Multielectron wave-packet propagation: General theory and application

Real-Time CASSCF (Ehrenfest) Modeling of Electron Dynamics in Organic Semiconductors. Dynamics Reaction Paths Driven by Quantum Coherences. Application to a Radical Organic Semiconductor

We present a strategy for the modeling of charge carrier dynamics in organic semiconductors using conventional quantum chemistry methods, including the analytic gradient for nuclear motion. The theoretical approach uses real-time CASSCF (Ehrenfest) all-electron dynamics coupled to classical nuclear dynamics for the special case of a small number (4-8) of molecular units. The objective is to obtain mechanistic/atomistic insight at the electronic structure level, relating to spin density dynamics, to the effect of crystal structure (e.g., slippage between spin/charge carriers), and to ferromagnetic and antiferromagnetic effects. The initial conditions for our simulations use the equilibrium structures of all the molecular units. At this geometry, a localized hole on one of the units corresponds to a coherent superposition of adiabatic states. We thus generate a dynamics reaction path driven by quantum coherences. Our aim is to inform experiment and to compare with parametrized theoretical models. The methodology is demonstrated for a perfectly π-stacked ethylene model (up to 8 eclipsed molecular units) for both hole transfer and localized exciton transfer. An application for hole transfer is presented for bisdithiazolyl (S,S) and bisdiselenazolyl (Se,Se) radicals for the special case of ferromagnetic coupling. For these examples, the embedded pyridine radical model organic chromophore (up to 6 eclipsed π-stacked molecular units) has been studied on its own as well as the target bisdithiazolyl (S,S) and bisdiselenazolyl (Se,Se) systems. A significant difference between these systems and the ethylene and pyridine stacks is that the (S,S) and (Se,Se) systems exhibit molecular slippage rather than being perfectly eclipsed. This slippage may result from crystal defects or intermolecular vibrations. For the model systems, the electron dynamics is dominated by the initial and final molecular units, irrespective of the length of the chain. The intervening units act as a "superexchange bridge". Our simulations reveal that, in the presence of slippage, charge migration cannot propagate across the entire system; instead, the coherence length is limited to 3 molecular units. The results also suggest that the mechanism of charge transport is different for bisdiselenazolyl (Se,Se) (superexchange-like A -[B]→ C) and bisdithiazolyl (S,S) (direct A → C). An analysis of the spin density suggests that, in the charge carrier dynamics, the additional charge carried by the Se versus S in the "scaffold" is small. Since we use a small number of molecular units, the coupled nuclear dynamics is seen to be complementary to the electron dynamics (i.e., creating a hole causes bond length contraction while filling a hole with an electron lengthens the bond). In all the cases studied, the mechanism of charge mobility is wave-like, rather than hopping, because we use the time dependent Schrödinger equation to propagate the electronic wave function.

Simulating Real-Time Molecular Electron Dynamics Efficiently Using the Time-Dependent Density Matrix Renormalization Group

Compared to ground-state electronic structure optimizations, accurate simulations of molecular real-time electron dynamics are usually much more difficult to perform. To simulate electron dynamics, the time-dependent density matrix renormalization group (TDDMRG) has been shown to offer an attractive compromise between accuracy and cost. However, many simulation parameters significantly affect the quality and efficiency of a TDDMRG simulation. So far, it is unclear whether common wisdom from ground-state DMRG carries over to the TDDMRG, and a guideline on how to choose these parameters is missing. Here, in order to establish such a guideline, we investigate the convergence behavior of the main TDDMRG simulation parameters, such as time integrator, the choice of orbitals, and the choice of matrix-product-state representation for complex-valued nonsinglet states. In addition, we propose a method to select orbitals that are tailored to optimize the dynamics. Lastly, we showcase the TDDMRG by applying it to charge migration ionization dynamics in furfural, where we reveal a rapid conversion from an ionized state with a σ character to one with a π character within less than a femtosecond.

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.

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.

Coherent Mixing of Singlet and Triplet States in Acrolein and Ketene: A Computational Strategy for Simulating the Electron-Nuclear Dynamics of Intersystem Crossing

We present a theoretical study of intersystem crossing (ISC) in acrolein and ketene with the Ehrenfest method that can describe a superposition of singlet and triplet states. Our simulations illustrate a new mechanistic effect of ISC, namely, that a superposition of singlets and triplets yields nonadiabatic dynamics characteristic of that superposition rather than the constituent state potential energy surfaces. This effect is particularly significant in ketene, where mixing of singlet and triplet states along the approach to a singlet/singlet conical intersection occurs, with the spin-orbit coupling (SOC) remaining small throughout. In both cases, the effects require many recrossings of the singlet/triplet state crossing seam, consistent with the textbook treatment of ISC.

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.

Density Matrix via Few Dominant Observables for the Ultrafast Non-Radiative Decay in Pyrazine

Unraveling the density matrix of a non-stationary quantum state as an explicit function of a few observables provides a complementary view of quantum dynamics. We have recently developed a practical way to identify the minimal set of the dominant observables that govern the quantal dynamics even in the case of strong non-adiabatic effects and large anharmonicity [Komarova et al., J. Chem. Phys. 155, 204110 (2021)]. Fast convergence in the number of the dominant contributions is achieved when instead of the density matrix we describe the time-evolution of the surprisal, the logarithm of the density operator. In the present work, we illustrate the efficiency of the proposed approach using an example of the early time dynamics in pyrazine in a Hilbert space accounting for up to four vibrational normal modes, {Q10a, Q6a, Q1, and Q9a}, and two coupled electronic states, the optically dark B 1 3 u ( n π * ) and the bright B 1 2 u ( π π * ) states. Dynamics in four-dimensional (4D) configurational space involve 19,600 vibronic eigenstates. Our results reveal that the rate of the ultrafast population decay as well as the shape of the nuclear wave packets in 2D, accounting only for {Q10a,Q6a} normal modes, are accurately captured with only six dominant time-independent observables in the surprisal. Extension of the dynamics to 3D and 4D vibrational subspace requires only five additional constraints. The time-evolution of a quantum state in 4D vibrational space on two electronic states is thus compacted to only 11 time-dependent coefficients of these observables.

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.

Charge-induced chemical dynamics in glycine probed with time-resolved Auger electron spectroscopy

In the present contribution, we use x-rays to monitor charge-induced chemical dynamics in the photoionized amino acid glycine with femtosecond time resolution. The outgoing photoelectron leaves behind the cation in a coherent superposition of quantum mechanical eigenstates. Delayed x-ray pulses track the induced coherence through resonant x-ray absorption that induces Auger decay. Temporal modulation of the Auger electron signal correlated with specific ions is observed, which is governed by the initial electronic coherence and subsequent vibronic coupling to nuclear degrees of freedom. In the time-resolved x-ray absorption measurement, we monitor the time-frequency spectra of the resulting many-body quantum wave packets for a period of 175 fs along different reaction coordinates. Our experiment proves that by measuring specific fragments associated with the glycine dication as a function of the pump-probe delay, one can selectively probe electronic coherences at early times associated with a few distinguishable components of the broad electronic wave packet created initially by the pump pulse in the cation. The corresponding coherent superpositions formed by subsets of electronic eigenstates and evolving along parallel dynamical pathways show different phases and time periods in the range of ( - 0.3 ± 0.1 ) π ≤ ϕ ≤ ( 0.1 ± 0.2 ) π and 18.2 - 1.4 + 1.7 ≤ T ≤ 23.9 - 1.1 + 1.2 fs. Furthermore, for long delays, the data allow us to pinpoint the driving vibrational modes of chemical dynamics mediating charge-induced bond cleavage along different reaction coordinates.

Photoelectron-photoion(s) coincidence studies of molecules of biological interest

Photoelectron-photoion(s) coincidence, PEPICO, experiments with synchrotron radiation have become one of the most powerful tools to investigate dissociative photoionization thanks to their selectivity. In this paper their application to the study of molecular species of biological interest in the gas phase is reviewed. Some applications of PEPICO to the study of potential radiosensitizers, amino acids and small peptides and opportunities offered by the advent of novel methods for the production of beams of these molecules are discussed.

Quantum coherence in molecular photoionization

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

How electronic superpositions drive nuclear motion following the creation of a localized hole in the glycine radical cation

In this work, we have studied the nuclear and electron dynamics in the glycine cation starting from localized hole states using the quantum Ehrenfest method. The nuclear dynamics is controlled both by the initial gradient and by the instantaneous gradient that results from the oscillatory electron dynamics (charge migration). We have used the Fourier transform (FT) of the spin densities to identify the “normal modes” of the electron dynamics. We observe an isomorphic relationship between the electron dynamics normal modes and the nuclear dynamics, seen in the vibrational normal modes. The FT spectra obtained this way show bands that are characteristic of the energy differences between the adiabatic hole states. These bands contain individual peaks that are in one-to-one correspondence with atom pair (+·) ↔ (·+) resonances, which, in turn, stimulate nuclear motion involving the atom pair. With such understanding, we anticipate “designer” coherent superpositions that can drive nuclear motion in a particular direction.

Electronic quantum coherence in glycine molecules probed with ultrashort x-ray pulses in real time

Here, we use x-rays to create and probe quantum coherence in the photoionized amino acid glycine. The outgoing photoelectron leaves behind the cation in a coherent superposition of quantum mechanical eigenstates. Delayed x-ray pulses track the induced coherence through resonant x-ray absorption that induces Auger decay and by photoelectron emission from sequential double photoionization. Sinusoidal temporal modulation of the detected signal at early times (0 to 25 fs) is observed in both measurements. Advanced ab initio many-electron simulations allow us to explain the first 25 fs of the detected coherent quantum evolution in terms of the electronic coherence. In the kinematically complete x-ray absorption measurement, we monitor its dynamics for a period of 175 fs and observe an evolving modulation that may implicate the coupling of electronic to vibronic coherence at longer time scales. Our experiment provides a direct support for the existence of long-lived electronic coherence in photoionized biomolecules.

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.

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.

Short Iterative Lanczos Integration in Time-Dependent Equation-of-Motion Coupled-Cluster Theory

A time-dependent (TD) formulation of equation-of-motion coupled-cluster (EOM-CC) theory can provide excited-state information over an arbitrarily wide energy window with a reduced memory footprint relative to conventional, frequency-domain EOM-CC theory. However, the floating-point costs of the time-integration required by TD-EOM-CC are generally far larger than those of the frequency-domain form of the approach. This work considers the potential of the short iterative Lanczos (SIL) integration scheme [J. Chem. Phys. 1986, 85, 5870-5876] to reduce the floating-point costs of TD-EOM-CC simulations. Low-energy and K-edge absorption features for small molecules are evaluated using TD-EOM-CC with single and double excitations, with the time-integrations carried out via SIL and fourth-order Runge-Kutta (RK4) schemes. Spectra derived from SIL- and RK4-driven simulations are nearly indistinguishable, and with an appropriately chosen subspace dimension, the SIL requires far fewer floating-point operations than are required by RK4. For K-edge spectra, SIL is the more efficient scheme by an average factor of 7.2.

Coupled nuclear and electron dynamics in the vicinity of a conical intersection

Ultrafast optical techniques allow us to study ultrafast molecular dynamics involving both nuclear and electronic motion. To support interpretation, theoretical approaches are needed that can describe both the nuclear and electron dynamics. Hence, we revisit and expand our ansatz for the coupled description of the nuclear and electron dynamics in molecular systems (NEMol). In this purely quantum mechanical ansatz, the quantum-dynamical description of the nuclear motion is combined with the calculation of the electron dynamics in the eigenfunction basis. The NEMol ansatz is applied to simulate the coupled dynamics of the molecule NO₂ in the vicinity of a conical intersection (CoIn) with a special focus on the coherent electron dynamics induced by the non-adiabatic coupling. Furthermore, we aim to control the dynamics of the system when passing the CoIn. The control scheme relies on the carrier envelope phase of a few-cycle IR pulse. The laser pulse influences both the movement of the nuclei and the electrons during the population transfer through the CoIn.

On the generation of electronic ring currents under vibronic coupling effects

We study the generation of electronic ring currents in the presence of nonadiabatic coupling using circularly polarized light. For this, we introduce a solvable model consisting of an electron and a nucleus rotating around a common center and subject to their mutual Coulomb interaction. The simplicity of the model brings to the forefront the non-trivial properties of electronic ring currents in the presence of coupling to the nuclear coordinates and enables the characterization of various limiting situations transparently. Employing this model, we show that vibronic coupling effects play a crucial role even when a single E degenerate eigenstate of the system supports the current. The maximum current of a degenerate eigenstate depends on the strength of the nonadiabatic interactions. In the limit of large nuclear to electronic masses, in which the Born-Oppenheimer approximation becomes exact, constant ring currents and time-averaged oscillatory currents necessarily vanish.

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.

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.

Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation

Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In the first paper of this series ["Paper I," S. Choi and J. Vaníček, J. Chem. Phys. 150, 204112 (2019)], we presented numerical integrators of arbitrary-order of accuracy that preserve these geometric properties exactly even in the adiabatic representation, in which the molecular Hamiltonian is not separable into kinetic and potential terms. Here, we focus on the separable Hamiltonian in diabatic representation, where the split-operator algorithm provides a popular alternative because it is explicit and easy to implement, while preserving most geometric invariants. Whereas the standard version has only second-order accuracy, we implemented, in an automated fashion, its recursive symmetric compositions, using the same schemes as in Paper I, and obtained integrators of arbitrary even order that still preserve the geometric properties exactly. Because the automatically generated splitting coefficients are redundant, we reduce the computational cost by pruning these coefficients and lower memory requirements by identifying unique coefficients. The order of convergence and preservation of geometric properties are justified analytically and confirmed numerically on a one-dimensional two-surface model of NaI and a three-dimensional three-surface model of pyrazine. As for efficiency, we find that to reach a convergence error of 10^-10, a 600-fold speedup in the case of NaI and a 900-fold speedup in the case of pyrazine are obtained with the higher-order compositions instead of the second-order split-operator algorithm. The pyrazine results suggest that the efficiency gain survives in higher dimensions.

Charge migration in photo-ionized aromatic amino acids

Attosecond pump-probe spectroscopy is a unique tool for the direct observation of the light-activated electronic motion in molecules and it offers the possibility to capture the first instants of a chemical reaction. Recently, advances in attosecond technology allowed the charge migration processes to be revealed in biochemically relevant molecules. Although this purely electronic process might be key for a future chemistry at the electron time scale, the influence of this ultrafast charge flow on the reactivity of a molecule is still debated. In this work, we exploit extreme ultraviolet attosecond pulses to activate charge migration in two aromatic amino acids, namely phenylalanine and tryptophan. Advanced numerical calculations are performed to interpret the experimental data and to discuss the effects of the nuclear dynamics on the activated quantum coherences. By comparing the experimental results obtained in the two molecules, we show that the presence of different functional groups strongly affects the fragmentation pathways, as well as the charge rearrangement. The observed charge dynamics indeed present peculiar aspects, including characteristic periodicities and decoherence times. Numerical results indicate that, even for a very large molecule such as tryptophan, the quantum coherences can survive the nuclear dynamics for several femtoseconds. These results open new and important perspectives for a deeper understanding of the photo-induced charge dynamics, as a promising tool to control the reactivity of bio-relevant molecules via photo-excitation. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Spin trapping and flipping in FeCO through relativistic electron dynamics

Transition metal compounds are very versatile, and their characteristics can differ profoundly depending on their electronic structure. Compounds in which a spin transition from a low-spin to a high-spin state can be achieved through means of an optical excitation are particularly intriguing, as a controlled spin-flip opens promising avenues in areas such as sensing, information technology, molecular switches and energy technology. The fundamental mechanisms in spin crossover and spin transitions remain unanswered, due to the complexity of electronic structure and interplay of relativistic effects. Presented here is a new approach that allows the first direct study of spin flip dynamics through a mapping of spin-mixed to spin-pure states. The method is applied to FeCO and addresses the spin-flip dynamics during a spin transition. Wave packets that combine different spin states are generated through optical excitation and relevant mechanisms in optically triggered spin transitions are discussed.

Ultrafast charge dynamics in glycine induced by attosecond pulses

The combination of attosecond pump-probe techniques with mass spectrometry methods has recently led to the first experimental demonstration of ultrafast charge dynamics in a biomolecule, the amino acid phenylalanine [Calegari et al., Science, 2014, 346, 336]. Using an extension of the static-exchange density functional theory (DFT) method, the observed dynamics was explained as resulting from the coherent superposition of ionic states produced by the broadband attosecond pulse. Here, we have used the static-exchange DFT method to investigate charge migration induced by attosecond pulses in the glycine molecule. We show that the observed dynamics follows patterns similar to those previously found in phenylalanine, namely that charge fluctuations occur all over the molecule and that they can be explained in terms of a few typical frequencies of the system. We have checked the validity of our approach by explicitly comparing with the photoelectron spectra obtained in synchrotron radiation experiments and with the charge dynamics that follows the removal of an electron from a given molecular orbital, for which fully correlated ab initio results are available in the literature. From this comparison, we conclude that our method provides an accurate description of both the coherent superposition of cationic states generated by the attosecond pulse and its subsequent time evolution. Hence, we expect that the static-exchange DFT method should perform equally well for other medium-size and large molecules, for which the use of fully correlated ab initio methods is not possible.

Insights into the dissociative ionization of glycine by PEPICO experiments

The fragmentation of glycine (NH₂CH₂COOH) has been studied by photoelectron–photoion coincidence, PEPICO, experiments at 60 eV photon energy.

Charge migration and charge transfer in molecular systems

The transfer of charge at the molecular level plays a fundamental role in many areas of chemistry, physics, biology and materials science. Today, more than 60 years after the seminal work of R. A. Marcus, charge transfer is still a very active field of research. An important recent impetus comes from the ability to resolve ever faster temporal events, down to the attosecond time scale. Such a high temporal resolution now offers the possibility to unravel the most elementary quantum dynamics of both electrons and nuclei that participate in the complex process of charge transfer. This review covers recent research that addresses the following questions. Can we reconstruct the migration of charge across a molecule on the atomic length and electronic time scales? Can we use strong laser fields to control charge migration? Can we temporally resolve and understand intramolecular charge transfer in dissociative ionization of small molecules, in transition-metal complexes and in conjugated polymers? Can we tailor molecular systems towards specific charge-transfer processes? What are the time scales of the elementary steps of charge transfer in liquids and nanoparticles? Important new insights into each of these topics, obtained from state-of-the-art ultrafast spectroscopy and/or theoretical methods, are summarized in this review.

Molecular attochemistry in non-polar liquid environments: ultrafast charge migration dynamics through gold-thiolate and gold-selenolate linkages

Molecular attosecond science has already started contributing to our fundamental understanding of ultrafast purely electron dynamics in isolated molecules under vacuum. Extending attosecond science to the liquid phase is expected to offer new insight into the influence of a surrounding solvent environment on the attosecond electron dynamics in solvated molecules. A systematic theoretical investigation of the attochemistry of solvated molecules would help one design attosecond experiments under ambient conditions to explore the attochemistry in a liquid environment. With this goal in mind, for the first time, we have explored the attochemistry of molecules surrounded by different non-polar solvent environments. For this work, we have focused on the attosecond charge conduction through gold-thiolate and gold-selenolate linkages following the vertical ionization of the S/Se(CH₃)-CH₂-phenyl-X unit anchored to a gold dimeric cluster (Au₂), where X represents either a strong electron donating N(CH₃)₂ group or a strong electron withdrawing NO₂ group. To model solvation effects on the attochemistry of molecules containing gold-chalcogen linkages, we have used an implicit solvent model (Polarizable Continuum Model) under the density functional theory (DFT) formalism for non-polar solvents. We have found that the charge migration time scale in molecules becomes faster in the presence of the solvent environment as compared to that under vacuum. Charge oscillation does not damp quickly in molecules surrounded by the solvent environment as compared to that under vacuum. Furthermore, the direction of the charge migration may change in molecules when they are surrounded by the solvent environment as compared to that under vacuum. Thus, the present work has laid the foundation, for the first time, for thinking of the attochemistry into the realm of liquids.

Attosecond interferometry with self-amplified spontaneous emission of a free-electron laser

Light-phase-sensitive techniques, such as coherent multidimensional spectroscopy, are well-established in a broad spectral range, already spanning from radio-frequencies in nuclear magnetic resonance spectroscopy to visible and ultraviolet wavelengths in nonlinear optics with table-top lasers. In these cases, the ability to tailor the phases of electromagnetic waves with high precision is essential. Here we achieve phase control of extreme-ultraviolet pulses from a free-electron laser (FEL) on the attosecond timescale in a Michelson-type all-reflective interferometric autocorrelator. By varying the relative phase of the generated pulse replicas with sub-cycle precision we observe the field interference, that is, the light-wave oscillation with a period of 129 as. The successful transfer of a powerful optical method towards short-wavelength FEL science and technology paves the way towards utilization of advanced nonlinear methodologies even at partially coherent soft X-ray FEL sources that rely on self-amplified spontaneous emission.

Phase-sensitive measurements are important to gain insights of light-matter interactions and require phase-controlled pulses. Here the authors demonstrate the phase control and interferometric autocorrelation on a free electron laser using SASE pulse pair created with a split and delay unit.

Generating high-contrast, near single-cycle waveforms with third-order dispersion compensation

Femtosecond laser pulses lasting only a few optical periods hold the potential for probing and manipulating the electronic degrees of freedom within matter. However, the generation of high-contrast, few-cycle pulses in the high power limit still remains nontrivial. In this Letter, we present the application of ammonium dihydrogen phosphate (ADP) as an optical medium for compensating for the higher-order dispersion of a carrier-envelope stable few-cycle waveform centered at 735 nm. The ADP crystal is capable of removing the residual third-order dispersion present in the spectral phase of an input pulse, resulting in near-transform-limited 2.9 fs pulses lasting only 1.2 optical cycles in duration. By utilizing these high-contrast, few-cycle pulses for high-harmonic generation, we are able to produce nanojoule-scale, isolated attosecond pulses.

Core Ionization Initiates Subfemtosecond Charge Migration in the Valence Shell of Molecules

After the ionization of a valence electron, the created hole can migrate ultrafast from one end of the molecule to another. Because of the advent of attosecond pulse techniques, the measuring and understanding of charge migration has become a central topic in attosecond science. Here, we pose the hitherto unconsidered question whether ionizing a core electron will also lead to charge migration. It is found that the created hole in the core stays put, but in response to this hole interesting electron dynamics takes place which can lead to intense charge migration in the valence shell. This migration is typically faster than that after the ionization of a valence electron and transpires on a shorter time scale than the natural decay of the core hole by the Auger process, making the subject very challenging to attosecond science.

Observation of an Excitonic Quantum Coherence in CdSe Nanocrystals

Recent observations of excitonic coherences within photosynthetic complexes suggest that quantum coherences could enhance biological light harvesting efficiencies. Here, we employ optical pump-probe spectroscopy with few-femtosecond pulses to observe an excitonic quantum coherence in CdSe nanocrystals, a prototypical artificial light harvesting system. This coherence, which encodes the high-speed migration of charge over nanometer length scales, is also found to markedly alter the displacement amplitudes of phonons, signaling dynamics in the non-Born-Oppenheimer regime.