The role of the low-lying dark nπ* states in the photophysics of pyrazine: a quantum dynamics study

A size-consistent multi-state mapping approach to surface hopping

We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.

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.

Time-Dependent Resonant Inelastic X-ray Scattering of Pyrazine at the Nitrogen K-Edge: A Quantum Dynamics Approach

We calculate resonant inelastic X-ray scattering spectra of pyrazine at the nitrogen K-edge in the time domain including wavepacket dynamics in both the valence and core-excited state manifolds. Upon resonant excitation, we observe ultrafast non-adiabatic population transfer between core-excited states within the core-hole lifetime, leading to molecular symmetry distortions. Importantly, our time-domain approach inherently contains the ability to manipulate the dynamics of this process by detuning the excitation energy, which effectively shortens the scattering duration. We also explore the impact of pulsed incident X-ray radiation, which provides a foundation for state-of-the-art time-resolved experiments with coherent pulsed light sources.

Artificial-Intelligence-Enhanced On-the-Fly Simulation of Nonlinear Time-Resolved Spectra

Time-resolved spectroscopy is an important tool for unraveling the minute details of structural changes in molecules of biological and technological significance. The nonlinear femtosecond signals detected for such systems must be interpreted, but it is a challenging task for which theoretical simulations are often indispensable. Accurate simulations of transient absorption or two-dimensional electronic spectra are, however, computationally very expensive, prohibiting the wider adoption of existing first-principles methods. Here, we report an artificial-intelligence-enhanced protocol to drastically reduce the computational cost of simulating nonlinear time-resolved electronic spectra, which makes such simulations affordable for polyatomic molecules of increasing size. The protocol is based on the doorway-window approach for the on-the-fly surface-hopping simulations. We show its applicability for the prototypical molecule of pyrazine for which it produces spectra with high precision with respect to ab initio reference while cutting the computational cost by at least 95% compared to pure first-principles simulations.

Tuning UV Pump X-ray Probe Spectroscopy on the Nitrogen K Edge Reveals the Radiationless Relaxation of Pyrazine: Ab Initio Simulations Using the Quasiclassical Doorway-Window Approximation

Transient absorption UV pump X-ray probe spectroscopy has been established as a versatile technique for the exploration of ultrafast photoinduced dynamics in valence-excited states. In this work, an ab initio theoretical framework for the simulation of time-resolved UV pump X-ray probe spectra is presented. The method is based on the description of the radiation-matter interaction in the classical doorway-window approximation and a surface-hopping algorithm for the nonadiabatic nuclear excited-state dynamics. Using the second-order algebraic-diagrammatic construction scheme for excited states, UV pump X-ray probe signals were simulated for the carbon and nitrogen K edges of pyrazine, assuming a duration of 5 fs of the UV pump and X-ray probe pulses. It is predicted that spectra measured at the nitrogen K edge carry much richer information about the ultrafast nonadiabatic dynamics in the valence-excited states of pyrazine than those measured at the carbon K edge.

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.

Ab Initio Quasiclassical Simulation of Femtosecond Time-Resolved Two-Dimensional Electronic Spectra of Pyrazine

Two-dimensional (2D) electronic spectroscopy is a powerful nonlinear technique which provides spectroscopic information on two frequency axes as well as dynamical information as a function of the so-called waiting time. Herein, an ab initio theoretical framework for the simulation of electronic 2D spectra has been developed. The method is based on the classical approximation to the doorway-window representation of three-pulse photon-echo signals and the description of nuclear motion by classical trajectories. Nonadiabatic effects are taken into account by a trajectory surface-hopping algorithm. 2D electronic spectra were simulated with ab initio on-the-fly trajectory calculations using the ADC(2) electronic-structure method for the pyrazine molecule, which is a benchmark system for ultrafast radiationless decay through conical intersections. It is demonstrated that 2D spectroscopy with subfemtosecond UV pulses can provide unprecedented detailed information on the ultrafast photodynamics of polyatomic molecules.

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.

Combined Surface-Hopping, Dyson Orbital, and B-Spline Approach for the Computation of Time-Resolved Photoelectron Spectroscopy Signals: The Internal Conversion in Pyrazine

A computational protocol for simulating time-resolved photoelectron signals of medium-sized molecules is presented. The procedure is based on a trajectory surface-hopping description of the excited-state dynamics and a combined Dyson orbital and multicenter B-spline approach for the computation of cross sections and asymmetry parameters. The accuracy of the procedure has been illustrated for the case of ultrafast internal conversion of gas-phase pyrazine excited to the ¹B_2u(ππ*) state. The simulated spectra and the asymmetry map are compared to the experimental data, and a very good agreement was obtained without applying any energy-dependent rescaling or broadening. An interesting side result of this work is the finding that the signature of the ¹A_u(nπ*) state is indistinguishable from that of the ¹B_3u(nπ*) state in the time-resolved photoelectron spectrum. By locating four symmetrically equivalent minima on the lowest-excited (S₁) adiabatic potential energy surface of pyrazine, we revealed the strong vibronic coupling of the ¹A_u(nπ*) and ¹B_3u(nπ*) states near the S₁ ← S₀ band origin.

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.

Ab Initio Surface-Hopping Simulation of Femtosecond Transient-Absorption Pump-Probe Signals of Nonadiabatic Excited-State Dynamics Using the Doorway-Window Representation

An ab initio theoretical framework for the simulation of femtosecond time-resolved transient absorption (TA) pump-probe (PP) spectra with quasi-classical trajectories is presented. The simulations are based on the classical approximation to the doorway-window (DW) representation of third-order four-wave-mixing signals. The DW formula accounts for the finite duration and spectral shape of the pump and probe pulses. In the classical DW formalism, classical trajectories are stochastically sampled from a positive definite doorway distribution, and the signals are evaluated by averaging over a positive definite window distribution. Nonadiabatic excited-state dynamics is described by a stochastic surface-hopping algorithm. The method has been implemented for the pyrazine molecule with the second-order algebraic-diagrammatic construction (ADC(2)) ab initio electronic-structure method. The methodology is illustrated by ab initio simulations of the ground-state bleach, stimulated emission, and excited-state absorption contributions to the TA PP spectrum of gas-phase pyrazine.

Nonadiabatic Absorption Spectra and Ultrafast Dynamics of DNA and RNA Photoexcited Nucleobases

We have recently proposed a protocol for Quantum Dynamics (QD) calculations, which is based on a parameterisation of Linear Vibronic Coupling (LVC) Hamiltonians with Time Dependent (TD) Density Functional Theory (TD-DFT), and exploits the latest developments in multiconfigurational TD-Hartree methods for an effective wave packet propagation. In this contribution we explore the potentialities of this approach to compute nonadiabatic vibronic spectra and ultrafast dynamics, by applying it to the five nucleobases present in DNA and RNA. For all of them we computed the absorption spectra and the dynamics of ultrafast internal conversion (100 fs timescale), fully coupling the first 2-3 bright states and all the close by dark states, for a total of 6-9 states, and including all the normal coordinates. We adopted two different functionals, CAM-B3LYP and PBE0, and tested the effect of the basis set. Computed spectra are in good agreement with the available experimental data, remarkably improving over pure electronic computations, but also with respect to vibronic spectra obtained neglecting inter-state couplings. Our QD simulations indicate an effective population transfer from the lowest energy bright excited states to the close-lying dark excited states for uracil, thymine and adenine. Dynamics from higher-energy states show an ultrafast depopulation toward the more stable ones. The proposed protocol is sufficiently general and automatic to promise to become useful for widespread applications.

Parameterization of a linear vibronic coupling model with multiconfigurational electronic structure methods to study the quantum dynamics of photoexcited pyrene

With this work, we present a protocol for the parameterization of a Linear Vibronic Coupling (LVC) Hamiltonian for quantum dynamics using highly accurate multiconfigurational electronic structure methods such as RASPT2/RASSCF, combined with a maximum-overlap diabatization technique. Our approach is fully portable and can be applied to many medium-size rigid molecules whose excited state dynamics requires a quantum description. We present our model and discuss the details of the electronic structure calculations needed for the parameterization, analyzing critical situations that could arise in the case of strongly interacting excited states. The protocol was applied to the simulation of the excited state dynamics of the pyrene molecule, starting from either the first or the second bright state (S₂ or S₅). The LVC model was benchmarked against state-of-the-art quantum mechanical calculations with optimizations and energy scans and turned out to be very accurate. The dynamics simulations, performed including all active normal coordinates with the multilayer multiconfigurational time-dependent Hartree method, show good agreement with the available experimental data, endorsing prediction of the excited state mechanism, especially for S₅, whose ultrafast deactivation mechanism was not yet clearly understood.

Efficient simulation of time- and frequency-resolved four-wave-mixing signals with a multiconfigurational Ehrenfest approach

We have extended the multiconfigurational Ehrenfest approach to the simulation of four-wave-mixing signals of systems involving multiple electronic and vibrational degrees of freedom. As an illustration, we calculate signals of three widely used spectroscopic techniques, time- and frequency-resolved fluorescence spectroscopy, transient absorption spectroscopy, and two-dimensional (2D) electronic spectroscopy, for a two-electronic-state, twenty-four vibrational-mode conical intersection model. It has been shown that all these three spectroscopic signals characterize fast population transfer from the higher excited electronic state to the lower excited electronic state. While the time- and frequency-resolved spectrum maps the wave packet propagation exclusively on the electronically excited states, the transient absorption and 2D electronic spectra reflect the wave packet dynamics on both electronically excited states and the electronic ground state. Combining trajectory-guided Gaussian basis functions and the nonlinear response function formalism, the present approach provides a promising general technique for the applications of various Gaussian basis methods to the calculations of four-wave-mixing spectra of polyatomic molecules.

PySurf: A Framework for Database Accelerated Direct Dynamics

The greatest restriction to the theoretical study of the dynamics of photoinduced processes is computationally expensive electronic structure calculations. Machine learning algorithms have the potential to reduce the number of these computations significantly. Here, PySurf is introduced as an innovative code framework, which is specifically designed for rapid prototyping and development tasks for data science applications in computational chemistry. It comes with powerful Plugin and Workflow engines, which allows intuitive customization for individual tasks. Data is automatically stored through the database framework, which enables additional interpolation of properties in previously evaluated regions of the conformational space. To illustrate the potential of the framework, a code for nonadiabatic surface hopping simulations based on the Landau-Zener algorithm is presented here. Deriving gradients from the interpolated potential energy surfaces allows for full-dimensional nonadiabatic surface hopping simulations using only adiabatic energies (energy only). Simulations of a pyrazine model and ab initio-based calculations of the SO2 molecule show that energy-only calculations with PySurf are able to correctly predict the nonadiabatic dynamics of these prototype systems. The results reveal the degree of sophistication, which can be achieved by the database accelerated energy-only surface hopping simulations being competitive to commonly used semiclassical approaches.

Ultrafast nonadiabatic dynamics probed by nitrogen K-edge absorption spectroscopy

Quantum dynamics simulations are used to simulate the ultrafast X-ray Absorption Near-Edge Structure (XANES) spectra of photoexcited pyrazine including two strongly coupled electronically excited states and four normal mode degrees of freedom.

Transient X-ray Absorption Spectral Fingerprints of the S1 Dark State in Uracil

Low-lying dark nπ* states play an important role in many photophysical and photochemical processes of organic chromophores. Transient X-ray absorption spectroscopy (TXAS) provides a powerful technique for probing the dynamics of valence states by exciting the electrons into high-lying core excited states. We employ multiconfigurational self-consistent field calculations to investigate the TXAS of uracil along its nonradiative photodecay pathways. An open issue is whether dark nπ* state S₁ (n is the lone pair localized on an oxygen atom) is accessible when bright ππ* state S₂ is selectively excited. Vertical core excitations were calculated along the potential energy surfaces of the three lowest states, S₀-S₂, interpolated between two minima and two minimum-energy conical intersections. Computed TXAS data from the C, N, and O K edges show distinct spectral fingerprints of the dark state in all spectral regimes. At the O 1s edge, the nπ* state has a very strong absorption at 526-527 eV, while at the C (N) 1s edge, by contrast, there is almost zero (very weak) absorption at 279-282 eV (397-398 eV). All K-edge spectra can be used to sensitively detect the dark states. Our proposed O 1s feature has already been observed in a recent TXAS experiment with thymine. Natural transition orbital analysis is used to interpret all dominant features of the three lowest-valence states along the reaction coordinate and reveal some important valence fine-structure information from the core excitation.

Time-resolved near-edge X-ray absorption fine structure of pyrazine from electronic structure and nuclear wave packet dynamics simulations

As a demonstration of the analysis of the electronic structure and the nuclear dynamics from time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS), we present the TR-NEXAFS spectra of pyrazine following the excitation to the ¹B_2u(ππ^*) state. The spectra are calculated combining the frozen-core/core-valence separated equation-of-motion coupled cluster singles and doubles approach for the spectral signatures and the multiconfiguration time-dependent Hartree method for the wave packet propagation. The population decay from the ¹B_2u(ππ^*) state to the ¹B_3u(nπ^*) and ¹A_u(nπ^*) states, followed by oscillatory flow of population between the ¹B_3u(nπ^*) and ¹A_u(nπ^*) states, is interpreted by means of visualization of the potential energy curves and the reduced nuclear densities. By examining the electronic structure of the three valence-excited states and the final core-excited states, we observe that the population dynamics is explicitly reflected in the TR-NEXAFS spectra, especially when the heteroatoms are selected as the X-ray absorption sites. This work illustrates the feasibility of extracting fine details of molecular photophysical processes from TR-NEXAFS spectra by using currently available theoretical methods.

Imaging large amplitude out-of-plane motion in photoexcited pentafluorobenzene using time-resolved photoelectron spectroscopy: a computational study

Excited-state dynamics of pentafluorobenzene is studied in detail for a quartic vibronic coupling model including the six b1 vibrational modes of the molecule and the two lowest excited electronic states. The study analyzes the influence of the large-amplitude out-of-plane vibrational motion on the electronic dynamics and extends to the simulation of the emerging time-resolved photoelectron spectra. The mapping of coherent non-separable electron-nuclear motion into oscillatory photoelectron signals is discussed.

Theory and Calculation of the Phosphorescence Phenomenon

Phosphorescence is a phenomenon of delayed luminescence that corresponds to the radiative decay of the molecular triplet state. As a general property of molecules, phosphorescence represents a cornerstone problem of chemical physics due to the spin prohibition of the underlying triplet-singlet emission and because its analysis embraces a deep knowledge of electronic molecular structure. Phosphorescence is the simplest physical process which provides an example of spin-forbidden transformation with a characteristic spin selectivity and magnetic field dependence, being the model also for more complicated chemical reactions and for spin catalysis applications. The bridging of the spin prohibition in phosphorescence is commonly analyzed by perturbation theory, which considers the intensity borrowing from spin-allowed electronic transitions. In this review, we highlight the basic theoretical principles and computational aspects for the estimation of various phosphorescence parameters, like intensity, radiative rate constant, lifetime, polarization, zero-field splitting, and spin sublevel population. Qualitative aspects of the phosphorescence phenomenon are discussed in terms of concepts like structure-activity relationships, donor-acceptor interactions, vibronic activity, and the role of spin-orbit coupling under charge-transfer perturbations. We illustrate the theory and principles of computational phosphorescence by highlighting studies of classical examples like molecular nitrogen and oxygen, benzene, naphthalene and their azaderivatives, porphyrins, as well as by reviewing current research on systems like electrophosphorescent transition metal complexes, nucleobases, and amino acids. We furthermore discuss modern studies of phosphorescence that cover topics of applied relevance, like the design of novel photofunctional materials for organic light-emitting diodes (OLEDs), photovoltaic cells, chemical sensors, and bioimaging.

Ab initio quantum dynamical analysis of ultrafast nonradiative transitions via conical intersections in pyrazine

Ab initio quantum dynamical calculations reveal the contributions of the optically dark S₁ (¹B_3u), S₃ (¹A_u), and S₄ (¹B_2g) states to ultrafast nonradiative transition from the optically bright S₂ (¹B_2u) state in pyrazine and suggest a much faster transition rate than previously believed.

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.