Attosecond Dynamics of Molecular Electronic Ring Currents

Inverse Optically-Induced Ring Currents in Ring-Shaped Molecules

Permanent electronic ring currents are supported within manifolds of ΓE degenerate excited electronic states as E± = Ex ± iEy excitations. In [ Phys. Rev. Res. 2021, 3, L042003] we showed the existence of inverse-current manifolds, where the direction of the electronic ring current in each degenerate state E± is opposite to the circular polarization of the generating light fields. This vibronic effect is caused by the exchange of orbital angular momentum between the electrons and the vibrational modes with the required symmetry. Here we consider the case of fixed nuclei and find that ring-shaped molecular systems possess inverse-current manifolds on a purely electronic-structure basis, i.e., without intervention of vibronic coupling. The effect is explained first on a tight-binding model with cyclic symmetry and then considering the ab initio electronic structure of benzene and sym-triazine. A framework for discriminating regular- and inverse-current ΓE manifolds in molecules using quantum chemistry calculations is provided.

Generation of the isolated highly elliptically polarized attosecond pulse using the polarization gating technique: TDDFT approach

This paper theoretically investigates the generation of isolated elliptically polarized attosecond pulses with a tunable ellipticity from the interaction of Cl₂ molecule and a polarization-gating laser pulse. A three-dimensional calculation based on the time-dependent density functional theory is done. Two different methods are proposed for generating elliptically polarized single attosecond pulses. The first method is based on applying a single-color polarization gating laser and controlling the orientation angle of the Cl₂ molecule with respect to the polarization direction of the laser at the gate window. An attosecond pulse with an ellipticity of 0.66 and a pulse duration of 275 as is achieved by tuning the molecule orientation angle to 40° in this method and superposing harmonics around the harmonic cutoff. The second method is based on irradiating an aligned Cl₂ molecule with a two-color polarization gating laser. The ellipticity of the attosecond pulses obtained by this method can be controlled by adjusting the intensity ratio of the two colors. Employing an optimized intensity ratio and superposing harmonics around the harmonic cutoff would lead to the generation of an isolated, highly elliptically polarized attosecond pulse with an ellipticity of 0.92 and a pulse duration of 648 as.

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.

Coherent ring-current migration of Mg-phthalocyanine probed by time-resolved X-ray circular dichroism

The coherent ring current of Mg-phthalocyanine created by a broad band UV-visible pump pulse shows variation with time, where the ring currents at the corner benzene rings, around the Mg cation and on the outer ring oscillate with different time periods and the current density migrates among these regions. The 7 pairs of E_u degenerate excited states populated upon photoexcitation, generate 21 distinct coherent ring currents. We further calculate the time-resolved X-ray circular dichroism (TRXCD) spectrum of the coherences contributing to the ring current obtained by an attosecond X-ray probe pulse resonant with the nitrogen K-edge. A frequency domain TRXCD signal obtained by a Fourier transform of the signal with respect to the pump-probe delay time clearly separates the currents induced by different state pairs.

The coherent ring current of Mg-phthalocyanine are created by a broad band UV-visible pump pulse and migrate into different regions within the molecule. This coherent ring current dynamics is probed by time-resolved X-ray circular dichroism.

Controlling the atomic-orbital-resolved photoionization for neon atoms by counter-rotating circularly polarized attosecond pulses

We theoretically investigate the atomic-orbital-resolved vortex-shaped photoelectron momentum distributions (PMDs) and ionization probabilities by solving the two-dimensional time-dependent Schrödinger equation (2D-TDSE) of neon in a pair of delayed counter-rotating circularly polarized attosecond pulses. We found that the number of spiral arms in vortex patterns is twice the number of absorbed photons when the initial state is the ψ_m=±1 state, which satisfy a change from c_2n+2 to c_2n (n is the number of absorbed photons) rotational symmetry of the vortices if the 2p state is replaced by 2p₊ or 2p_- states. For two- and three-photon ionization, the magnetic quantum number dependence of ionization probabilities is quite weak. Interestingly, single-photon ionization is preferred when the electron and laser field corotate and ionization probabilities of 2p_- is much larger than that of 2p₊ if the proper time delay and wavelength are used. The relative ratio of ionization probabilities between 2p_- and 2p₊ is insensitive to laser peak intensity, which can be controlled by changing the wavelength, time delay, relative phase and amplitude ratio of two attosecond pulses.

Signature of Molecular Orbital Symmetry in High-Order Harmonic Generation by Bichromatic Circularly Polarized Laser Pulses

Molecular orbital symmetry is shown to be an important factor in determining orders and helicities (polarizations) of high-order harmonic generation (HHG) by intense femtosecond counter-rotating bichromatic circularly polarized laser pulses. Numerical solutions of time-dependent Schrödinger equations (TDSE) for the one-electron molecular ions H₂⁺ and H₃²⁺ for different initial electronic states show that harmonic orders and helicities are dependent on orbital symmetries and of the net incident pulse electric field. The numerical results and properties of the harmonics are described by dynamical symmetry theory and time profile analysis of the high-order harmonics, thus confirming that orbital and laser pulse symmetry dependence are generic in HHG of molecules.

Laser-Induced Electron Symmetry Restoration in Oriented Molecules Made Simple

Electron symmetry determines many important properties of molecules, from selection rules for photoelectron spectroscopy to symmetry selection rules for chemical reactions. The original electron symmetry is broken if a laser pulse changes the initial state, typically the ground state g, to a superposition of g and an excited state e with different irreducible representations (IRREPs). Quantum dynamics simulations for two examples, the oriented benzene and LiCN molecules, show that the original electron symmetry can be restored by means of a reoptimized π-laser pulse which transfers the component in the excited state e to another state e', or to several others with the same IRREP as the ground state. This method lends itself to much easier experimental applications than all previous ones because it allows the healing of electron symmetry immediately, without any attosecond constraint on the timing of the second pulse.

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.

Monitoring aromatic ring-currents in Mg-porphyrin by time-resolved circular dichroism

Time-resolved circular dichroism signals (TRCD) in the X-ray regime can directly probe the magnitude and the direction of ring currents in molecules. The electronic ring currents in Mg-porphyrin, generated by a coherent superposition of electronic states induced by a circularly polarized UV pulse, are tracked by a time-delayed circularly polarized attosecond X-ray pulse. The signals are calculated using the minimal coupling Hamiltonian, which directly makes use of transition current densities. The TRCD signals obtained from the left and right circularly polarized light pump have opposite signs, revealing the direction of the ring current. Molecular aromaticity and its role in photochemical reactions such as ring opening or closure can be studied using this technique.

Attosecond all-optical control and visualization of quantum interference between degenerate magnetic states by circularly polarized pulses

Controlling coherence and interference of quantum states is one of the central goals in quantum science. Different from energetically discrete quantum states, however, it remains a demanding task to visualize coherent properties of degenerate states (e.g., magnetic sublevels). It becomes further inaccessible in the absence of an external perturbation (e.g., Zeeman effect). Here, we present a theoretical analysis of all-optical control of degenerate magnetic states in the molecular hydrogen ion, $ {\rm H}_2^ + $H2+, by using two time-delayed co- and counterrotating circularly polarized attosecond extreme-ultraviolet (XUV) pulses. We perform accurate simulations to examine this model by solving the three-dimensional time-dependent Schrödinger equation. A counterintuitive phenomenon of quantum interference between degenerate magnetic sublevels appears in the time-dependent electronic probability density, which is observable by using x-ray-induced transient angular and energy-resolved photoelectron spectra. This work provides an insight into quantum interference of electron dynamics inside molecules at the quantum degeneracy level.

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

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

Background-Free Measurement of Ring Currents by Symmetry-Breaking High-Harmonic Spectroscopy

We propose and explore an all-optical technique for ultrafast characterization of electronic ring currents in atoms and molecules, based on high-harmonic generation (HHG). In our approach, a medium is irradiated by an intense reflection-symmetric laser pulse that leads to HHG, where the polarization of the emitted harmonics is strictly linear if the medium is reflection invariant (e.g., randomly oriented atomic or molecular media). The presence of a ring current in the medium breaks this symmetry, causing the emission of elliptically polarized harmonics, where the harmonics' polarization directly maps the ring current, and the signal is background-free. Scanning the delay between the current excitation and the HHG driving pulse provides an attosecond time-resolved signal for the multielectron dynamics in the excited current (including electron-electron interactions). We analyze the responsible physical mechanism and derive the analytic dependence of the HHG emission on the ring current. The method is numerically demonstrated using quantum models for neon and benzene, as well as through ab initio calculations.

De- and Recoherence of Charge Migration in Ionized Iodoacetylene

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

Probing Attosecond Electron Coherence in Molecular Charge Migration by Ultrafast X-Ray Photoelectron Imaging

Electron coherence is a fundamental quantum phenomenon in today’s ultrafast physics and chemistry research. Based on attosecond pump–probe schemes, ultrafast X-ray photoelectron imaging of molecules was used to monitor the coherent electron dynamics which is created by an XUV pulse. We performed simulations on the molecular ion H 2 + by numerically solving time-dependent Schrödinger equations. It was found that the X-ray photoelectron angular and momentum distributions depend on the time delay between the XUV pump and soft X-ray probe pulses. Varying the polarization and helicity of the soft X-ray probe pulse gave rise to a modulation of the time-resolved photoelectron distributions. The present results provide a new approach for exploring ultrafast coherent electron dynamics and charge migration in reactions of molecules on the attosecond time scale.

Optimal and robust control of quantum state transfer by shaping the spectral phase of ultrafast laser pulses

Achieving fast and efficient quantum state transfer is a fundamental task in physics, chemistry and quantum information science. However, the successful implementation of the perfect quantum state transfer also requires robustness under practically inevitable perturbative defects. Here, we demonstrate how an optimal and robust quantum state transfer can be achieved by shaping the spectral phase of an ultrafast laser pulse in the framework of frequency domain quantum optimal control theory. Our numerical simulations of the single dibenzoterrylene molecule as well as in atomic rubidium show that optimal and robust quantum state transfer via spectral phase modulated laser pulses can be achieved by incorporating a filtering function of the frequency into the optimization algorithm, which in turn has potential applications for ultrafast robust control of photochemical reactions.

Ultrafast Charge Migration in XUV Photoexcited Phenylalanine: A First-Principles Study Based on Real-Time Nonequilibrium Green's Functions

The early-stage density oscillations of the electronic charge in molecules irradiated by an attosecond XUV pulse takes place on femto- or subfemtosecond time scales. This ultrafast charge migration process is a central topic in attoscience because it dictates the relaxation pathways of the molecular structure. A predictive quantum theory of ultrafast charge migration should incorporate the atomistic details of the molecule, electronic correlations, and the multitude of ionization channels activated by the broad-bandwidth XUV pulse. We propose a first-principles nonequilibrium Green's function method fulfilling all three requirements and apply it to a recent experiment on the photoexcited phenylalanine amino acid. Our results show that dynamical correlations are necessary for a quantitative overall agreement with the experimental data. In particular, we are able to capture the transient oscillations at frequencies 0.15 and 0.30 PHz in the hole density of the amine group as well as their suppression and the concomitant development of a new oscillation at frequency 0.25 PHz after ∼14 fs.

Quantum control of coherent π-electron ring currents in polycyclic aromatic hydrocarbons

We present results for quantum optimal control (QOC) of the coherent π electron ring currents in polycyclic aromatic hydrocarbons (PAHs). Since PAHs consist of a number of condensed benzene rings, in principle, there exist various coherent ring patterns. These include the ring current localized to a designated benzene ring, the perimeter ring current that flows along the edge of the PAH, and the middle ring current of PAHs having an odd number of benzene rings such as anthracene. In the present QOC treatment, the best target wavefunction for generation of the ring current through a designated path is determined by a Lagrange multiplier method. The target function is integrated into the ordinary QOC theory. To demonstrate the applicability of the QOC procedure, we took naphthalene and anthracene as the simplest examples of linear PAHs. The mechanisms of ring current generation were clarified by analyzing the temporal evolutions of the electronic excited states after coherent excitation by UV pulses or (UV+IR) pulses as well as those of electric fields of the optimal laser pulses. Time-dependent simulations of the perimeter ring current and middle ring current of anthracene, which are induced by analytical electric fields of UV pulsed lasers, were performed to reproduce the QOC results.

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.

Exploring coherent electron excitation and migration dynamics by electron diffraction with ultrashort X-ray pulses

Exploring ultrafast charge migration is of great importance in biological and chemical reactions.