Relationship between x-ray emission and absorption spectroscopy and the local H-bond environment in water

TDDFT and the x-ray absorption spectrum of liquid water: Finding the "best" functional

We investigate the performance of time-dependent density functional theory (TDDFT) for reproducing high-level reference x-ray absorption spectra of liquid water and water clusters. For this, we apply the integrated absolute difference (IAD) metric, previously used for x-ray emission spectra of liquid water [T. Fransson and L. G. M. Pettersson, J. Chem. Theory Comput. 19, 7333-7342 (2023)], in order to investigate which exchange-correlation (xc) functionals yield TDDFT spectra in best agreement to reference, as well as to investigate the suitability of IAD for x-ray absorption spectroscopy spectrum calculations. Considering highly asymmetric and symmetric six-molecule clusters, it is seen that long-range corrected xc-functionals are required to yield good agreement with the reference coupled cluster (CC) and algebraic-diagrammatic construction spectra, with 100% asymptotic Hartree-Fock exchange resulting in the lowest IADs. The xc-functionals with best agreement to reference have been adopted for larger water clusters, yielding results in line with recently published CC theory, but which still show some discrepancies in the relative intensity of the features compared to experiment.

Evaluating the Impact of the Tamm-Dancoff Approximation on X-ray Spectrum Calculations

The impact of the Tamm-Dancoff approximation (TDA) for time-dependent density functional theory (TDDFT) calculations of X-ray absorption and X-ray emission spectra (XAS and XES) is investigated, showing small discrepancies in the excitation energies and intensities. Through explicit diagonalization of the TDDFT Hessian, XES was considered by using full TDDFT with a core-hole reference state. This has previously not been possible with most TDDFT implementations as a result of the presence of negative eigenvalues. Furthermore, a core-valence separation (CVS) scheme for XES is presented, in which only elements including the core-hole are considered, resulting in a small Hessian with the dimension of the number of remaining occupied orbitals of the same spin as the core-hole (CH). The resulting spectra are in surprisingly good agreement with the full-space counterpart, illustrating the weak coupling between the valence-valence and valence-CH transitions. Complications resulting from contributions from the discretized continuum are discussed, which can occur for TDDFT calculations of XAS and XES and for TDA calculations of XAS. In conclusion, we recommend that TDA be used when calculating X-ray emission spectra, and either CVS-TDA or CVS-TDDFT can be used for X-ray absorption spectra.

Deciphering Density Fluctuations in the Hydration Water of Brownian Nanoparticles via Upconversion Thermometry

We investigate the intricate relationship among temperature, pH, and Brownian velocity in a range of differently sized upconversion nanoparticles (UCNPs) dispersed in water. These UCNPs, acting as nanorulers, offer insights into assessing the relative proportion of high-density and low-density liquid in the surrounding hydration water. The study reveals a size-dependent reduction in the onset temperature of liquid-water fluctuations, indicating an augmented presence of high-density liquid domains at the nanoparticle surfaces. The observed upper-temperature threshold is consistent with a hypothetical phase diagram of water, validating the two-state model. Moreover, an increase in pH disrupts the organization of water molecules, similar to external pressure effects, allowing simulation of the effects of temperature and pressure on hydrogen bonding networks. The findings underscore the significance of the surface of suspended nanoparticles for understanding high- to low-density liquid fluctuations and water behavior at charged interfaces.

Tracking Cavity Formation in Electron Solvation: Insights from X-ray Spectroscopy and Theory

We present time-resolved X-ray absorption spectra of ionized liquid water and demonstrate that OH radicals, H3O+ ions, and solvated electrons all leave distinct X-ray-spectroscopic signatures. Particularly, this allows us to characterize the electron solvation process through a tool that focuses on the electronic response of oxygen atoms in the immediate vicinity of a solvated electron. Our experimental results, supported by ab initio calculations, confirm the formation of a cavity in which the solvated electron is trapped. We show that the solvation dynamics are governed by the magnitude of the random structural fluctuations present in water. As a consequence, the solvation time is highly sensitive to temperature and to the specific way the electron is injected into water.

Calibrating TDDFT Calculations of the X-ray Emission Spectrum of Liquid Water: The Effects of Hartree-Fock Exchange

The structure and dynamics of liquid water continue to be debated, with insight provided by, among others, X-ray emission spectroscopy (XES), which shows a split in the high-energy 1b1 feature. This split is yet to be reproduced by theory, and it remains unclear if these difficulties are related to inaccuracies in dynamics simulations, spectrum calculations, or both. We investigate the performance of different methods for calculating XES of liquid water, focusing on the ability of time-dependent density functional theory (TDDFT) to reproduce reference spectra obtained by high-level coupled cluster and algebraic-diagrammatic construction scheme calculations. A metric for evaluating the agreement between theoretical spectra termed the integrated absolute difference (IAD), which considers the integral of shifted difference spectra, is introduced and used to investigate the performance of different exchange-correlation functionals. We find that computed spectra of symmetric and asymmetric model water structures are strongly and differently influenced by the amount of Hartree-Fock exchange, with best agreement to reference spectra for ∼40-50%. Lower percentages tend to yield high density of contributing states, resulting in too broad features. The method introduced here is useful also for other spectrum calculations, in particular where the performance for ensembles of structures are evaluated.

Many-body effects in the X-ray absorption spectra of liquid water

SignificanceIn X-ray absorption spectroscopy, an electron-hole excitation probes the local atomic environment. The interpretation of the spectra requires challenging theoretical calculations, particularly in a system like liquid water, where quantum many-body effects and molecular disorder play an important role. Recent advances in theory and simulation make possible new calculations that are in good agreement with experiment, without recourse to commonly adopted approximations. Based on these calculations, the three features observed in the experimental spectra are unambiguously attributed to excitonic effects with different characteristic correlation lengths, which are distinctively affected by perturbations of the underlying H-bond structure induced by temperature changes and/or by isotopic substitution. The emerging picture of the water structure is fully consistent with the conventional tetrahedral model.

Interpretation of the X-Ray Emission Spectra of Liquid Water through Temperature and Isotope Dependence

The interpretation of x-ray emission spectroscopy (XES) spectra in terms of their sensitivity to the hydrogen bonding and the consequent microheterogeneity in liquid water has been debated over a decade. To shed a light on this problem, we report the theoretical reproduction of the debated 1b_{1} peaks observed in the XES spectra of liquid water using semiclassical Kramers-Heisenberg formula. The essence of the temperature and isotope dependence of the 1b_{1} double peaks is explained by molecular dynamics simulations including full vibrational (O─H stretching, bending, and) modes, rotational combined with the density functional theory and core-hole induced dynamics. Some inconsistencies exist with the experimental XES profile, which illustrates the need to employ a more precise theoretical calculations for both geometry sampling and electronic structure using a more sophisticated procedure.

X-ray emission spectroscopy: a genetic algorithm to disentangle core–hole-induced dynamics

A genetic algorithm (GA) is developed and applied to make proper connections of final-state potential-energy surfaces and X-ray emission (XES) cross sections between steps in the time-propagation of H-bonded systems after a core–hole is created. We show that this modification results in significantly improved resolution of spectral features in XES with the semiclassical Kramers–Heisenberg approach which takes into account important interference effects. We demonstrate the effects on a water pentamer model as well as on two 17-molecules water clusters representing, respectively, tetrahedral (D2A2) and asymmetric (D1A1) H-bonding environments. For D2A2, the applied procedure improves significantly the obtained intensities, whereas for D1A1 the effects are smaller due to milder dynamics during the core–hole life-time as only one hydrogen is involved. We reinvestigate XES for liquid ethanol and, by properly disentangling the relevant states in the dense manifold of states using the GA, now resolve the important 3a′′ state as a peak rather than a shoulder. Furthermore, by applying the SpecSwap-RMC procedure, we reweigh the distribution of structures in the sampling of the liquid to fit to experiment and estimate the ratio between the main anti and gauche conformers in the liquid at room temperature. This combination of techniques will be generally applicable to challenging problems in liquid-phase spectroscopy.

Hydrogen-Bonded Structure of Water in the Loop of Anchored Polyrotaxane Chain Controlled by Anchoring Density

Hydrogen-bonded network of water surrounding polymers is expected to be one of the most relevant factors affecting biocompatibility, while the specific hydrogen-bonded structure of water responsible for biocompatibility is still under debate. Here we study the hydrogen-bonded structure of water in a loop-shaped poly(ethylene glycol) chain in a polyrotaxane using synchrotron soft X-ray emission spectroscopy. By changing the density of anchoring molecules, hydrogen-bonded structure of water confined in the poly(ethylene glycol) loop was identified. The XES profile of the confined water indicates the absence of the low energy lone-pair peak, probably because the limited space of the polymer loop entropically inhibits the formation of tetrahedrally coordinated water. The volume of the confined water can be changed by the anchoring density, which implies the ability to control the biocompatibility of loop-shaped polymers.

Relationship between Hydrogen-Bonding Motifs and the 1b1 Splitting in the X-ray Emission Spectrum of Liquid Water

The split of the 1b₁ peak observed in the X-ray emission (XE) spectrum of liquid water has been the focus of intense research. Although several hypotheses have been proposed to explain the origin of this split, a consensus has not yet been reached. Here, we introduce a novel theoretical/computation approach which, combining path-integral molecular dynamics simulations with the MB-pol model and time-dependent density functional theory calculations, predicts the 1b₁ splitting in liquid water and not in crystalline ice, in agreement with the experimental observations. A systematic analysis of the underlying local structure of liquid water at ambient conditions indicates that several different hydrogen-bonding motifs contribute to the overall XE line shape in the energy range corresponding to emissions from the 1b₁ orbitals. This suggests that it is not possible to unambiguously attribute the split of the 1b₁ peak to only two specific structural arrangements of the underlying hydrogen-bonding network.

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.

Zinc 1s Valence-to-Core X-ray Emission Spectroscopy of Halozincate Complexes

The Zn 1s valence-to-core (VtC) X-ray emission spectra of seven ionic liquids have been measured experimentally and simulated on the basis of time-dependent density-functional theory (TDDFT) calculations. Six of the ionic liquids were made by mixing [C₈C₁Im]X and Zn(II)X₂ at three different ZnX₂ mole fractions (0.33, 0.50, or 0.67) for X = Cl or Br, and a further ionic liquid was made by mixing [P_6,6,6,14]Cl and a mole fraction of ZnCl₂ of 0.33. Calculations were performed for the [ZnX₄]^2-, [Zn₂X₆]^2-, and [Zn₄X₁₀]^2- ions to capture the expected metal complex speciation. The VtC emission spectra showed three bands arising from single-electron processes that can be assigned to emission from ligand p-type orbitals, zinc d-orbitals, and ligand s-type orbitals. For all seven ionic liquids, the highest occupied molecular orbital arises from the ligand p orbitals, and the spectra for the different size metal complexes for the same X were found to be very similar, in terms of both relative peak intensities and peak energies. For both experiments and TDDFT calculations, there was an energy difference of 0.5 eV between the Cl-based and Br-based metal complexes for the ligand s and p orbitals, while the Zn 3d orbital energies were relatively unaffected by the identity of the ligand. The TDDFT calculations find that for the ions with symmetrically equivalent zinc atoms ([Zn₂X₆]^2- and [Zn₄X₁₀]^2-), the most appropriate core-ionized reference state has a core-hole that is localized on a single zinc atom. In this framework, the spectra for the larger ions can be viewed as a sum of spectra for the tetrahedral complex with a single zinc atom with small variations in the structure of the coordinating ligands. Because the spectra are relatively insensitive to small changes in the geometry of the ligands, this is consistent with the small variation in the spectra measured in the experiment.

A proposal for the structure of high- and low-density fluctuations in liquid water

Based on recent experimental data that can be interpreted as indicating the presence of specific structures in liquid water, we build and optimize two structural models which we compare with the available experimental data. To represent the proposed high-density liquid structures, we use a model consisting of chains of water molecules, and for low-density liquid, we investigate fused dodecahedra as templates for tetrahedral fluctuations. The computed infrared spectra of the models are in very good agreement with the extracted experimental spectra for the two components, while the extracted structures from molecular dynamics (MD) simulations give spectra that are intermediate between the experimentally derived spectra. Computed x-ray absorption and emission spectra as well as the O-O radial distribution functions of the proposed structures are not contradicted by experiment. The stability of the proposed dodecahedral template structures is investigated in MD simulations by seeding the starting structure, and remnants found to persist on an ∼30 ps time scale. We discuss the possible significance of such seeds in simulations and whether they can be viable candidates as templates for structural fluctuations below the compressibility minimum of liquid water.

Translational and rotational dynamics of high and low density TIP4P/2005 water

We use molecular dynamics simulations using TIP4P/2005 to investigate the self- and distinct-van Hove functions for different local environments of water, classified using the local structure index as an order parameter. The orientational dynamics were studied through the calculation of the time-correlation functions of different-order Legendre polynomials in the OH-bond unit vector. We found that the translational and orientational dynamics are slower for molecules in a low-density local environment and correspondingly the mobility is enhanced upon increasing the local density, consistent with some previous works, but opposite to a recent study on the van Hove function. From the analysis of the distinct dynamics, we find that the second and fourth peaks of the radial distribution function, previously identified as low density-like arrangements, show long persistence in time. The analysis of the time-dependent interparticle distance between the central molecule and the first coordination shell shows that particle identity persists longer than distinct van Hove correlations. The motion of two first-nearest-neighbor molecules thus remains coupled even when this correlation function has been completely decayed. With respect to the orientational dynamics, we show that correlation functions of molecules in a low-density environment decay exponentially, while molecules in a local high-density environment exhibit bi-exponential decay, indicating that dynamic heterogeneity of water is associated with the heterogeneity among high-density and between high-density and low-density species. This bi-exponential behavior is associated with the existence of interstitial waters and the collapse of the second coordination sphere in high-density arrangements, but not with H-bond strength.

Measurements of ultrafast dissociation in resonant inelastic x-ray scattering of water

There has been a discussion on the interpretation of the resonant inelastic x-ray scattering (RIXS) spectra of liquid water in terms of either different structural environments or that core hole dynamics can generate well-resolved dissociative spectral components. We have used RIXS with high resolution in the OH stretch vibration energy part, at extremely high overtones going toward the continuum of full OH bond breakage, to identify the amount of dissociative contributions in the valence band RIXS spectra at different excitation energies. We observe that at low excitation energies, corresponding to population of states with strongly antibonding character, the valence band RIXS spectra have a large contribution from a well-resolved dissociative feature. Instead, at higher excitations, this spectral component diminishes and becomes a weak structure on the high-energy side of one of the spectral peaks related to the 1b₁ state from tetrahedral configurations. This result brings both interpretations to be essential for the understanding of RIXS spectra of liquid water.

Probing hydrogen bond strength in liquid water by resonant inelastic X-ray scattering

Local probes of the electronic ground state are essential for understanding hydrogen bonding in aqueous environments. When tuned to the dissociative core-excited state at the O1s pre-edge of water, resonant inelastic X-ray scattering back to the electronic ground state exhibits a long vibrational progression due to ultrafast nuclear dynamics. We show how the coherent evolution of the OH bonds around the core-excited oxygen provides access to high vibrational levels in liquid water. The OH bonds stretch into the long-range part of the potential energy curve, which makes the X-ray probe more sensitive than infra-red spectroscopy to the local environment. We exploit this property to effectively probe hydrogen bond strength via the distribution of intramolecular OH potentials derived from measurements. In contrast, the dynamical splitting in the spectral feature of the lowest valence-excited state arises from the short-range part of the OH potential curve and is rather insensitive to hydrogen bonding.