Nonlinear Spectroscopy of Core and Valence Excitations Using Short X-Ray Pulses: Simulation Challenges

Core Hole Effect to Valence Excitations: Tracking and Visualizing the Same Excitation in XPS Shake-Up Satellites and UV Absorption Spectra

Introducing a core hole significantly alters the electronic structure of a molecule, and various X-ray spectroscopy techniques are available for probing the valence electronic structure in the presence of a core hole. In this study, we visually demonstrate the influence of a core hole on valence excitations by computing the ultraviolet absorption spectra and the shake-up satellites in X-ray photoelectron spectra for pyrrole, furan, and thiophene, as complemented by the natural transition orbital (NTO) analysis over transitions with and without a core hole. Employing equivalent core hole time-dependent density functional theory (ECH-TDDFT) and TDDFT methods, we achieved balanced accuracy in both spectra for reliable comparative analysis. We tracked the same involved valence transition in both spectra, offering a vivid illustration of the core hole effect via the change in corresponding particle NTOs introduced by a 1s core hole on a Cα, Cβ, or O atom. Our analysis deepens the understanding of the core hole effect on valence transitions, a phenomenon ubiquitously observed in general X-ray spectroscopic analyses.

Efficient All-Electron Time-Dependent Density Functional Theory Calculations Using an Enriched Finite Element Basis

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with a compactly supported numerical atom-centered basis, obtained from atomic ground-state DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on a priori error estimates to guide our choice of an adaptive finite element mesh as well as the time step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretizations. Notably, we attain a 50-100 times speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear responses by studying the absorption spectra in sodium clusters, the linear to nonlinear response transition in the green fluorescence protein chromophore, and the higher harmonic generation in the magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to ∼1000 processors, using a benchmark system of a 50-atom sodium nanocluster.

Molecular Chirality and Its Monitoring by Ultrafast X-ray Pulses

Major advances in X-ray sources including the development of circularly polarized and orbital angular momentum pulses make it possible to probe matter chirality at unprecedented energy regimes and with Ångström and femtosecond spatiotemporal resolutions. We survey the theory of stationary and time-resolved nonlinear chiral measurements that can be carried out in the X-ray regime using tabletop X-ray sources or large scale (XFEL, synchrotron) facilities. A variety of possible signals and their information content are discussed.

Computational approaches for XANES, VtC-XES, and RIXS using linear-response time-dependent density functional theory based methods

The emergence of state-of-the-art X-ray light sources has paved the way for novel spectroscopies that take advantage of their atomic specificity to shed light on fundamental physical, chemical, and biological processes both in the static and time domains. The success of these experiments hinges on the ability to interpret and predict core-level spectra, which has opened avenues for theory to play a key role. Over the last two decades, linear-response time-dependent density functional theory (LR-TDDFT), despite various theoretical challenges, has become a computationally attractive and versatile framework to study excited-state spectra including X-ray spectroscopies. In this context, we focus our discussion on LR-TDDFT approaches for the computation of X-ray Near-Edge Structure (XANES), Valence-to-Core X-ray Emission (VtC-XES), and Resonant Inelastic X-ray Scattering (RIXS) spectroscopies in molecular systems with an emphasis on Gaussian basis set implementations. We illustrate these approaches with applications and provide a brief outlook of possible new directions.

A theoretical library of N1s core binding energies of polynitrogen molecules and ions in the gas phase

Polynitrogen molecules and ions are important building blocks of high energy density compounds(HEDCs). High energy bonds formed at the N sites can be effectively probed by the X-ray photoelectron spectroscopy...

Resonantly Enhanced Difference-Frequency Generation in the Core X-ray Absorption of Molecules

We use real-time time-dependent density functional theory simulations to numerically demonstrate that resonantly enhanced difference-frequency generation (re-DFG) involving intense ultrashort coherent X-ray pulses can selectively excite core states of atoms in molecules. As a model case, we evaluate the spectral selectivity of re-DFG excitation of the oxygen K-edge by illumination of a single gas-phase water molecule with two-color X-ray pulses of different photon energies and durations. The re-DFG excitation is further probed by a small delayed pulse with central photon energy resonant with the oxygen K-edge peak absorption line. Based on these results, we anticipate that highly selective excitation by re-DFG X-ray nonlinear processes might be achieved in more complex molecular systems and bulk materials by using highly penetrating two-color hard X-ray pulses, with extensive applications.

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.

Site-specific generation of excited state wavepackets with high-intensity attosecond x rays

High-intensity attosecond x rays can produce coherent superpositions of valence-excited states through two-photon Raman transitions. The broad-bandwidth, high-field nature of the pulses results in a multitude of accessible excited states. Multiconfigurational quantum chemistry with the time-dependent Schrödinger equation is used to examine population transfer dynamics in stimulated x-ray Raman scattering of the nitric oxide oxygen and nitrogen K-edges. Two pulse schemes initiate wavepackets of different characters and demonstrate how chemical differences between core-excitation pathways affect the dynamics. The population transfer to valence-excited states is found to be sensitive to the electronic structure and pulse conditions, highlighting complexities attributed to the Rabi frequency. The orthogonally polarized two-color-pulse setup has increased selectivity while facilitating longer, less intense pulses than the one-pulse setup. Population transfer in the 1s → Rydberg region is more effective but less selective at the nitrogen K-edge; the selectivity is reduced by double core-excited states. Result interpretation is aided by resonant inelastic x-ray scattering maps.

Ultrafast strong-field dissociation of vinyl bromide: An attosecond transient absorption spectroscopy and non-adiabatic molecular dynamics study

Attosecond extreme ultraviolet (XUV) and soft x-ray sources provide powerful new tools for studying ultrafast molecular dynamics with atomic, state, and charge specificity. In this report, we employ attosecond transient absorption spectroscopy (ATAS) to follow strong-field-initiated dynamics in vinyl bromide. Probing the Br M edge allows one to assess the competing processes in neutral and ionized molecular species. Using ab initio non-adiabatic molecular dynamics, we simulate the neutral and cationic dynamics resulting from the interaction of the molecule with the strong field. Based on the dynamics results, the corresponding time-dependent XUV transient absorption spectra are calculated by applying high-level multi-reference methods. The state-resolved analysis obtained through the simulated dynamics and related spectral contributions enables a detailed and quantitative comparison with the experimental data. The main outcome of the interaction with the strong field is unambiguously the population of the first three cationic states, D ₁, D ₂, and D ₃. The first two show exclusively vibrational dynamics while the D ₃ state is characterized by an ultrafast dissociation of the molecule via C-Br bond rupture within 100 fs in 50% of the analyzed trajectories. The combination of the three simulated ionic transient absorption spectra is in excellent agreement with the experimental results. This work establishes ATAS in combination with high-level multi-reference simulations as a spectroscopic technique capable of resolving coupled non-adiabatic electronic-nuclear dynamics in photoexcited molecules with sub-femtosecond resolution.

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.

Theoretical assessment of vibrationally resolved C1s X-ray photoelectron spectra of simple cyclic molecules

Vibrationally-resolved K-edge XPS simulation by the full/equivalent core-hole method is enabled and assessment of the C1s spectra of cyclic molecules shows excellent/acceptable agreement with the experiment.

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.

Lighting Up the Invisible Twisted Intramolecular Charge Transfer State by High Pressure

The twisted intramolecular charge transfer (TICT) state plays an important role in determining the performance of optoelectronic devices. However, for some nonfluorescent TICT molecules, the "invisible" TICT state could only be visualized by modifying the molecular structure. Here, we introduce a new facile pressure-induced approach to light up the TICT state through the use of a pressure-related liquid-solid phase transition of the surrounding solvent. Combining ultrafast spectroscopy and quantum chemical calculations, it reveals that the "invisible" TICT state can emit fluorescence when the rotation of a donor group is restricted by the frozen acetonitrile solution. Furthermore, the TICT process can even be effectively regulated by the external pressure. Our study offers a unique strategy to achieve dual fluorescence behavior in charge transfer molecules and is of significance for optoelectronic and biomedical applications.

Towards an ab initio theory for metal L-edge soft X-ray spectroscopy of molecular aggregates

The Frenkel exciton model was adapted to describe X-ray absorption and resonant inelastic scattering spectra of polynuclear transition metal complexes by means of the restricted active space self-consistent field method. The proposed approach allows to substantially decrease the requirements on computational resources if compared to a full supermolecular quantum chemical treatment. This holds true, in particular, in cases where the dipole approximation to the electronic transition charge density can be applied. The computational protocol was applied to the calculation of X-ray spectra of the hemin complex, which forms dimers in aqueous solution. The aggregation effects were found to be comparable to the spectral alterations due to the replacement of the axial ligand by solvent molecules.

Study of double core hole excitations in molecules by X-ray double-quantum-coherence signals: a multi-configuration simulation

The multi-configurational self-consistent field method is employed to simulate the two-dimensional all-X-ray double-quantum-coherence (XDQC) spectroscopy, a four-wave mixing signal that provides direct signatures of double core hole (DCH) states. The valence electronic structure is probed by capturing the correlation between the single (SCH) and double core hole states. The state-averaged restricted-active-space self-consistent field (SA-RASSCF) approach is used which can treat the valence, SCH, and DCH states at the same theoretical level, and applies to all types of DCHs (located on one or two atoms, K-edge or L-edge), with both accuracy and efficiency. Orbital relaxation introduced by the core hole(s) and the static electron correlation is properly accounted for. The XDQC process can take place via different intermediate DCH state channels by tuning the pulse frequencies. We simulate the XDQC signals for the three isomers of aminophenol at 8 pulse frequency configurations, covering all DCH pathways involving the N1s and O1s core hole (N1sN1s, O1sO1s and N1sO1s), which reveal different patterns of valence excitations.

A Polarization Propagator for Nonlinear X-ray Spectroscopies

A complex polarization propagator approach has been developed to third order and implemented in density functional theory (DFT), allowing for the direct calculation of nonlinear molecular properties in the X-ray wavelength regime without explicitly addressing the excited-state manifold. We demonstrate the utility of this propagator method for the modeling of coherent near-edge X-ray two-photon absorption using, as an example, DFT as the underlying electronic structure model. Results are compared with the corresponding near-edge X-ray absorption fine structure spectra, illuminating the differences in the role of symmetry, localization, and correlation between the two spectroscopies. The ramifications of this new technique for nonlinear X-ray research are briefly discussed.

Stimulated X-ray Raman scattering – a critical assessment of the building block of nonlinear X-ray spectroscopy

With the invention of femtosecond X-ray free-electron lasers (XFELs), studies of light-induced chemical reaction dynamics and structural dynamics reach a new era, allowing for time-resolved X-ray diffraction and spectroscopy. To ultimately probe coherent electron and nuclear dynamics on their natural time and length scales, coherent nonlinear X-ray spectroscopy schemes have been proposed. In this contribution, we want to critically assess the experimental realisation of nonlinear X-ray spectroscopy at current-day XFEL sources, by presenting first experimental attempts to demonstrate stimulated resonant X-ray Raman scattering in molecular gas targets.