Coherent electron hole dynamics near a conical intersection

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

Probing ultrafast excited-state dynamics using EUV-IR six-wave-mixing emission spectroscopy

Non-linear processes such as four-wave-mixing have become instrumental in attosecond EUV spectroscopy. Using EUV high harmonics in conjunction with collinear near-infrared and mid-infrared fields, we extended this approach to high-order-mixing between three colors. Specifically, we find that atomic resonances in neon exhibit a significant cross section for six-wave mixing. The MIR probe frequency tunability in our multicolor scheme is employed to access several optically dark resonances and probe the quantum beat of a coherent electronic wavepacket using background-free EUV emission as a diagnostic. This technique can be easily extended to other atomic and molecular systems, and opens the door to multi-dimensional non-linear spectroscopy.

A laboratory frame density matrix for ultrafast quantum molecular dynamics

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

Optical Cavity Manipulation and Nonlinear UV Molecular Spectroscopy of Conical Intersections in Pyrazine

Optical cavities provide a versatile platform for manipulating the excited-state dynamics of molecules via strong light-matter coupling. We employ optical absorption and two-multidimensional electronic spectroscopy simulations to investigate the effect of optical cavity coupling in the nonadiabatic dynamics of photoexcited pyrazine. We observe the emergence of a novel polaritonic conical intersection (PCI) between the electronic dark state and photonic surfaces as the cavity frequency is tuned. The PCI could significantly change the nonadiabatic dynamics of pyrazine by doubling the decay rate constant of the S₂ state population. Moreover, the absorption spectrum and excited-state dynamics could be systematically manipulated by tuning the strong light-matter interaction, e.g., the cavity frequency and cavity coupling strength. We propose that a tunable optical cavity-molecule system may provide promising approaches for manipulating the photophysical properties of molecules.

Conical Intersection Passages of Molecules Probed by X-ray Diffraction and Stimulated Raman Spectroscopy

Conical intersections (CoIns) play an important role in ultrafast relaxation channels. Their monitoring remains a formidable experimental challenge. We theoretically compare the probing of the S₂ → S₁ CoIn passage in 4-thiouracil by monitoring its vibronic coherences, using off-resonant X-ray-stimulated Raman spectroscopy (TRUECARS) and time-resolved X-ray diffraction (TRXD). The quantum nuclear wavepacket (WP) dynamics provides an accurate picture of the photoinduced dynamics. Upon photoexcitation, the WP oscillates among the Franck-Condon point, the S₂ minimum, and the CoIn with a 70 fs period. A vibronic coherence first emerges at 20 fs and can be observed until the S₂ state is fully depopulated. The distribution of the vibronic frequencies involved in the coherence is recorded by the TRUECARS spectrogram. The TRXD signal provides spatial images of electron densities associated with the CoIn. In combination, the two signals provide a complementary picture of the nonadiabatic passage, which helps in the study of the underlying photophysics in thiobases.

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.

Extreme ultraviolet-excited time-resolved luminescence spectroscopy using an ultrafast table-top high-harmonic generation source

We present a table-top extreme ultraviolet (XUV) beamline for measuring time- and frequency-resolved XUV-excited optical luminescence (XEOL) with additional femtosecond-resolution XUV transient absorption spectroscopy functionality. XUV pulses are generated via high-harmonic generation using a near-infrared pulse in a noble gas medium and focused to excite luminescence from a solid sample. The luminescence is collimated and guided into a streak camera where its spectral components are temporally resolved with picosecond temporal resolution. We time-resolve XUV-excited luminescence and compare the results to luminescence decays excited at longer wavelengths for three different materials: (i) sodium salicylate, an often used XUV scintillator; (ii) fluorescent labeling molecule 4-carbazole benzoic (CB) acid; and (iii) a zirconium metal oxo-cluster labeled with CB, which is a photoresist candidate for extreme-ultraviolet lithography. Our results establish time-resolved XEOL as a new technique to measure transient XUV-driven phenomena in solid-state samples and identify decay mechanisms of molecules following XUV and soft-x-ray excitation.

Superposition-state N2 + produced in the intermolecular charge transfer from low-energy Ar+ to N2

Molecular electronic or vibrational states can be superimposed temporarily in an extremely short laser pulse, and the superposition-state transients formed therein receive much attention, owing to the extensive interest in molecular fundamentals and the potential applications in quantum information processing. Using the crossed-beam ion velocity map imaging technique, we disentangle two distinctly different pathways leading to the forward-scattered N₂ ⁺ yields in the large impact-parameter charge transfer from low-energy Ar⁺ to N₂. Besides the ground-state (X²Σ_g ⁺) N₂ ⁺ produced in the energy-resonant charge transfer, a few slower N₂ ⁺ ions are proposed to be in the superpositions of the X²Σ_g ⁺-A²Π_u and A²Π_u-B²Σ_u ⁺ states on the basis of the accidental degeneracy or energetic closeness of the vibrational states around the X²Σ_g ⁺-A²Π_u and A²Π_u-B²Σ_u ⁺ crossings in the non-Franck-Condon region. This finding potentially shows a brand-new way to prepare the superposition-state molecular ion.

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.

Stimulated X-ray Resonant Raman Spectroscopy of Conical Intersections in Thiophenol

The conical intersection dynamics of thiophenol is studied by computing the stimulated X-ray resonant Raman spectroscopy signals. The hybrid probing field is constructed of a hard X-ray narrowband femtosecond pulse combined with an attosecond broadband X-ray pulse to provide optimal spectral and temporal resolutions for electronic coherences in the level crossing region. The signal carries phase information about the valence-core electronic coupling in the vicinity of conical intersections. Two conical intersections occurring during the course of the S-H dissociation dynamics can be distinguished by their valence-core transition frequencies computed at the complete active space self-consistent field level. The X-ray pulse is tuned such that the Raman transition at the first conical intersection between ¹πσ* and 1¹ππ* involves higher core levels, while the Raman transition at the second conical intersection between ¹πσ* and S₀ involves the lowest core level in the sulfur K-edge.

Stimulated X-ray Raman Imaging of Conical Intersections

The conical intersection dynamics of thiophenol is studied theoretically using the stimulated X-ray Raman imaging (SXRI) technique. SXRI employs a hard X-ray narrowband/broadband hybrid probe field and provides a real-time and real-space image of the passage through conical intersections. The signal, calculated using the minimal-coupling radiation/matter Hamiltonian, carries the phase information, and the real-space image of the transition charge density can be reconstructed by its Fourier transform. The two conical intersections (S₂/S₁ (1¹ππ*/¹πσ*) and S₁/S₀ (¹πσ*/S₀)) can be distinguished and identified by the diffraction patterns in the level crossing regimes.

Tunable high-order frequency mixing for XUV transient absorption and photoelectron spectroscopies

We generate tunable extreme ultraviolet emission through high-order frequency mixing between a strong near-infrared field and a weak shortwave-infrared pulse whose wavelength can be adjusted. In this two-color driving scheme, new harmonics appear in between the single-color harmonics at energies which are linear combinations of photons from the two pulses. We demonstrate the utility of tunable two-color harmonics by employing them for XUV transient absorption spectroscopy and time-resolved photoelectron spectroscopy. We show that the two-color harmonics can be used to address the dynamics associated with excited states in Helium and Oxygen which are inaccessible using single-color harmonics. Specifically, we show the ability to switch between excitation of 3p and 4p states in Helium, control of transitions to the light induced states, observe new four-wave-mixing emissions, and selectively address different principal and vibrational quantum numbers associated with Oxygen Rydberg states.

Disentangling conical intersection and coherent molecular dynamics in methyl bromide with attosecond transient absorption spectroscopy

Attosecond probing of core-level electronic transitions provides a sensitive tool for studying valence molecular dynamics with atomic, state, and charge specificity. In this report, we employ attosecond transient absorption spectroscopy to follow the valence dynamics of strong-field initiated processes in methyl bromide. By probing the 3d core-to-valence transition, we resolve the strong field excitation and ensuing fragmentation of the neutral σ* excited states of methyl bromide. The results provide a clear signature of the non-adiabatic passage of the excited state wavepacket through a conical intersection. We additionally observe competing, strong field initiated processes arising in both the ground state and ionized molecule corresponding to vibrational and spin-orbit motion, respectively. The demonstrated ability to resolve simultaneous dynamics with few-femtosecond resolution presents a clear path forward in the implementation of attosecond XUV spectroscopy as a general tool for probing competing and complex molecular phenomena with unmatched temporal resolution.

Probing Rydberg-Rydberg interactions in N2 by ultrafast EUV-NIR photoelectron spectroscopy

The ultrafast dynamics of molecular nitrogen (N₂) just below the ionization threshold has been investigated by time-resolved photoelectron spectroscopy using a single harmonic centered at hν = 15.38 eV. The evolution of the Rydberg wavepacket launched by the ultrashort EUV pulse is probed by a time-delayed femtosecond NIR laser pulse. The observed photoelectron spectra show two series of vibrational peaks to the ground X²Σg+ state and the first excited A²Πu state of N2+. Among these, two photoelectron peaks with the vibrational quantum numbers v_X+ = 4 and v_A+ = 1 exhibit clear anti-phase oscillation with a period of 300 fs, showing that two Rydberg states converging to the X²Σg+ and A²Πu ionic states interact with each other, thus causing periodic switching in the population of the ion core states.

Electron correlation driven non-adiabatic relaxation in molecules excited by an ultrashort extreme ultraviolet pulse

The many-body quantum nature of molecules determines their static and dynamic properties, but remains the main obstacle in their accurate description. Ultrashort extreme ultraviolet pulses offer a means to reveal molecular dynamics at ultrashort timescales. Here, we report the use of time-resolved electron-momentum imaging combined with extreme ultraviolet attosecond pulses to study highly excited organic molecules. We measure relaxation timescales that increase with the state energy. High-level quantum calculations show these dynamics are intrinsic to the time-dependent many-body molecular wavefunction, in which multi-electronic and non-Born−Oppenheimer effects are fully entangled. Hints of coherent vibronic dynamics, which persist despite the molecular complexity and high-energy excitation, are also observed. These results offer opportunities to understand the molecular dynamics of highly excited species involved in radiation damage and astrochemistry, and the role of quantum mechanical effects in these contexts.

The many-body quantum nature of molecules determines their static and dynamic properties, but remains the main obstacle in their accurate description. Here, the authors employ ultrafast spectroscopic methods to explore the dynamics of highly excited organic molecules, revealing many-body effects and hints of coherent vibronic dynamics which persist despite their molecular complexity.

Signatures of a Conical Intersection in Attosecond Transient Absorption Spectroscopy

We characterize attosecond transient absorption spectroscopy (ATAS) in molecules with coupled nuclear and electronic dynamics in the vicinity of a conical intersection between adiabatic potential energy surfaces. With respect to ATAS, the nonadiabatic vibronic coupling strength can be divided into weak, intermediate, and strong, and the characteristics of spectra belonging to each of these domains are discussed. The results can guide the analysis of ATAS experiments in molecules with conical intersections.

Few-femtosecond passage of conical intersections in the benzene cation

Observing the crucial first few femtoseconds of photochemical reactions requires tools typically not available in the femtochemistry toolkit. Such dynamics are now within reach with the instruments provided by attosecond science. Here, we apply experimental and theoretical methods to assess the ultrafast nonadiabatic vibronic processes in a prototypical complex system-the excited benzene cation. We use few-femtosecond duration extreme ultraviolet and visible/near-infrared laser pulses to prepare and probe excited cationic states and observe two relaxation timescales of 11 ± 3 fs and 110 ± 20 fs. These are interpreted in terms of population transfer via two sequential conical intersections. The experimental results are quantitatively compared with state-of-the-art multi-configuration time-dependent Hartree calculations showing convincing agreement in the timescales. By characterising one of the fastest internal conversion processes studied to date, we enter an extreme regime of ultrafast molecular dynamics, paving the way to tracking and controlling purely electronic dynamics in complex molecules.

Strong-field-induced wave packet dynamics in carbon dioxide molecule

Temporal evolution of electronic and nuclear wave packets created in strong-field excitation of the carbon dioxide molecule is studied employing momentum-resolved ion spectroscopy and channel-selective Fourier analysis. Combining the data obtained with two different pump-probe set-ups, we observed signatures of vibrational dynamics in both, ionic and neutral states of the molecule. We consider far-off-resonance two-photon Raman scattering to be the most likely mechanism of vibrational excitation in the electronic ground state of the neutral CO₂. Using the measured phase relation between the time-dependent yields of different fragmentation channels, which is consistent with the proposed mechanism, we suggest an intuitive picture of the underlying vibrational dynamics. For ionic states, we found signatures of both, electronic and vibrational excitations, which involve the ground and the first excited electronic states, depending on the particular final state of the fragmentation. While our results for ionic states are consistent with the recent observations by Erattupuzha et al. [J. Chem. Phys.144, 024306 (2016)], the neutral state contribution was not observed there, which we attribute to a larger bandwidth of the 8 fs pulses we used for this experiment. In a complementary measurement employing longer, 35 fs pulses in a 30 ps delay range, we study the influence of rotational excitation on our observables, and demonstrate how the coherent electronic wave packet created in the ground electronic state of the ion completely decays within 10 ps due to the coupling to rotational motion.

Probing the Interstate Coupling near a Conical Intersection by Optical Spectroscopy

Conical intersections are points where adiabatic potential energy surfaces cross. The interstate coupling between the potential energy surfaces plays a crucial role in many processes associated with conical intersections. Still no method exists to measure this coupling driving the chemical reactions between the potential energy surfaces involved. In this Letter, using a generic model for photoisomerization, we propose a novel experimental approach to estimate the coupling that mixes the electronic states near a conical intersection. The approach is based on analyzing the vibrational wavepacket of the reactant in the adiabatic ground and excited electronic states. The nuclear wavepacket dynamics are extracted from linear absorption and two-dimensional electronic spectroscopy. Comparing the frequencies of the coupling mode in the adiabatic ground and excited states from models with and without coupling between the potential energy surfaces suggests an experimental tool to determine the interstate coupling.

Monitoring Nonadiabatic Electron-Nuclear Dynamics in Molecules by Attosecond Streaking of Photoelectrons

Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences. We demonstrate how streaked photoelectrons offer a novel tool for monitoring nonadiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can provide high time resolution direct signatures of electronic coherences, which affect many primary photochemical and biological events.

Dynamics from noisy data with extreme timing uncertainty

Imperfect knowledge of the times at which 'snapshots' of a system are recorded degrades our ability to recover dynamical information, and can scramble the sequence of events. In X-ray free-electron lasers, for example, the uncertainty--the so-called timing jitter--between the arrival of an optical trigger ('pump') pulse and a probing X-ray pulse can exceed the length of the X-ray pulse by up to two orders of magnitude, marring the otherwise precise time-resolution capabilities of this class of instruments. The widespread notion that little dynamical information is available on timescales shorter than the timing uncertainty has led to various hardware schemes to reduce timing uncertainty. These schemes are expensive, tend to be specific to one experimental approach and cannot be used when the record was created under ill-defined or uncontrolled conditions such as during geological events. Here we present a data-analytical approach, based on singular-value decomposition and nonlinear Laplacian spectral analysis, that can recover the history and dynamics of a system from a dense collection of noisy snapshots spanning a sufficiently large multiple of the timing uncertainty. The power of the algorithm is demonstrated by extracting the underlying dynamics on the few-femtosecond timescale from noisy experimental X-ray free-electron laser data recorded with 300-femtosecond timing uncertainty. Using a noisy dataset from a pump-probe experiment on the Coulomb explosion of nitrogen molecules, our analysis reveals vibrational wave-packets consisting of components with periods as short as 15 femtoseconds, as well as more rapid changes, which have yet to be fully explored. Our approach can potentially be applied whenever dynamical or historical information is tainted by timing uncertainty.

Quantum Mechanical Wave Packet Dynamics at a Conical Intersection with Strong Vibrational Dissipation

We derive a reduced model for the nonadiabatic quantum dynamics of an electronic wave packet moving through a conical intersection in the presence of strong vibrational damping. Starting from the dissipative two-state two-model model, we transform the tuning and the coupling mode to the bath. The resulting quantum two-state model with two highly structured environments is solved numerically exactly in the regime of strong vibrational damping. We find negative cross peaks in the ultrafast optical 2D spectra as clear signatures of the conical intersection. They arise from secondary excitations of the wave packet after having passed through the photophysical energy funnel. This feature is in agreement with recent transient absorption measurements of rhodopsin.

Catching Conical Intersections in the Act: Monitoring Transient Electronic Coherences by Attosecond Stimulated X-Ray Raman Signals

Conical intersections (CIs) dominate the pathways and outcomes of virtually all photophysical and photochemical molecular processes. Despite extensive experimental and theoretical effort, CIs have not been directly observed yet and the experimental evidence is being inferred from fast reaction rates and some vibrational signatures. We show that short x-ray (rather than optical) pulses can directly detect the passage through a CI with the adequate temporal and spectral sensitivity. The technique is based on a coherent Raman process that employs a composite femtosecond or attosecond x-ray pulse to detect the electronic coherences (rather than populations) that are generated as the system passes through the CI.

Ultrafast Charge Transfer of a Valence Double Hole in Glycine Driven Exclusively by Nuclear Motion

We explore theoretically the ultrafast transfer of a double electron hole between the functional groups of glycine after K-shell ionization and subsequent Auger decay. Although a large energy gap of about 15 eV initially exists between the two electronic states involved and coherent electronic dynamics play no role in the hole transfer, we find that the double hole is transferred within 3 to 4 fs between both functional ends of the glycine molecule driven solely by specific nuclear displacements and non-Born-Oppenheimer effects. The nuclear displacements along specific vibrational modes are of the order of 15% of a typical chemical bond between carbon, oxygen, and nitrogen atoms and about 30% for bonds involving hydrogen atoms. The time required for the hole transfer corresponds to less than half a vibrational period of the involved nuclear modes. This finding challenges the common wisdom that nuclear dynamics of the molecular skeleton are unimportant for charge transfer processes at the few-femtosecond time scale and shows that they can even play a prominent role. It also indicates that in x-ray imaging experiments, in which ionization is unavoidable, valence electron redistribution caused by nuclear dynamics might be much faster than previously anticipated. Thus, non-Born-Oppenheimer effects may affect the apparent electron densities extracted from such measurements.

Attosecond Hole Migration in Benzene Molecules Surviving Nuclear Motion

Hole migration is a fascinating process driven by electron correlation, in which purely electronic dynamics occur on a very short time scale in complex ionized molecules, prior to the onset of nuclear motion. However, it is expected that due to coupling to the nuclear dynamics, these oscillations will be rapidly damped and smeared out, which makes experimental observation of the hole migration process rather difficult. In this Letter, we demonstrate that the instantaneous ionization of benzene molecules initiates an ultrafast hole migration characterized by a periodic breathing of the hole density between the carbon ring and surrounding hydrogen atoms on a subfemtosecond time scale. We show that these oscillations survive the dephasing introduced by the nuclear motion for a long enough time to allow their observation. We argue that this offers an ideal benchmark for studying the influence of hole migration on molecular reactivity.

A comprehensive spectroscopic investigation of α-(2-naphthyl)-N-methylnitrone: a computational study on photochemical nitrone–oxaziridine conversion and thermal E–Z isomerization processes

CASSCF and 2-layer hybrid ONIOM-based computational studies on α-(2-naphthyl)-N-methylnitrone have proposed its photochemical oxaziridine formation and thermal E–Z isomerization mechanisms.