Atomic-scale observation of solvent reorganization influencing photoinduced structural dynamics in a copper complex photosensitizer

Real-time structural dynamics of the ultrafast solvation process around photo-excited aqueous halides

This work investigates and describes the structural dynamics taking place following charge-transfer-to-solvent photo-abstraction of electrons from I- and Br- ions in aqueous solution following single- and 2-photon excitation at 202 nm and 400 nm, respectively. A Time-Resolved X-ray Solution Scattering (TR-XSS) approach with direct sensitivity to the structure of the surrounding solvent as the water molecules adopt a new equilibrium configuration following the electron-abstraction process is utilized to investigate the structural dynamics of solvent shell expansion and restructuring in real-time. The structural sensitivity of the scattering data enables a quantitative evaluation of competing models for the interaction between the nascent neutral species and surrounding water molecules. Taking the I0-O distance as the reaction coordinate, we find that the structural reorganization is delayed by 0.1 ps with respect to the photoexcitation and completes on a time scale of 0.5-1 ps. On longer time scales we determine from the evolution of the TR-XSS difference signal that I0: e- recombination takes place on two distinct time scales of ∼20 ps and 100 s of picoseconds. These dynamics are well captured by a simple model of diffusive evolution of the initial photo-abstracted electron population where the charge-transfer-to-solvent process gives rise to a broad distribution of electron ejection distances, a significant fraction of which are in the close vicinity of the nascent halogen atoms and recombine on short time scales.

Resolving Photoinduced Femtosecond Three-Dimensional Solute-Solvent Dynamics through Surface Hopping Simulations

Photoinduced dynamics in solution is governed by mutual solute-solvent interactions, which give rise to phenomena like solvatochromism, the Stokes shift, dual fluorescence, or charge transfer. Understanding these phenomena requires simulating the solute's photoinduced dynamics and simultaneously resolving the three-dimensional solvent distribution dynamics. If using trajectory surface hopping (TSH) to this aim, thousands of trajectories are required to adequately sample the time-dependent three-dimensional solvent distribution functions, and thus resolve the solvent dynamics with sub-Ångstrom and femtosecond accuracy and sufficiently low noise levels. Unfortunately, simulating thousands of trajectories with TSH in the framework of hybrid quantum mechanical/molecular mechanical (QM/MM) can be prohibitively expensive when employing ab initio electronic structure methods. To tackle this challenge, we recently introduced a computationally efficient approach that combines efficient linear vibronic coupling models with molecular mechanics (LVC/MM) via electrostatic embedding [Polonius et al., JCTC 2023, 19, 7171-7186]. This method provides solvent-embedded, nonadiabatically coupled potential energy surfaces while scaling similarly to MM force fields. Here, we employ TSH with LVC/MM to unravel the photoinduced dynamics of two small thiocarbonyl compounds solvated in water. We describe how to estimate the number of trajectories required to produce nearly noise-free three-dimensional solvent distribution functions and present an analysis based on approximately 10,000 trajectories propagated for 3 ps. In the electronic ground state, both molecules exhibit in-plane hydrogen bonds to the sulfur atom. Shortly after excitation, these bonds are broken and reform perpendicular to the molecular plane on timescales that differ by an order of magnitude due to steric effects. We also show that the solvent relaxation dynamics is coupled to the electronic dynamics, including intersystem crossing. These findings are relevant to advance the understanding of the coupled solute-solvent dynamics of solvated photoexcited molecules, e.g., biologically relevant thio-nucleobases.

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States

The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. -2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

Deciphering Photoinduced Catalytic Reaction Mechanisms in Natural and Artificial Photosynthetic Systems on Multiple Temporal and Spatial Scales Using X-ray Probes

Utilization of renewable energies for catalytically generating value-added chemicals is highly desirable in this era of rising energy demands and climate change impacts. Artificial photosynthetic systems or photocatalysts utilize light to convert abundant CO2, H2O, and O2 to fuels, such as carbohydrates and hydrogen, thus converting light energy to storable chemical resources. The emergence of intense X-ray pulses from synchrotrons, ultrafast X-ray pulses from X-ray free electron lasers, and table-top laser-driven sources over the past decades opens new frontiers in deciphering photoinduced catalytic reaction mechanisms on the multiple temporal and spatial scales. Operando X-ray spectroscopic methods offer a new set of electronic transitions in probing the oxidation states, coordinating geometry, and spin states of the metal catalytic center and photosensitizers with unprecedented energy and time resolution. Operando X-ray scattering methods enable previously elusive reaction steps to be characterized on different length scales and time scales. The methodological progress and their application examples collected in this review will offer a glimpse into the accomplishments and current state in deciphering reaction mechanisms for both natural and synthetic systems. Looking forward, there are still many challenges and opportunities at the frontier of catalytic research that will require further advancement of the characterization techniques.

A comparative review of time-resolved x-ray and electron scattering to probe structural dynamics

The structure of molecules, particularly the dynamic changes in structure, plays an essential role in understanding physical and chemical phenomena. Time-resolved (TR) scattering techniques serve as crucial experimental tools for studying structural dynamics, offering direct sensitivity to molecular structures through scattering signals. Over the past decade, the advent of x-ray free-electron lasers (XFELs) and mega-electron-volt ultrafast electron diffraction (MeV-UED) facilities has ushered TR scattering experiments into a new era, garnering significant attention. In this review, we delve into the basic principles of TR scattering experiments, especially focusing on those that employ x-rays and electrons. We highlight the variations in experimental conditions when employing x-rays vs electrons and discuss their complementarity. Additionally, cutting-edge XFELs and MeV-UED facilities for TR x-ray and electron scattering experiments and the experiments performed at those facilities are reviewed. As new facilities are constructed and existing ones undergo upgrades, the landscape for TR x-ray and electron scattering experiments is poised for further expansion. Through this review, we aim to facilitate the effective utilization of these emerging opportunities, assisting researchers in delving deeper into the intricate dynamics of molecular structures.

Toward a quantitative description of solvation structure: a framework for differential solution scattering measurements

Appreciating that the role of the solute-solvent and other outer-sphere interactions is essential for understanding chemistry and chemical dynamics in solution, experimental approaches are needed to address the structural consequences of these interactions, complementing condensed-matter simulations and coarse-grained theories. High-energy X-ray scattering (HEXS) combined with pair distribution function analysis presents the opportunity to probe these structures directly and to develop quantitative, atomistic models of molecular systems in situ in the solution phase. However, at concentrations relevant to solution-phase chemistry, the total scattering signal is dominated by the bulk solvent, prompting researchers to adopt a differential approach to eliminate this unwanted background. Though similar approaches are well established in quantitative structural studies of macromolecules in solution by small- and wide-angle X-ray scattering (SAXS/WAXS), analogous studies in the HEXS regime-where sub-ångström spatial resolution is achieved-remain underdeveloped, in part due to the lack of a rigorous theoretical description of the experiment. To address this, herein we develop a framework for differential solution scattering experiments conducted at high energies, which includes concepts of the solvent-excluded volume introduced to describe SAXS/WAXS data, as well as concepts from the time-resolved X-ray scattering community. Our theory is supported by numerical simulations and experiment and paves the way for establishing quantitative methods to determine the atomic structures of small molecules in solution with resolution approaching that of crystallography.

The photochemistry of Rydberg-excited cyclobutanone: Photoinduced processes and ground state dynamics

Owing to ring strain, cyclic ketones exhibit complex excited state dynamics with multiple competing photochemical channels active on the ultrafast timescale. While the excited state dynamics of cyclobutanone after π* ← n excitation into the lowest-energy excited singlet (S1) state has been extensively studied, the dynamics following 3s ← n excitation into the higher-lying singlet Rydberg (S2) state are less well understood. Herein, we employ fully quantum multiconfigurational time-dependent Hartree (MCTDH) simulations using a model Hamiltonian as well as "on-the-fly" trajectory-based surface-hopping dynamics (TSHD) simulations to study the relaxation dynamics of cyclobutanone following 3s ← n excitation and to predict the ultrafast electron diffraction scattering signature of these relaxation dynamics. Our MCTDH and TSHD simulations indicate that relaxation from the initially-populated singlet Rydberg (S2) state occurs on the timescale of a few hundreds of femtoseconds to a picosecond, consistent with the symmetry-forbidden nature of the state-to-state transition involved. There is no obvious involvement of excited triplet states within the timeframe of our simulations (<2 ps). After non-radiative relaxation to the electronic ground state (S0), vibrationally hot cyclobutanone has sufficient internal energy to form multiple fragmented products including C2H4 + CH2CO (C2; 20%) and C3H6 + CO (C3; 2.5%). We discuss the limitations of our MCTDH and TSHD simulations, how these may influence the excited state dynamics we observe, and-ultimately-the predictive power of the simulated experimental observable.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Experimental capabilities for liquid jet samples at sub-MHz rates at the FXE Instrument at European XFEL

The Femtosecond X-ray Experiments (FXE) instrument at the European X-ray Free-Electron Laser (EuXFEL) provides an optimized platform for investigations of ultrafast physical, chemical and biological processes. It operates in the energy range 4.7-20 keV accommodating flexible and versatile environments for a wide range of samples using diverse ultrafast X-ray spectroscopic, scattering and diffraction techniques. FXE is particularly suitable for experiments taking advantage of the sub-MHz repetition rates provided by the EuXFEL. In this paper a dedicated setup for studies on ultrafast biological and chemical dynamics in solution phase at sub-MHz rates at FXE is presented. Particular emphasis on the different liquid jet sample delivery options and their performance is given. Our portfolio of high-speed jets compatible with sub-MHz experiments includes cylindrical jets, gas dynamic virtual nozzles and flat jets. The capability to perform multi-color X-ray emission spectroscopy (XES) experiments is illustrated by a set of measurements using the dispersive X-ray spectrometer in von Hamos geometry. Static XES data collected using a multi-crystal scanning Johann-type spectrometer are also presented. A few examples of experimental results on ultrafast time-resolved X-ray emission spectroscopy and wide-angle X-ray scattering at sub-MHz pulse repetition rates are given.

Eliminating finite-size effects on the calculation of x-ray scattering from molecular dynamics simulations

Structural studies using x-ray scattering methods for investigating molecules in solution are shifting focus toward describing the role and effects of the surrounding solvent. However, forward models based on molecular dynamics (MD) simulations to simulate structure factors and x-ray scattering from interatomic distributions such as radial distribution functions (RDFs) face limitations imposed by simulations, particularly at low values of the scattering vector q. In this work, we show how the value of the structure factor at q = 0 calculated from RDFs sampled from finite MD simulations is effectively dependent on the size of the simulation cell. To eliminate this error, we derive a new scheme to renormalize the sampled RDFs based on a model of the excluded volume of the particle-pairs they were sampled from, to emulate sampling from an infinite system. We compare this new correction method to two previous RDF-correction methods, developed for Kirkwood-Buff theory applications. We present a quantitative test to assess the reliability of the simulated low-q scattering signal and show that our RDF-correction successfully recovers the correct q = 0 limit for neat water. We investigate the effect of MD-sampling time on the RDF-corrections, before advancing to a molecular example system, comprised of a transition metal complex solvated in a series of water cells with varying densities. We show that our correction recovers the correct q = 0 behavior for all densities. Furthermore, we employ a simple continuum scattering model to dissect the total scattering signal from the solvent-solvent structural correlations in a solute-solvent model system to find two distinct contributions: a non-local density-contribution from the finite, fixed cell size in NVT simulations, and a local contribution from the solvent shell. We show how the second contribution can be approximated without also including the finite-size contribution. Finally, we provide a "best-practices"-checklist for experimentalists planning to incorporate explicit solvation MD simulations in future work, offering guidance for improving the accuracy and reliability of structural studies using x-ray scattering methods in solution.

Ultrafast electronic, infrared, and X-ray absorption spectroscopy study of Cu(I) phosphine diimine complexes

The study aims to understand the role of the transient bonding in the interplay between the structural and electronic changes in heteroleptic Cu(I) diimine diphosphine complexes. This is an emerging class of photosensitisers which absorb in the red region of the spectrum, whilst retaining a sufficiently long excited state lifetime. Here, the dynamics of these complexes are explored by transient absorption (TA) and time-resolved infrared (TRIR) spectroscopy, which reveal ultrafast intersystem crossing and structural distortion occurring. Two potential mechanisms affecting excited state decay in these complexes involve a transient formation of a solvent adduct, made possible by the opening up of the Cu coordination centre in the excited state due to structural distortion, and by a transient coordination of the O-atom of the phosphine ligand to the copper center. X-ray absorption studies of the ground electronic state have been conducted as a prerequisite for the upcoming X-ray spectroscopy studies which will directly determine structural dynamics. The potential for these complexes to be used in bimolecular applications is confirmed by a significant yield of singlet oxygen production.

Solvent-Dependent Structural Dynamics in the Ultrafast Photodissociation Reaction of Triiodide Observed with Time-Resolved X-ray Solution Scattering

Resolving the structural dynamics of bond breaking, bond formation, and solvation is required for a deeper understanding of solution-phase chemical reactions. In this work, we investigate the photodissociation of triiodide in four solvents using femtosecond time-resolved X-ray solution scattering following 400 nm photoexcitation. Structural analysis of the scattering data resolves the solvent-dependent structural evolution during the bond cleavage, internal rearrangements, solvent-cage escape, and bond reformation in real time. The nature and structure of the reaction intermediates during the recombination are determined, elucidating the full mechanism of photodissociation and recombination on ultrafast time scales. We resolve the structure of the precursor state for recombination as a geminate pair. Further, we determine the size of the solvent cages from the refined structures of the radical pair. The observed structural dynamics present a comprehensive picture of the solvent influence on structure and dynamics of dissociation reactions.