Vibrational Motions in Ultrafast Electronic Relaxation of Pyrazine

Ultrafast internal conversion via a conical intersection is ubiquitous in highly efficient photochemical reactions. Internal conversion from the 1ππ* to the 1nπ* state of pyrazine is the paradigm for this phenomenon; however, the relaxation occurs in such a short time (<20 fs) that the nuclear motion is difficult to observe in real time. The present study precisely measures the vibrational coherence transferred from the 1ππ* state to the 1nπ* state using time-resolved photoelectron spectroscopy with an unprecedented time resolution of 13.3 fs and reveals the key nuclear motions that drive the internal conversion.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

Multi-state Energy Landscape for Photoreaction of Stilbene and Dimethyl-stilbene

We have recently developed the reaction space projector (ReSPer) method, which constructs a reduced-dimensionality reaction space uniquely determined from reference reaction paths for a polyatomic molecular system and projects classical trajectories into the same reaction space. In this paper, we extend ReSPer to the analysis of photoreaction dynamics and relaxation processes of stilbene and present the concept of a "multi-state energy landscape," incorporating the ground- and excited-state reaction subspaces. The multi-state energy landscape successfully explains the previously established photoreaction processes of cis-stilbene, such as the cis-trans photoisomerization and photocyclization. In addition, we discuss the difference in the excited-state reaction dynamics between stilbene and 1,1'-dimethyl stilbene based on a common reaction subspace determined from the framework part of reference structures with different number of atoms. This approach allows us to target any molecule with a common framework, greatly expanding the applicability of the ReSPer analysis. The multi-state energy landscape provides fruitful insight into photochemical reactions, exploring the excited- and ground-state potential energy surfaces, as well as comprehensive reaction processes with nonradiative transitions between adiabatic states, within the stage of a reduced-dimensionality reaction space.

X-ray transient absorption reveals the 1Au (nπ*) state of pyrazine in electronic relaxation

Electronic relaxation in organic chromophores often proceeds via states not directly accessible by photoexcitation. We report on the photoinduced dynamics of pyrazine that involves such states, excited by a 267 nm laser and probed with X-ray transient absorption spectroscopy in a table-top setup. In addition to the previously characterized ¹B_2u (ππ*) (S₂) and ¹B_3u (nπ*) (S₁) states, the participation of the optically dark ¹A_u (nπ*) state is assigned by a combination of experimental X-ray core-to-valence spectroscopy, electronic structure calculations, nonadiabatic dynamics simulations, and X-ray spectral computations. Despite ¹A_u (nπ*) and ¹B_3u (nπ*) states having similar energies at relaxed geometry, their X-ray absorption spectra differ largely in transition energy and oscillator strength. The ¹A_u (nπ*) state is populated in 200 ± 50 femtoseconds after electronic excitation and plays a key role in the relaxation of pyrazine to the ground state.

Identification of an ultrafast internal conversion pathway of pyrazine by time-resolved vacuum ultraviolet photoelectron spectrum simulations

The internal conversion from the optically bright S₂ (¹B_2u, ππ*) state to the dark S₁ (¹B_3u, nπ*) state in pyrazine is a standard benchmark for experimental and theoretical studies on ultrafast radiationless decay. Since 2008, a few theoretical groups have suggested significant contributions of other dark states S₃ (¹A_u, nπ*) and S₄ (¹B_2g, nπ*) to the decay of S₂. We have previously reported the results of nuclear wave packet simulations [Kanno et al., Phys. Chem. Chem. Phys. 17, 2012 (2015)] and photoelectron spectrum calculations [Mignolet et al., Chem. Phys. 515, 704 (2018)] that support the conventional two-state picture. In this article, the two different approaches, i.e., wave packet simulation and photoelectron spectrum calculation, are combined: We computed the time-resolved vacuum ultraviolet photoelectron spectrum and photoelectron angular distribution for the ionization of the wave packet transferred from S₂ to S₁. The present results reproduce almost all the characteristic features of the corresponding experimental time-resolved spectrum [Horio et al., J. Chem. Phys. 145, 044306 (2016)], such as a rapid change from a three-band to two-band structure. This further supports the existence and character of the widely accepted pathway (S₂ → S₁) of ultrafast internal conversion in pyrazine.

Spiers Memorial Lecture: Introduction to ultrafast spectroscopy and imaging of photochemical reactions

A brief overview is presented on ultrafast spectroscopy and imaging of photochemical reactions by highlighting several experimental studies reported in the last five years. A particular focus is placed on new experiments performed using high-order harmonic generation, X-ray free electron lasers, and relativistic electron beams. Exploration of fundamental chemical reaction dynamics using these advanced experimental methodologies is in an early stage, and exciting new research opportunities await in this rapidly expanding and advancing research field. At the same time, there is no experimental methodology that provides all aspects of the electronic and structural dynamics in a single experiment, and investigations using different methodologies with various perspectives need to be considered in a comprehensive manner.

An efficient approximate algorithm for nonadiabatic molecular dynamics

We propose a modification to the nonadiabatic surface hopping calculation method formulated in a paper by Yu et al. [Phys. Chem. Chem. Phys. 16, 25883 (2014)], which is a multidimensional extension of the Zhu-Nakamura theory with a practical diabatic gradient estimation algorithm. In our modification, their diabatic gradient estimation algorithm, which is based on a simple interpolation of the adiabatic potential energy surfaces, is replaced by an algorithm using the numerical derivatives of the adiabatic gradients. We then apply the algorithm to several models of nonadiabatic dynamics, both analytic and ab initio models, to numerically demonstrate that our method indeed widens the applicability and robustness of their method. We also discuss the validity and limitations of our new nonadiabatic surface hopping method while considering in mind potential applications to excited-state dynamics of biomolecules or unconventional nonadiabatic dynamics such as radiation decay processes in ultraintense X-ray fields.

Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method

The effect of a dissipative environment on the ultrafast nonadiabatic dynamics at conical intersections is analyzed for a two-state two-mode model chosen to represent the S₂(ππ*)–S₁(nπ*) conical intersection in pyrazine (the system) which is bilinearly coupled to infinitely many harmonic oscillators in thermal equilibrium (the bath). The system–bath coupling is modeled by the Drude spectral function. The equation of motion for the reduced density matrix of the system is solved numerically exactly with the hierarchy equation of motion method using graphics-processor-unit (GPU) technology. The simulations are valid for arbitrary strength of the system–bath coupling and arbitrary bath memory relaxation time. The present computational studies overcome the limitations of weak system–bath coupling and short memory relaxation time inherent in previous simulations based on multi-level Redfield theory [A. Kühl and W. Domcke, J. Chem. Phys. 2002, 116, 263]. Time evolutions of electronic state populations and time-dependent reduced probability densities of the coupling and tuning modes of the conical intersection have been obtained. It is found that even weak coupling to the bath effectively suppresses the irregular fluctuations of the electronic populations of the isolated two-mode conical intersection. While the population of the upper adiabatic electronic state (S₂) is very efficiently quenched by the system–bath coupling, the population of the diabatic ππ* electronic state exhibits long-lived oscillations driven by coherent motion of the tuning mode. Counterintuitively, the coupling to the bath can lead to an enhanced lifetime of the coherence of the tuning mode as a result of effective damping of the highly excited coupling mode, which reduces the strong mode–mode coupling inherent to the conical intersection. The present results extend previous studies of the dissipative dynamics at conical intersections to the nonperturbative regime of system–bath coupling. They pave the way for future first-principles simulations of femtosecond time-resolved four-wave-mixing spectra of chromophores in condensed phases which are nonperturbative in the system dynamics, the system–bath coupling as well as the field-matter coupling.

Simulation of femtosecond two-dimensional electronic spectra of conical intersections

We have simulated femtosecond two-dimensional (2D) electronic spectra for an excited-state conical intersection using the wave-function version of the equation-of-motion phase-matching approach. We show that 2D spectra at fixed values of the waiting time provide information on the structure of the vibronic eigenstates of the conical intersection, while the evolution of the spectra with the waiting time reveals predominantly ground-state wave-packet dynamics. The results show that 2D spectra of conical intersection systems differ significantly from those obtained for chromophores with well separated excited-state potential-energy surfaces. The spectral signatures which can be attributed to conical intersections are discussed.

Quantum dynamics of the photostability of pyrazine

We propose a new mechanism for the radiationless decay of photoexcited pyrazine to its ground electronic state involving a conical intersection between the dark A_u(nπ) state and the ground state.