Time-Resolved Photoelectron Spectroscopy of Conical Intersections with Attosecond Pulse Trains

Conical Intersections at Interfaces Revealed by Phase-Cycling Interface-Specific Two-Dimensional Electronic Spectroscopy (i2D-ES)

Conical intersections (CIs) hold significant stake in manipulating and controlling photochemical reaction pathways of molecules at interfaces and surfaces by affecting molecular dynamics therein. Currently, there is no tool for characterizing CIs at interfaces and surfaces. To this end, we have developed phase-cycling interface-specific two-dimensional electronic spectroscopy (i2D-ES) and combined it with advanced computational modeling to explore nonadiabatic CI dynamics of molecules at the air/water interface. Specifically, we integrated the phase locked pump pulse pair with an interface-specific electronic probe to obtain the two-dimensional interface-specific responses. We demonstrate that the nonadiabatic transitions of an interface-active azo dye molecule that occur through the CIs at the interface have different kinetic pathways from those in the bulk water. Upon photoexcitation, two CIs are present: one from an intersection of an optically active S2 state with a dark S1 state and the other from the intersection of the progressed S1 with the ground state S0. We find that the molecular conformations in the ground state are different for interfacial molecules. The interfacial molecules are intimately correlated with the locally populated excited state S2 being farther away from the CI region. This leads to slower nonadiabatic dynamics at the interface than in bulk water. Moreover, we show that the nonadiabatic transition from the S1 dark state to the ground state is significantly longer at the interface than that in the bulk, which is likely due to the orientationally restricted configuration of the excited state at the interface. Our findings suggest that orientational configurations of molecules manipulate reaction pathways at interfaces and surfaces.

Evidence of Excited-State Vibrational Mode Governing the Photorelaxation of a Charge-Transfer Complex

Modern, nonlinear, time-resolved spectroscopic techniques have opened new doors for investigating the intriguing but complex world of photoinduced ultrafast out-of-equilibrium phenomena and charge dynamics. The interaction between light and matter introduces an additional dimension, where the complex interplay between electronic and vibrational dynamics needs the most advanced theoretical-computational protocols to be fully understood on the molecular scale. In this study, we showcase the capabilities of ab initio molecular dynamics simulation integrated with a multiresolution wavelet protocol to carefully investigate the excited-state relaxation dynamics in a noncovalent complex involving tetramethylbenzene (TMB) and tetracyanoquinodimethane (TCNQ) undergoing charge transfer (CT) upon photoexcitation. Our protocol provides an accurate description that facilitates a direct comparison between transient vibrational analysis and time-resolved spectroscopic signals. This molecular level perspective enhances our understanding of photorelaxation processes confined in the adiabatic regime and offers an improved interpretation of vibrational spectra. Furthermore, it enables the quantification of anharmonic vibrational couplings between high- and low-frequency modes, specifically the TCNQ "rocking" and "bending" modes. Additionally, it identifies the primary vibrational mode that governs the adiabaticity between the ground state and the CT state. This comprehensive understanding of photorelaxation processes holds significant importance in the rational design and precise control of more efficient photovoltaic and sensor devices.

Coherent x-ray spontaneous emission spectroscopy of conical intersections

Conical intersections are known to play a vital role in many photochemical processes. The breakdown of the Born-Oppenheimer approximation in the vicinity of a conical intersection causes exciting phenomena, such as the ultrafast radiationless decay of excited states. The passage of a molecule through a conical intersection creates a coherent superposition of electronic states via nonadiabatic couplings. Detecting this coherent superposition may serve as a direct probe of the conical intersection. In this paper, we theoretically demonstrate the use of coherent spontaneous emission in samples with long-range order for probing the occurrence of a conical intersection in a molecule. Our simulations show that the spectrum contains clear signatures of the created coherent superposition of electronic states. We investigate the bandwidth requirements for the x-ray probes, which influence the observation of coherent superposition generated by the conical intersection.

Raman Spectroscopy of Conical Intersections Using Entangled Photons

Ultrafast Raman spectroscopy with attosecond pulses in the extreme ultraviolet and X-ray regime has been proposed theoretically for tracking the non-adiabatic dynamics of molecules in great detail. The large bandwidth of these pulses, which span several electronvolts within a couple of femtoseconds, provides a unique tool for tracking non-adiabatic phenomena. However, spectroscopy with classical light is limited by the time-bandwidth product of the probe laser pulse. In this work, we theoretically investigate an ultrafast Raman spectroscopy scheme that utilizes pairs of entangled photons. Our model simulations demonstrate that the dynamics in the vicinity of a conical intersection can be resolved with unprecedented resolution in the time and frequency domain.

Ab initio simulation of peak evolutions and beating maps for electronic two-dimensional signals of a polyatomic chromophore

By employing the doorway-window (DW) on-the-fly simulation protocol, we performed ab initio simulations of peak evolutions and beating maps of electronic two-dimensional (2D) spectra of a polyatomic molecule in the gas phase. As the system under study, we chose pyrazine, which is a paradigmatic example of photodynamics dominated by conical intersections (CIs). From the technical perspective, we demonstrate that the DW protocol is a numerically efficient methodology suitable for simulations of 2D spectra for a wide range of excitation/detection frequencies and population times. From the information content perspective, we show that peak evolutions and beating maps not only reveal timescales of transitions through CIs but also pinpoint the most relevant coupling and tuning modes active at these CIs.

Ultrafast X-Ray Probes of Elementary Molecular Events

Elementary events that determine photochemical outcomes and molecular functionalities happen on the femtosecond and subfemtosecond timescales. Among the most ubiquitous events are the nonadiabatic dynamics taking place at conical intersections. These facilitate ultrafast, nonradiative transitions between electronic states in molecules that can outcompete slower relaxation mechanisms such as fluorescence. The rise of ultrafast X-ray sources, which provide intense light pulses with ever-shorter durations and larger observation bandwidths, has fundamentally revolutionized our spectroscopic capabilities to detect conical intersections. Recent theoretical studies have demonstrated an entirely new signature emerging once a molecule traverses a conical intersection, giving detailed insights into the coupled nuclear and electronic motions that underlie, facilitate, and ultimately determine the ultrafast molecular dynamics. Following a summary of current sources and experiments, we survey these techniques and provide a unified overview of their capabilities. We discuss their potential to dramatically increase our understanding of ultrafast photochemistry.

Fluorescence in quantum dynamics: Accurate spectra require post-mean-field approaches

Real time modeling of fluorescence with vibronic resolution entails the representation of the light-matter interaction coupled to a quantum-mechanical description of the phonons and is therefore a challenging problem. In this work, taking advantage of the difference in timescales characterizing internal conversion and radiative relaxation-which allows us to decouple these two phenomena by sequentially modeling one after the other-we simulate the electron dynamics of fluorescence through a master equation derived from the Redfield formalism. Moreover, we explore the use of a recent semiclassical dissipative equation of motion [C. M. Bustamante et al., Phys. Rev. Lett. 126, 087401 (2021)], termed coherent electron electric-field dynamics (CEED), to describe the radiative stage. By comparing the results with those from the full quantum-electrodynamics treatment, we find that the semiclassical model does not reproduce the right amplitudes in the emission spectra when the radiative process involves the de-excitation to a manifold of closely lying states. We argue that this flaw is inherent to any mean-field approach and is the case with CEED. This effect is critical for the study of light-matter interaction, and this work is, to our knowledge, the first one to report this problem. We note that CEED reproduces the correct frequencies in agreement with quantum electrodynamics. This is a major asset of the semiclassical model, since the emission peak positions will be predicted correctly without any prior assumption about the nature of the molecular Hamiltonian. This is not so for the quantum electrodynamics approach, where access to the spectral information relies on knowledge of the Hamiltonian eigenvalues.

Time-resolved X-ray and XUV based spectroscopic methods for nonadiabatic processes in photochemistry

The photochemistry of numerous molecular systems is influenced by conical intersections (CIs). These omnipresent nonadiabatic phenomena provide ultra-fast radiationless relaxation channels by creating degeneracies between electronic states and decide over the final photoproducts. In their presence, the Born-Oppenheimer approximation breaks down, and the timescales of the electron and nuclear dynamics become comparable. Due to the ultra-fast dynamics and the complex interplay between nuclear and electronic degrees of freedom, the direct experimental observation of nonadiabatic processes close to CIs remains challenging. In this article, we give a theoretical perspective on novel spectroscopic techniques capable of observing clear signatures of CIs. We discuss methods that are based on ultra-short laser pulses in the extreme ultraviolet and X-ray regime, as their spectral and temporal resolution allow for resolving the ultra-fast dynamics near CIs.

Probing nonadiabatic dynamics with attosecond pulse trains and soft x-ray Raman spectroscopy

Linear off-resonant x-ray Raman techniques are capable of detecting the ultrafast electronic coherences generated when a photoexcited wave packet passes through a conical intersection. A hybrid femtosecond or attosecond probe pulse is employed to excite the system and stimulate the emission of the signal photon, where both fields are components of a hybrid pulse scheme. In this paper, we investigate how attosecond pulse trains, as provided by high-harmonic generation processes, perform as probe pulses in the framework of this spectroscopic technique, instead of single Gaussian pulses. We explore different combination schemes for the probe pulse as well as the impact of parameters of the pulse trains on the signals. Furthermore, we show how Raman selection rules and symmetry consideration affect the spectroscopic signal, and we discuss the importance of vibrational contributions to the overall signal. We use two different model systems, representing molecules of different symmetries, and quantum dynamics simulations to study the difference in the spectra. The results suggest that such pulse trains are well suited to capture the key features associated with the electronic coherence.

A localized view on molecular dissociation via electron-ion partial covariance

Inner-shell photoelectron spectroscopy provides an element-specific probe of molecular structure, as core-electron binding energies are sensitive to the chemical environment. Short-wavelength femtosecond light sources, such as Free-Electron Lasers (FELs), even enable time-resolved site-specific investigations of molecular photochemistry. Here, we study the ultraviolet photodissociation of the prototypical chiral molecule 1-iodo-2-methylbutane, probed by extreme-ultraviolet (XUV) pulses from the Free-electron LASer in Hamburg (FLASH) through the ultrafast evolution of the iodine 4d binding energy. Methodologically, we employ electron-ion partial covariance imaging as a technique to isolate otherwise elusive features in a two-dimensional photoelectron spectrum arising from different photofragmentation pathways. The experimental and theoretical results for the time-resolved electron spectra of the 4d_3/2 and 4d_5/2 atomic and molecular levels that are disentangled by this method provide a key step towards studying structural and chemical changes from a specific spectator site.

Time-resolved photoelectron spectroscopy: the continuing evolution of a mature technique

Time-resolved photoelectron spectroscopy (TRPES) has become one of the most widespread techniques for probing nonadiabatic dynamics in the excited electronic states of molecules. Furthermore, the complementary development of ab initio approaches for the simulation of TRPES signals has enabled the interpretation of these transient spectra in terms of underlying coupled electronic-nuclear dynamics. In this perspective, we discuss the current state-of-the-art approaches, including efforts to push femtosecond pulses into vacuum ultraviolet and soft X-ray regimes as well as the utilization of novel polarizations to use time-resolved optical activity as a probe of nonadiabatic dynamics. We close this perspective with a forward-looking prospectus on the new areas of application for this technique.

Electronic coherences in nonadiabatic molecular photophysics revealed by time-resolved photoelectron spectroscopy

Time-resolved photoelectron spectroscopy (TRPES) is a promising technique for the study of ultrafast molecular processes, such as the nonadiabatic dynamics taking place at conical intersections. Directly accessing the evolution of the coherences generated at the conical intersection should provide most valuable dynamical information. However, the signals are dominated by background contributions due to state populations, and most theoretical treatments completely neglect the role of the coherences. Here we show that distinguishable signatures of molecular coherences appear in TRPES. These can be recorded using currently available ultrashort pulses and unambiguously extracted at the postprocessing stage. The technique thus provides direct access to nonadiabatic coherence dynamics.