven chiral dynamics in neutral molecules have not yet been demonstrated owing to the lack of ultrashort, non-ionizing and perturbative light pulses. Here we use time-resolved photoelectron circular dichroism (TR-PECD)11-15 with an unprecedented temporal resolution of 2.9 fs to map the coherent electronic motion initiated by ultraviolet (UV) excitation of neutral chiral molecules. We find that electronic beatings between Rydberg states lead to periodic modulations of the chiroptical response on the few-femtosecond timescale, showing a sign inversion in less than 10 fs. Calculations validate this and also confirm that the combination of the photoinduced chiral current with a circularly polarized probe pulse realizes an enantioselective filter of molecular orientations following photoionization. We anticipate that our approach will enable further investigations of ultrafast electron dynamics in chiral systems and reveal a route towards enantiosensitive charge-directed reactivity.

Gaussians for Electronic and Rovibrational Quantum Dynamics

The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this Article, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential, we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.

Electronic Coherences Excited by an Ultra Short Pulse Are Robust with Respect to Averaging over Randomly Oriented Molecules as Shown by Singular Value Decomposition

We report a methodology for averaging quantum photoexcitation vibronic dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the ensemble density matrix of the excited molecules, which allows the identification of the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The principal orientations provide insights into the specific stereodynamics of the corresponding principal molecular vibronic states. The massive compaction of the vibronic density matrix of the ensemble of randomly oriented pumped molecules enables a most efficient fully quantum mechanical time propagation scheme. Two examples are discussed for the quantum dynamics of the LiH molecule in the manifolds of its electronically excited Σ and Π states. Our results show that electronic and vibrational coherences between excited states of the same symmetry are resilient to averaging over an ensemble of molecular orientations and can be selectively excited at the ensemble level by tuning the pulse parameters.

Robust Isolated Attosecond Pulse Generation with Self-Compressed Subcycle Drivers from Hollow Capillary Fibers

High-order harmonic generation (HHG) arising from the nonperturbative interaction of intense light fields with matter constitutes a well-established tabletop source of coherent extreme-ultraviolet and soft X-ray radiation, which is typically emitted as attosecond pulse trains. However, ultrafast applications increasingly demand isolated attosecond pulses (IAPs), which offer great promise for advancing precision control of electron dynamics. Yet, the direct generation of IAPs typically requires the synthesis of near-single-cycle intense driving fields, which is technologically challenging. In this work, we theoretically demonstrate a novel scheme for the straightforward and compact generation of IAPs from multicycle infrared drivers using hollow capillary fibers (HCFs). Starting from a standard, intense multicycle infrared pulse, a light transient is generated by extreme soliton self-compression in a HCF with decreasing pressure and is subsequently used to drive HHG in a gas target. Owing to the subcycle confinement of the HHG process, high-contrast IAPs are continuously emitted almost independently of the carrier-envelope phase (CEP) of the optimally self-compressed drivers. This results in a CEP-robust scheme which is also stable under macroscopic propagation of the high harmonics in a gas target. Our results open the way to a new generation of integrated all-fiber IAP sources, overcoming the efficiency limitations of usual gating techniques for multicycle drivers.

Ionization Pathway Interference in Photoionization Time Delays in Molecules

The photoionization time-delay in linear conjugated molecules is computed using the Wigner scattering approach. We find that, in general, there are two additive contributions to the ionization time-delays. One originates from interferences between various ionization pathways that belong to different cationic eigenstates, while the other is due to time delays associated with each pathway and originates due to electron-electron correlations in the molecule. The former contribution scales up rapidly with the conjugation length, leading to larger time delays, as observed in recent experiments, while the latter is much less sensitive to the molecular conjugation.

Prediction challenge: First principles simulation of the ultrafast electron diffraction spectrum of cyclobutanone

Computer simulation has long been an essential partner of ultrafast experiments, allowing the assignment of microscopic mechanistic detail to low-dimensional spectroscopic data. However, the ability of theory to make a priori predictions of ultrafast experimental results is relatively untested. Herein, as a part of a community challenge, we attempt to predict the signal of an upcoming ultrafast photochemical experiment using state-of-the-art theory in the context of preexisting experimental data. Specifically, we employ ab initio Ehrenfest with collapse to a block mixed quantum-classical simulations to describe the real-time evolution of the electrons and nuclei of cyclobutanone following excitation to the 3s Rydberg state. The gas-phase ultrafast electron diffraction (GUED) signal is simulated for direct comparison to an upcoming experiment at the Stanford Linear Accelerator Laboratory. Following initial ring-opening, dissociation via two distinct channels is observed: the C3 dissociation channel, producing cyclopropane and CO, and the C2 channel, producing CH2CO and C2H4. Direct calculations of the GUED signal indicate how the ring-opened intermediate, the C2 products, and the C3 products can be discriminated in the GUED signal. We also report an a priori analysis of anticipated errors in our predictions: without knowledge of the experimental result, which features of the spectrum do we feel confident we have predicted correctly, and which might we have wrong?

Probing H_{2} Double Ionization with Bicircular Laser Fields

We present a kinematically complete study on strong-field double ionization of H_{2} molecules in two-color bicircular laser fields. The releasing times of electrons and protons are recorded with the double-hand attoclock. We observe the relative emission angles of two electrons oscillate with the kinetic energy release of protons, indicating the internal concerted four-body fragmentation. Using a three-dimensional molecular semiclassical ensemble model, we have disentangled the attosecond correlated electron emission in H_{2} double ionization. This work reveals the strong electron-nuclear coupling in the molecular bond breaking and may open up a new approach to experimentally accessing the intramolecular electron and bond dynamics with bicircular fields.

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.

High-Harmonic Generation Spectroscopy of Gas-Phase Bromoform

High-Harmonic Generation (HHG) spectra of randomly aligned bromoform (CHBr3) molecules have been experimentally measured and theoretically simulated at various laser pulse intensities. From the experiments, we obtained a significant number of harmonics that goes beyond the cutoff limit predicted by the three-step model (3SM) with ionization from HOMO. To interpret the experiment, we resorted to real-time time-dependent configuration interaction with single excitations. We found that electronic bound states provide an appreciable contribution to the harmonics. More in detail, we analyzed the electron dynamics by decomposing the HHG signal in terms of single molecular-orbital contributions, to explain the appearance of harmonics around 20-30 eV beyond the expected cutoff due to HOMO. HHG spectra can be therefore explained by considering the contribution at high energy of HOMO-6 and HOMO-9, thus indicating a complex multiple-orbital strong-field dynamics. However, even though the presence of the bromoform cation should be not enough to produce such a signal, we could not exclude a priori that the origin of harmonics in the H29-H45 to be due to the cation, which has more energetic ionization channels.

Dissociation and Isomerization Following Ionization of Ethylene: Insights from Nonadiabatic Dynamics Simulations

Photoionized and electronically excited ethylene C2H4+ can undergo H-loss, H2-loss, and ethylene-ethylidene isomerization, where the latter entails a hydrogen migration. Recent pioneering experiments with few-femtosecond extreme ultraviolet pulses and complementary theoretical studies have shed light on the photodynamics of this prototypical organic cation. However, no theoretical investigation based on dynamics simulations reported to date has described the mechanisms and time scales of dissociation and isomerization. Herein, we simulate the coupled electron-nuclear dynamics of ethylene following vertical ionization and electronic excitation to its four lowest-lying cationic states. The electronic structure is treated at the CASSCF level, with an active space large enough to describe bond breaking and formation. The simulations indicate that dissociation and isomerization take place mainly on the cationic ground state and allow the probing of previous hypotheses concerning the correlation between the photochemical outcome and the traversed conical intersections. The results, moreover, support the long-standing view that H2-loss may occur from the ethylidene form. However, the ethylene-ethylidene isomerization time predicted by the simulations is considerably longer than those previously inferred from indirect experimental measurements.

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

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

Tracing Photoinduced Hydrogen Migration in Alcohol Dications from Time-Resolved Molecular-Frame Photoelectron Angular Distributions

The recent implementation of attosecond and few-femtosecond X-ray pump/X-ray probe schemes in large-scale free-electron laser facilities has opened the way to visualize fast nuclear dynamics in molecules with unprecedented temporal and spatial resolution. Here, we present the results of theoretical calculations showing how polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) can be used to visualize the dynamics of hydrogen migration in methanol, ethanol, propanol, and isopropyl alcohol dications generated by X-ray irradiation of the corresponding neutral species. We show that changes in the PA-MFPADs with the pump-probe delay as a result of intramolecular photoelectron diffraction carry information on the dynamics of hydrogen migration in real space. Although visualization of this dynamics is more straightforward in the smaller systems, methanol and ethanol, one can still recognize the signature of that motion in propanol and isopropyl alcohol and assign a tentative path to it. A possible pathway for a corresponding experiment requires an angularly resolved detection of photoelectrons in coincidence with molecular fragment ions used to define a molecular frame of reference. Such studies have become, in principle, possible since the first XFELs with sufficiently high repetition rates have emerged. To further support our findings, we provide experimental evidence of H migration in ethanol-OD from ion-ion coincidence measurements performed with synchrotron radiation.

Attosecond Probing of Nuclear Vibrations in the D2+ and HeH+ Molecular Ions

We study the ultrafast photodissociation of small diatomic molecules using attosecond laser pulses of moderate intensity in the (extreme) ultraviolet regime. The simultaneous application of subfemtosecond laser pulses with different photon energies─resonant in the region of the molecular motion─allows one to monitor the vibrational dynamics of simple diatomics, like the D2+ and HeH+ molecular ions. In our real-time wave packet simulations, the nuclear dynamics is initiated either by sudden ionization (D2+) or by explicit pump pulses (HeH+) via distortion of the potential energy of the molecule. The application of time-delayed attosecond pulses leads to the breakup of the molecules, and the information on the underlying bound-state dynamics is imprinted in the kinetic energy release (KER) spectra of the outgoing fragments. We show that the KER-delay spectrograms generated in our ultrafast pump-probe schemes are able to reconstruct the most important features of the molecular motion within a given electronic state, such as the time period or amplitude of oscillations, interference patterns, or the revival and splitting of the nuclear wave packet. The impact of probe pulse duration, which is key to the applicability of the presented mapping scheme, is investigated in detail.

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states

Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.

Nonadiabatic quantum dynamics explores non-monotonic photodissociation branching of N2 into the N(4S) + N(2D) and N(4S) + N(2P) product channels

Vacuum ultraviolet (VUV) photodissociation of N2 molecules is a source of reactive N atoms in the interstellar medium. In the energy range of VUV optical excitation of N2, the N-N triple bond cleavage leads to three types of atoms: ground-state N(4S) and excited-state N(2P) and N(2D). The latter is the highest reactive and it is believed to be the primary participant in reactions with hydrocarbons in Titan's atmosphere. Experimental studies have observed a non-monotonic energy dependence and non-statistical character of the photodissociation of N2. This implies different dissociation pathways and final atomic products for different wavelength regions in the sunlight spectrum. We here apply ab initio quantum chemical and nonadiabatic quantum dynamical techniques to follow the path of an electronic state from the excitation of a particular singlet 1Σ+u and 1Πu vibronic level of N2 to its dissociation into different atomic products. We simulate dynamics for two isotopomers of the nitrogen molecule, 14N2 and 14N15N for which experimental data on the branching are available. Our computations capture the non-monotonic energy dependence of the photodissociation branching ratios in the energy range 108 000-116 000 cm-1. Tracing the quantum dynamics in a bunch of electronic states enables us to identify the key components that determine the efficacy of singlet to triplet population transfer and therefore predissociation lifetimes and branching ratios for different energy regions.

Tracking Charge Migration with Frequency-Matched Strobo-Spectroscopy

We present frequency-matched strobo-spectroscopy (FMSS) of charge migration (CM) in bromobutadiyne, simulated with time-dependent density functional theory. CM + FMSS is a pump-probe scheme that uses a frequency-matched high harmonic generation (HHG)-driving laser as an independent probe step, following the creation of a localized hole on the bromine atom that induces CM dynamics. We show that the delay-dependent harmonic yield tracks the phase of the CM dynamics through its sensitivity to the amount of electron density on the bromine end of the molecule. FMSS takes advantage of the intrinsic attosecond time resolution of the HHG process in which different harmonics are emitted at different times and thus probe different locations of the electron hole. Finally, we show that the CM-induced modulation of the HHG signal is dominated by the recombination step of the HHG process, with a negligible contribution from the ionization step.

Resonant Photoionization of CO2 up to the Fourth Ionization Threshold

We present a comprehensive theoretical study of valence-shell photoionization of the CO2 molecule by using the XCHEM methodology. This method makes use of a fully correlated molecular electronic continuum at a level comparable to that provided by state-of-the-art quantum chemistry packages in bound-state calculations. The calculated total and angularly resolved photoionization cross sections are presented and discussed, with particular emphasis on the series of autoionizing resonances that appear between the first and the fourth ionization thresholds. Ten series of Rydberg autoionizing states are identified, including some not previously reported in the literature, and their energy positions and widths are provided. This is relevant in the context of ongoing experimental and theoretical efforts aimed at observing in real-time (attosecond time scale) the autoionization dynamics in molecules.

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.

Magnetic optical rotation from real-time simulations in finite magnetic fields

We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation.

Following the Nonadiabatic Ultrafast Dynamics of Uracil via Simulated X-ray Absorption Spectra

The nucleobase uracil exhibits high photostability due to ultrafast relaxation processes mediated by conical intersections (CoIns), where the interplay between nuclear and electron dynamics becomes crucial. In our previous study, we observed seemingly long-lived traces of electronic coherence for the relaxation process through the S2/S1 CoIn by applying our ansatz for coupled nuclear and electron dynamics in molecules (NEMol). In this work, we theoretically investigate how time-dependent transient X-ray absorption spectroscopy can be used to observe this ultrafast dynamics. Therefore, we calculated X-ray absorption spectra (XAS) for the oxygen K-edge, using a multireference protocol in combination with NEMol dynamics. Thus, we have access to both the transient XAS based on the nuclear wavepacket dynamics and the modulation of the signals caused by the electronic coherence induced by the excitation process and the presence of a CoIn seam. In both cases, we were able to qualitatively predict its influence on the resulting XAS.

Cost-Efficient High-Resolution Linear Absorption Spectra through Extrapolating the Dipole Moment from Real-Time Time-Dependent Electronic-Structure Theory

We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require discrete Fourier transforms of the electric dipole moment. The spectral resolution is determined by the total propagation time, i.e., the trajectory length of the dipole moment, causing a high computational cost. Our developed method uses function fitting on shorter trajectories of the dipole moment, achieving arbitrary spectral resolution through extrapolation. Numerical testing shows that the fitting method can reproduce high-resolution spectra by using short dipole trajectories. The method converges with as little as 100 a.u. dipole trajectories for some systems, though the difficulty converging increases with the spectral density. We also introduce an error estimate of the fit, reliably assessing its convergence and hence the quality of the approximated spectrum.

Strong Laser Field-Driven Coupled Electron-Nuclear Dynamics: Quantum vs Classical Description

We have performed a coupled electron-nuclear dynamics study of H2+ molecular ions under the influence of an intense few-cycle 4.5 fs laser pulse with an intensity of 4 × 1014 W/cm2 and a central wavelength of 750 nm. Both quantum and classical dynamical methods are employed in the exact similar initial conditions with the aim of head-to-head comparison of two methodologies. A competition between ionization and dissociation channel is explained under the framework of quantum and classical dynamics. The origin of the electron localization phenomena is elucidated by observing the molecular and electronic wave packet evolution pattern. By probing with different carrier envelope phase (CEP) values of the ultrashort pulse, the possibility of electron localization on either of the two nuclei is investigated. The effects of initial vibrational states on final dissociation and ionization probabilities for several CEP values are studied in detail. Finally, asymmetries in the dissociation probabilities are calculated and mutually compared for both quantum and classical dynamical methodologies, whereas Franck-Condon averaging over the initial vibrational states is carried out in order to mimic the existing experimental conditions.

Harmonic Suppression Induced by Three-Electron Dynamics of Li in Strong Laser Fields

We build a model to elucidate the high harmonic generation in combined EUV and midinfrared laser fields by embodying the spin-resolved three-electron dynamics. The EUV pulse ionizes an inner-shell electron, and the midinfrared laser drives the photoelectron and steers the electron-ion rescattering. Depending on the spin of the photoelectron, the residual ion including two bound electrons can be either in a single spin configuration or in a coherent superposition of different spin configurations. In the latter case, the two electrons in the ion swap their orbits, leading to a deep valley in the harmonic spectrum. The model results agree with the time-dependent Schrödinger equation simulations including three active electrons. The intriguing picture explored in this work is fundamentally distinguished from all reported scenarios relied on spin-orbit coupling, but originates from the exchanges asymmetry of two-electron wave functions.

Spin current in the early stage of radical reactions and its mechanisms

We study the electronic spin flux (atomic-scale flow of the spin density in molecules) by a perturbation analysis and ab initio nonadiabatic calculations. We derive a general perturbative expression of the charge and spin fluxes and identify the driving perturbation of the fluxes to be the time derivative of the electron-nucleus interaction term in the Hamiltonian. We then expand the expression in molecular orbitals so as to identify relevant components of the fluxes. Our perturbation theory describes the electronic fluxes in the early stage of reactions in an intuitively clear manner. The perturbation theory is then applied to an analysis of the spin flux obtained in ab initio calculations of the radical reaction of O2 and CH3· starting from three distinct spin configurations; (a) CH3· and triplet O2 with total spin of the system set Stot=1/2 (b) CH3· and singlet O2, Stot=1/2, and (c) CH3· and triplet O2, Stot=3/2. Further analysis of the time-dependent behaviors of the spin flux in these numerical simulations reveals (i) the spin flux induces rearrangement of the local spin structure, such as reduction of the spin polarization arising from the triplet O2 and (ii) the spin flux flows from O2 to CH3· in the reaction starting from spin configuration (a) and from CH3· to O2 in that starting from configuration (b), whereas no major intermolecular spin flux was observed in that starting from configuration (c). Our study thus establishes the mechanism of the spin flux that rearranges the local spin structures associated with chemical bonds.

Quantitative performance analysis and comparison of optimal-continuum Gaussian basis sets for high-harmonic generation spectra

Quantum-chemistry methods in the time domain with Gaussian basis sets are increasingly used to compute high-harmonic generation (HHG) spectra of atomic and molecular systems. The quality of these approaches is limited by the accuracy of Gaussian basis sets to describe continuum energy states. In the literature, optimal-continuum Gaussian basis sets have been proposed: Kaufmann et al. [J. Phys. B: At., Mol. Opt. Phys. 22, 2223 (1989)], Woźniak et al. [J. Chem. Phys. 154, 094111 (2021)], Nestmann and Peyerimhoff [J. Phys. B: At., Mol. Opt. Phys. 23, L773 (1990)], Faure et al. [Comput. Phys. Commun. 144, 224 (2002)], and Krause et al. [J. Chem. Phys. 140, 174113 (2014)]. In this work, we have compared the performances of these basis sets to simulate HHG spectra of H atom at different laser intensities. We have also investigated different strategies to balance basis sets with these continuum functions, together with the role of angular momentum. To quantify the performance of the different basis sets, we introduce local and global HHG descriptors. Comparisons with the grid and exact calculations are also provided.

Spin-flip dynamics in core-excited states in the basis of irreducible spherical tensor operators

Recent experimental advances in ultrafast science have put different processes occurring on the electronic timescale below a few femtoseconds in focus. In the present theoretical work, we demonstrate how the transformation and propagation of the density matrix in the basis of irreducible spherical tensors can be conveniently used to study sub-few fs spin-flip dynamics in core-excited transition metal compounds. With the help of the Wigner-Eckart theorem, such a transformation separates the essential dynamical information from the geometric factors governed by the angular momentum algebra. We show that an additional reduction can be performed by the physically motivated truncation of the spherical tensor basis. In particular, depending on the degree of coherence, the ultrafast dynamics can be considered semi-quantitative in the notably reduced spherical basis when only the total populations of the basis states of the given spin are of interest. Such truncation should be especially beneficial when the number of high-spin basis states is vast, as it reduces computational costs.

Role of Inner Molecular Orbitals in High-Harmonic Generation Spectra of Aligned Uracil

In this work, we decompose the high-harmonic generation (HHG) signal of aligned gas-phase uracil into single molecular-orbital (MO) contributions. We compute HHG spectra for a pulse linearly polarized perpendicular to the molecular plane, with an intensity of 0.6 and 0.85 × 1014 W/cm2 and a wavelength of 800 nm. We use the real-time time-dependent Configuration Interaction with singles method, coupled to a Gaussian-based representation of the time-dependent wavefunction. The strong-field dynamics is affected by the energy of the ionization/recombination channels and by the coupling between the orbital symmetry and laser polarization. In the configuration studied here, we expect that π-type MOs favorably couple with the incoming pulse and play a substantial role in generating the HHG spectrum. Indeed, we show that HOMO, HOMO - 1, and HOMO - 4, which all are π-like, determine the intensity of harmonic peaks at different energies, while HOMO - 2 and HOMO - 3 provide a smaller contribution. It is worth mentioning that HOMO - 4 produces a stronger signal than that from HOMO - 1, even though the corresponding ionization energy, in an one-electron picture, is around 2.5 eV larger and more than 4 eV larger than the HOMO one.

Influence of nuclear dynamics on molecular attosecond photoelectron interferometry

In extreme ultraviolet spectroscopy, the photoionization process occurring in a molecule due to the absorption of a single photon can trigger an ultrafast nuclear motion in the cation. Taking advantage of attosecond photoelectron interferometry, where the absorption of the extreme ultraviolet photon is accompanied by the exchange of an additional infrared quantum of light, one can investigate the influence of nuclear dynamics by monitoring the characteristics of the photoelectron spectra generated by the two-color field. Here, we show that attosecond photoelectron interferometry is sensitive to the nuclear response by measuring the two-color photoionization spectra in a mixture of methane (CH4) and deuteromethane (CD4). The effect of the different nuclear evolution in the two isotopologues manifests itself in the modification of the amplitude and contrast of the oscillations of the photoelectron peaks. Our work indicates that nuclear dynamics can affect the coherence properties of the electronic wave packet emitted by photoionization on a time scale as short as a few femtoseconds.