Following the Nonadiabatic Ultrafast Dynamics of Uracil via Simulated X-ray Absorption Spectra

The nucleobase uracil exhibits high photostability due to ultrafast relaxation processes mediated by conical intersections (CoIns), where the interplay between nuclear and electron dynamics becomes crucial. In our previous study, we observed seemingly long-lived traces of electronic coherence for the relaxation process through the S2/S1 CoIn by applying our ansatz for coupled nuclear and electron dynamics in molecules (NEMol). In this work, we theoretically investigate how time-dependent transient X-ray absorption spectroscopy can be used to observe this ultrafast dynamics. Therefore, we calculated X-ray absorption spectra (XAS) for the oxygen K-edge, using a multireference protocol in combination with NEMol dynamics. Thus, we have access to both the transient XAS based on the nuclear wavepacket dynamics and the modulation of the signals caused by the electronic coherence induced by the excitation process and the presence of a CoIn seam. In both cases, we were able to qualitatively predict its influence on the resulting XAS.

A Δ-learning strategy for interpretation of spectroscopic observables

Accurate computations of experimental observables are essential for interpreting the high information content held within x-ray spectra. However, for complicated systems this can be difficult, a challenge compounded when dynamics becomes important owing to the large number of calculations required to capture the time-evolving observable. While machine learning architectures have been shown to represent a promising approach for rapidly predicting spectral lineshapes, achieving simultaneously accurate and sufficiently comprehensive training data is challenging. Herein, we introduce Δ-learning for x-ray spectroscopy. Instead of directly learning the structure-spectrum relationship, the Δ-model learns the structure dependent difference between a higher and lower level of theory. Consequently, once developed these models can be used to translate spectral shapes obtained from lower levels of theory to mimic those corresponding to higher levels of theory. Ultimately, this achieves accurate simulations with a much reduced computational burden as only the lower level of theory is computed, while the model can instantaneously transform this to a spectrum equivalent to a higher level of theory. Our present model, demonstrated herein, learns the difference between TDDFT(BLYP) and TDDFT(B3LYP) spectra. Its effectiveness is illustrated using simulations of Rh L3-edge spectra tracking the C-H activation of octane by a cyclopentadienyl rhodium carbonyl complex.

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.

An on-the-fly deep neural network for simulating time-resolved spectroscopy: predicting the ultrafast ring opening dynamics of 1,2-dithiane

Revolutionary developments in ultrafast light source technology are enabling experimental spectroscopists to probe the structural dynamics of molecules and materials on the femtosecond timescale. The capacity to investigate ultrafast processes afforded by these resources accordingly inspires theoreticians to carry out high-level simulations which facilitate the interpretation of the underlying dynamics probed during these ultrafast experiments. In this Article, we implement a deep neural network (DNN) to convert excited-state molecular dynamics simulations into time-resolved spectroscopic signals. Our DNN is trained on-the-fly from first-principles theoretical data obtained from a set of time-evolving molecular dynamics. The train-test process iterates for each time-step of the dynamics data until the network can predict spectra with sufficient accuracy to replace the computationally intensive quantum chemistry calculations required to produce them, at which point it simulates the time-resolved spectra for longer timescales. The potential of this approach is demonstrated by probing dynamics of the ring opening of 1,2-dithiane using sulphur K-edge X-ray absorption spectroscopy. The benefits of this strategy will be more markedly apparent for simulations of larger systems which will exhibit a more notable computational burden, making this approach applicable to the study of a diverse range of complex chemical dynamics.

Accurate, affordable, and generalizable machine learning simulations of transition metal x-ray absorption spectra using the XANESNET deep neural network

The affordable, accurate, and generalizable prediction of spectroscopic observables plays a key role in the analysis of increasingly complex experiments. In this article, we develop and deploy a deep neural network-XANESNET-for predicting the lineshape of first-row transition metal K-edge x-ray absorption near-edge structure (XANES) spectra. XANESNET predicts the spectral intensities using only information about the local coordination geometry of the transition metal complexes encoded in a feature vector of weighted atom-centered symmetry functions. We address in detail the calibration of the feature vector for the particularities of the problem at hand, and we explore the individual feature importance to reveal the physical insight that XANESNET obtains at the Fe K-edge. XANESNET relies on only a few judiciously selected features-radial information on the first and second coordination shells suffices along with angular information sufficient to separate satisfactorily key coordination geometries. The feature importance is found to reflect the XANES spectral window under consideration and is consistent with the expected underlying physics. We subsequently apply XANESNET at nine first-row transition metal (Ti-Zn) K-edges. It can be optimized in as little as a minute, predicts instantaneously, and provides K-edge XANES spectra with an average accuracy of ∼±2%-4% in which the positions of prominent peaks are matched with a >90% hit rate to sub-eV (∼0.8 eV) error.

Excited state absorption of DNA bases in the gas phase and in chloroform solution: a comparative quantum mechanical study

We study the excited state absorption (ESA) properties of the four DNA bases (thymine, cytosine, adenine, and guanine) by different single reference quantum mechanical methods, namely, equation of motion coupled cluster singles and doubles (EOM-CCSD), singles, doubles and perturbative triples (EOM-CC3), and time-dependent density functional theory (TD-DFT), with the long-range corrected CAM-B3LYP functional. Preliminary results at the Tamm-Dancoff (TDA) CAM-B3LYP level using the maximum overlap method (MOM) are reported for thymine. In the gas phase, the three methods predict similar One Photon Absorption (OPA) spectra, which are consistent with the experimental results and with the most accurate computational studies available in the literature. The ESA spectra are then computed for the ππ* states (one for pyrimidine, two for purines) associated with the lowest-energy absorption band, and for the close-lying nπ* state. The EOM-CC3, EOM-CCSD and CAM-B3LYP methods provide similar ESA spectral patterns, which are also in qualitative agreement with literature RASPT2 results. Once validated in the gas phase, TD-CAM-B3LYP has been used to compute the ESA in chloroform, including solvent effects by the polarizable continuum model (PCM). The predicted OPA and ESA spectra in chloroform are very similar to those in the gas phase, most of the bands shifting by less than 0.1 eV, with a small increase of the intensities and a moderate destabilization of the nπ* state. Finally, ESA spectra have been computed from the minima of the lowest energy ππ* state, and found in line with the available experimental transient absorption spectra of the nucleosides in solution, providing further validation of our computational approach.

Resolving competing conical intersection pathways: time-resolved X-ray absorption spectroscopy of trans-1,3-butadiene

Time-resolved X-ray absorption spectroscopy is emerging as a uniquely powerful tool to probe coupled electronic-nuclear dynamics in photo-excited molecules. Theoretical studies to date have established that time-resolved X-ray absorption spectroscopy is an atom-specific probe of excited-state wave packet passage through a seam of conical intersections (CIs). However, in many molecular systems, there are competing dynamical pathways involving CIs of different electronic and nuclear character. Discerning these pathways remains an important challenge. Here, we demonstrate that time-resolved X-ray absorption spectroscopy (TRXAS) has the potential to resolve competing channels in excited-state non-adiabatic dynamics. Using the example of 1,3-butadiene, we show how TRXAS discerns the different electronic structures associated with passage through multiple conical intersections. trans-1,3-Butadiene exhibits a branching between polarized and radicaloid pathways associated with ethylenic "twisted-pyramidalized" and excited-state cis-trans isomerization dynamics, respectively. The differing electronic structures along these pathways give rise to different XAS signals, indicating the possibility of resolving them. Furthermore, this indicates that XAS, and other core-level spectroscopic techniques, offer the appealing prospect of directly probing the effects of selective chemical substitution and its ability to affect chemical control over excited-state molecular dynamics.

Predictions of Pre-edge Features in Time-Resolved Near-Edge X-ray Absorption Fine Structure Spectroscopy from Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory

Time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy is a powerful technique for studying photochemical reaction dynamics with femtosecond time resolution. In order to avoid ambiguity in TR-NEXAFS spectra from nonadiabatic dynamics simulations, core- and valence-excited states must be evaluated on equal footing and those valence states must also define the potential energy surfaces used in the nonadiabatic dynamics simulation. In this work, we demonstrate that hole-hole Tamm-Dancoff-approximated density functional theory (hh-TDA) is capable of directly simulating TR-NEXAFS spectroscopies. We apply hh-TDA to the excited-state dynamics of acrolein. We identify two pre-edge features in the oxygen K-edge TR-NEXAFS spectrum associated with the S₂ (ππ*) and S₁ (nπ*) excited states. We show that these features can be used to follow the internal conversion dynamics between the lowest three electronic states of acrolein. Due to the low, O(N²) apparent computational complexity of hh-TDA and our GPU-accelerated implementation, this method is promising for the simulation of pre-edge features in TR-NEXAFS spectra of large molecules and molecules in the condensed phase.

Self-Consistent Field Methods for Excited States in Strong Magnetic Fields: a Comparison between Energy- and Variance-Based Approaches

Self-consistent field methods for excited states offer an attractive low-cost route to study not only excitation energies but also properties of excited states. Here, we present the generalization of two self-consistent field methods, the maximum overlap method (MOM) and the σ-SCF method, to calculate excited states in strong magnetic fields and investigate their stability and accuracy in this context. These methods use different strategies to overcome the well-known variational collapse of energy-based optimizations to the lowest solution of a given symmetry. The MOM tackles this problem in the definition of the orbital occupations to constrain the self-consistent field procedure to converge on excited states, while the σ-SCF method is based on the minimization of the variance instead of the energy. To overcome the high computational cost of the variance minimization, we present a new implementation of the σ-SCF method with the resolution of identity approximation, allowing the use of large basis sets, which is an important requirement for calculations in strong magnetic fields. The accuracy of these methods is assessed by comparison with the benchmark literature data for He, H₂, and CH⁺. The results reveal severe limitations of the variance-based scheme, which become more acute in large basis sets. In particular, many states are not accessible using variance optimization. Detailed analysis shows that this is a general feature of variance optimization approaches due to the masking of local minima in the optimization. In contrast, the MOM shows promising performance for computing excited states under these conditions, yielding results consistent with available benchmark data for a diverse range of electronic states.

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.

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 assessment of different electronic structure approaches for modeling time-resolved x-ray absorption spectroscopy

We assess the performance of different protocols for simulating excited-state x-ray absorption spectra. We consider three different protocols based on equation-of-motion coupled-cluster singles and doubles, two of them combined with the maximum overlap method. The three protocols differ in the choice of a reference configuration used to compute target states. Maximum-overlap-method time-dependent density functional theory is also considered. The performance of the different approaches is illustrated using uracil, thymine, and acetylacetone as benchmark systems. The results provide guidance for selecting an electronic structure method for modeling time-resolved x-ray absorption spectroscopy.

The nuts and bolts of core-hole constrainedab initiosimulation forK-shell x-ray photoemission and absorption spectra

X-ray photoemission (XPS) and near edge x-ray absorption fine structure (NEXAFS) spectroscopy play an important role in investigating the structure and electronic structure of materials and surfaces.Ab initiosimulations provide crucial support for the interpretation of complex spectra containing overlapping signatures. Approximate core-hole simulation methods based on density functional theory (DFT) such as the delta-self-consistent-field (ΔSCF) method or the transition potential (TP) method are widely used to predictK-shell XPS and NEXAFS signatures of organic molecules, inorganic materials and metal-organic interfaces at reliable accuracy and affordable computational cost. We present the numerical and technical details of our variants of the ΔSCF and TP method (coined ΔIP-TP) to simulate XPS and NEXAFS transitions. Using exemplary molecules in gas-phase, in bulk crystals, and at metal-organic interfaces, we systematically assess how practical simulation choices affect the stability and accuracy of simulations. These include the choice of exchange-correlation functional, basis set, the method of core-hole localization, and the use of periodic boundary conditions (PBC). We particularly focus on the choice of aperiodic or periodic description of systems and how spurious charge effects in periodic calculations affect the simulation outcomes. For the benefit of practitioners in the field, we discuss sensible default choices, limitations of the methods, and future prospects.

Vibronic Dynamics of Photodissociating ICN from Simulations of Ultrafast X-Ray Absorption Spectroscopy

Ultrafast UV-pump/soft-X-ray-probe spectroscopy is a subject of great interest since it can provide detailed information about dynamical photochemical processes with ultrafast resolution and atomic specificity. Here, we focus on the photodissociation of ICN in the 1 Π1 excited state, with emphasis on the transient response in the soft-X-ray spectral region as described by the ab initio spectral lineshape averaged over the nuclear wavepacket probability density. We find that the carbon K-edge spectral region reveals a rich transient response that provides direct insights into the dynamics of frontier orbitals during the I-CN bond cleavage process. The simulated UV-pump/soft-X-ray-probe spectra exhibit detailed dynamical information, including a time-domain signature for coherent vibration associated with the photogenerated CN fragment.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Density Functional Theory Based Methods for the Calculation of X-ray Spectroscopy

The availability of new light sources combined with the realization of the unique capabilities of spectroscopy in the X-ray region has driven tremendous advances in the field of X-ray spectroscopy. Currently, these techniques are emerging as powerful analytical tools for the study of a wide range of problems encompassing liquids, materials, and biological systems. Time-resolved measurements add a further dimension to X-ray spectroscopy, opening up the potential to resolve ultrafast chemical processes at an atomic level. X-ray spectroscopy encompasses a range of techniques which provide complementary information, and these include X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES), and resonant inelastic X-ray scattering (RIXS). In many studies, the interpretation of the experimental data relies upon calculations to enable the nature of the underlying molecular structure, electronic structure, and bonding to be revealed. Density functional theory (DFT) based methods are some of the most widely used methods for the simulation of X-ray spectra. In this Account, we focus on our recent contributions to the simulation of a range of X-ray spectroscopic techniques using DFT and linear-response time-dependent density functional theory (TDDFT) and show how these methods can provide a computational toolkit for the simulation of X-ray spectroscopy. The importance of the exchange-correlation functional for the calculation of XAS is discussed, and the introduction of short-range corrected functionals is described. The application of these calculations to study large systems through the use of efficient implementations of TDDFT will be highlighted, with the use of these methods illustrated through studies of ionic liquids and transition metal complexes. The extension of TDDFT to calculate XES through the use of a reference determinant for the core-ionized state will be described, and the factors that affect the accuracy of the computed spectra discussed. The application of these approaches will be illustrated through the study of a range of organic molecules and transition metal complexes, which also show how going beyond the dipole approximation in determining the transition intensities can be critical. The application of these approaches to the simulation of the RIXS spectrum of water will also be described, highlighting how ultrafast dynamics on the femtoscale time scale are evident in the measured spectra. In these calculations, the description of the core-ionized and core-excited states becomes increasingly important, and the role of the basis set in accurately describing these states will be explored.

The Role of Structural Representation in the Performance of a Deep Neural Network for X-Ray Spectroscopy

An important consideration when developing a deep neural network (DNN) for the prediction of molecular properties is the representation of the chemical space. Herein we explore the effect of the representation on the performance of our DNN engineered to predict Fe K-edge X-ray absorption near-edge structure (XANES) spectra, and address the question: How important is the choice of representation for the local environment around an arbitrary Fe absorption site? Using two popular representations of chemical space-the Coulomb matrix (CM) and pair-distribution/radial distribution curve (RDC)-we investigate the effect that the choice of representation has on the performance of our DNN. While CM and RDC featurisation are demonstrably robust descriptors, it is possible to obtain a smaller mean squared error (MSE) between the target and estimated XANES spectra when using RDC featurisation, and converge to this state a) faster and b) using fewer data samples. This is advantageous for future extension of our DNN to other X-ray absorption edges, and for reoptimisation of our DNN to reproduce results from higher levels of theory. In the latter case, dataset sizes will be limited more strongly by the resource-intensive nature of the underlying theoretical calculations.

Efficient table-top dual-wavelength beamline for ultrafast transient absorption spectroscopy in the soft X-ray region

We present a table-top beamline providing a soft X-ray supercontinuum extending up to 370 eV from high-order harmonic generation with sub-13 fs 1300 nm driving pulses and simultaneous production of sub-5 fs pulses centered at 800 nm. Optimization of high harmonic generation in a long and dense gas medium yields a photon flux of  ~ 1.4 × 106 photons/s/1% bandwidth at 300 eV. The temporal resolution of X-ray transient absorption experiments with this beamline is measured to be 11 fs for 800 nm excitation. This dual-wavelength approach, combined with high flux and high spectral and temporal resolution soft X-ray absorption spectroscopy, is a new route to the study of ultrafast electronic dynamics in carbon-containing molecules and materials at the carbon K-edge.

Probing competing relaxation pathways in malonaldehyde with transient X-ray absorption spectroscopy

Excited-state intramolecular hydrogen transfer (ESIHT) is a fundamental reaction relevant to chemistry and biology. Malonaldehyde is the simplest example of ESIHT, yet only little is known experimentally about its excited-state dynamics. Several competing relaxation pathways have been proposed, including internal conversion mediated by ESIHT and C[double bond, length as m-dash]C torsional motion as well as intersystem crossing. We perform an in silico transient X-ray absorption spectroscopy (TRXAS) experiment at the oxygen K-edge to investigate its potential to monitor the proposed ultrafast decay pathways in malonaldehyde upon photoexcitation to its bright S₂(ππ*) state. We employ both restricted active space perturbation theory and algebraic-diagrammatic construction for the polarization propagator along interpolated reaction coordinates as well as representative trajectories from ab initio multiple spawning simulations to compute the TRXAS signals from the lowest valence states. Our study suggests that oxygen K-edge TRXAS can distinctly fingerprint the passage through the H-transfer intersection and the concomitant population transfer to the S₁(nπ*) state. Potential intersystem crossing to T₁(ππ*) is detectable from reappearance of the double pre-edge signature and reversed intensities. Moreover, the torsional deactivation pathway induces transient charge redistribution from the enol side towards the central C-atom and manifests itself as substantial shifts of the pre-edge features. Given the continuous advances in X-ray light sources, our study proposes an experimental route to disentangle ultrafast excited-state decay channels in this prototypical ESIHT system and provides a pathway-specific mapping of the TRXAS signal to facilitate the interpretation of future experiments.

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.