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.

A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-3 He2 @C60.

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two 3 He atoms encapsulated in C60 . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-3 He2 @C60 ) and triplet (ortho-3 He2 @C60 ) nuclear spin configurations, respectively. The ortho-3 He2 @C60 ground state is 5.69 cm-1 higher in energy than the para-3 He2 @C60 ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C60 embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of 3 He2 @C60 .

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.

Symmetry-resolved CO desorption and oxidation dynamics on O/Ru(0001) probed at the C K-edge by ultrafast x-ray spectroscopy.

We report on carbon monoxide desorption and oxidation induced by 400 nm femtosecond laser excitation on the O/Ru(0001) surface probed by time-resolved x-ray absorption spectroscopy (TR-XAS) at the carbon K-edge. The experiments were performed under constant background pressures of CO (6 × 10-8 Torr) and O2 (3 × 10-8 Torr). Under these conditions, we detect two transient CO species with narrow 2π* peaks, suggesting little 2π* interaction with the surface. Based on polarization measurements, we find that these two species have opposing orientations: (1) CO favoring a more perpendicular orientation and (2) CO favoring a more parallel orientation with respect to the surface. We also directly detect gas-phase CO2 using a mass spectrometer and observe weak signatures of bent adsorbed CO2 at slightly higher x-ray energies than the 2π* region. These results are compared to previously reported TR-XAS results at the O K-edge, where the CO background pressure was three times lower (2 × 10-8 Torr) while maintaining the same O2 pressure. At the lower CO pressure, in the CO 2π* region, we observed adsorbed CO and a distribution of OC-O bond lengths close to the CO oxidation transition state, with little indication of gas-like CO. The shift toward "gas-like" CO species may be explained by the higher CO exposure, which blocks O adsorption, decreasing O coverage and increasing CO coverage. These effects decrease the CO desorption barrier through dipole-dipole interaction while simultaneously increasing the CO oxidation barrier.

Adsorption energies on transition metal surfaces: towards an accurate and balanced description.

Density functional theory predictions of binding energies and reaction barriers provide invaluable data for analyzing chemical transformations in heterogeneous catalysis. For high accuracy, effects of band structure and coverage, as well as the local bond strength in both covalent and non-covalent interactions, must be reliably described and much focus has been put on improving functionals to this end. Here, we show that a correction from higher-level calculations on small metal clusters can be applied to improve periodic band structure adsorption energies and barriers. We benchmark against 38 reliable experimental covalent and non-covalent adsorption energies and five activation barriers with mean absolute errors of 2.2 kcal mol-1, 2.7 kcal mol-1, and 1.1 kcal mol-1, respectively, which are lower than for functionals widely used and tested for surface science evaluations, such as BEEF-vdW and RPBE.

In Situ Surface-Sensitive Investigation of Multiple Carbon Phases on Fe(110) in the Fischer-Tropsch Synthesis.

Carbide formation on iron-based catalysts is an integral and, arguably, the most important part of the Fischer-Tropsch synthesis process, converting CO and H2 into synthetic fuels and numerous valuable chemicals. Here, we report an in situ surface-sensitive study of the effect of pressure, temperature, time, and gas feed composition on the growth dynamics of two distinct iron-carbon phases with the octahedral and trigonal prismatic coordination of carbon sites on an Fe(110) single crystal acting as a model catalyst. Using a combination of state-of-the-art X-ray photoelectron spectroscopy at an unprecedentedly high pressure, high-energy surface X-ray diffraction, mass spectrometry, and theoretical calculations, we reveal the details of iron surface carburization and product formation under semirealistic conditions. We provide a detailed insight into the state of the catalyst's surface in relation to the reaction.

Simulations of x-ray absorption spectra for CO desorbing from Ru(0001) with transition-potential and time-dependent density functional theory approaches.

The desorption of a carbon monoxide molecule from a Ru(0001) surface was studied by means of X-ray Absorption Spectra (XAS) computed with Transition Potential (TP-DFT) and Time Dependent (TD-DFT) DFT methods. By unraveling the evolution of the CO electronic structure upon desorption, we observed that at 2.3 Å from the surface, the CO molecule has already predominantly gas-phase character. While C 1s XAS is quite insensitive to changes in the C-O bond length, the O 1s excitation is very sensitive with the π* coming down in energy upon CO bond stretching, which competes with the increase in orbital energy due to the repulsive interaction with the metallic surface. We show in a systematic way that the TP-DFT method can describe the XAS rather well at the endpoints (chemisorbed and gas phase) but is affected by artificial charge transfer and/or incorrect spin treatment in the transition region in cases like CO, where there are low-lying π* orbitals and large exchange interactions between the core 1s and valence-acceptor π* orbitals. As an alternative, we demonstrate by comparing with experimental data that a linear response approach using TD-DFT employing common exchange-correlation functionals and finite-size clusters can yield a good description of the spectral evolution of the 1s → π* transition with correct spin and gas-to-chemisorbed chemical shifts in good agreement with experiment.

Electrocatalytic Glycerol Oxidation with Concurrent Hydrogen Evolution Utilizing an Efficient MoOx /Pt Catalyst.

Glycerol electrolysis affords a green and energetically favorable route for the production of value-added chemicals at the anode and H2 production in parallel at the cathode. Here, a facile method for trapping Pt nanoparticles at oxygen vacancies of molybdenum oxide (MoOx ) nanosheets, yielding a high-performance MoOx /Pt composite electrocatalyst for both the glycerol oxidation reaction (GOR) and the hydrogen evolution reaction (HER) in alkaline electrolytes, is reported. Combined electrochemical experiments and theoretical calculations reveal the important role of MoOx nanosheets for the adsorption of glycerol molecules in GOR and the dissociation of water molecules in HER, as well as the strong electronic interaction with Pt. The MoOx /Pt composite thus significantly enhances the specific mass activity of Pt and the kinetics for both reactions. With MoOx /Pt electrodes serving as both cathode and anode, two-electrode glycerol electrolysis is achieved at a cell voltage of 0.70 V to reach a current density of 10 mA cm-2 , which is 0.90 V less than that required for water electrolysis.

Nanoscale Spatial Distribution of Supported Nanoparticles Controls Activity and Stability in Powder Catalysts for CO Oxidation and Photocatalytic H2 Evolution.

Supported metal nanoparticles are essential components of high-performing catalysts, and their structures are intensely researched. In comparison, nanoparticle spatial distribution in powder catalysts is conventionally not quantified, and the influence of this collective property on catalyst performance remains poorly investigated. Here, we demonstrate a general colloidal self-assembly method to control uniformity of nanoparticle spatial distribution on common industrial powder supports. We quantify distributions on the nanoscale using image statistics and show that the type of nanospatial distribution determines not only the stability, but also the activity of heterogeneous catalysts. Widely investigated systems (Au-TiO2 for CO oxidation thermocatalysis and Pd-TiO2 for H2 evolution photocatalysis) were used to showcase the universal importance of nanoparticle spatial organization. Spatially and temporally resolved microkinetic modeling revealed that nonuniformly distributed Au nanoparticles suffer from local depletion of surface oxygen, and therefore lower CO oxidation activity, as compared to uniformly distributed nanoparticles. Nanoparticle spatial distribution also determines the stability of Pd-TiO2 photocatalysts, because nonuniformly distributed nanoparticles sinter while uniformly distributed nanoparticles do not. This work introduces new tools to evaluate and understand catalyst collective (ensemble) properties in powder catalysts, which thereby pave the way to more active and stable heterogeneous catalysts.

Accurate SCC-DFTB Parametrization for Bulk Water.

The SCC-DFTB repulsion parameters based on the material science set (matsci) were redesigned to describe the structure and dynamic properties of bulk liquid water. The iterative Boltzman inversion (IBI) approach was applied by simultaneously correcting the O-H and O-O SCC-DFTB repulsion energy contribution to develop the new water-matsci and water-matsci-UFF set of parameters. The water-matsci parameters provide O-O and O-H radial distribution functions in excellent agreement with available state-of-the-art experimental data. The parametrization is applied to compute binding energies of a set of water clusters with 2-10 molecules and compared to other DFTB parameters and reference data. The self-diffusion coefficients of ambient and supercooled (254 K) water have been estimated and compared to other SCC-DFTB calculated values and experiment. The performance of the new parameters for describing the density of ambient water and reactions involving water dissociation into H3O+ and OH-, the self-diffusion coefficient, and neutralization energy were investigated. Finally, we show that the new parametrization can be reliably applied to adsorption of water on the mineral pyrite by combining the new water-matsci parameters with the available matsci set of parameters for pyrite. This opens opportunities for investigating materials and phenomena of increasing complexity involving water.

Time-resolved observation of transient precursor state of CO on Ru(0001) using carbon K-edge spectroscopy.

The transient dynamics of carbon monoxide (CO) molecules on a Ru(0001) surface following femtosecond optical laser pump excitation has been studied by monitoring changes in the unoccupied electronic structure using an ultrafast X-ray free-electron laser (FEL) probe. The particular symmetry of perpendicularly chemisorbed CO on the surface is exploited to investigate how the molecular orientation changes with time by varying the polarization of the FEL pulses. The time evolution of spectral features corresponding to the desorption precursor state was well distinguished due to the narrow line-width of the C K-edge in the X-ray absorption (XA) spectrum, illustrating that CO molecules in the precursor state rotated freely and resided on the surface for several picoseconds. Most of the CO molecules trapped in the precursor state ultimately cooled back down to the chemisorbed state, while we estimate that ∼14.5 ± 4.9% of the molecules in the precursor state desorbed into the gas phase. It was also observed that chemisorbed CO molecules diffused over the metal surface from on-top sites toward highly coordinated sites. In addition, a new "vibrationally hot precursor" state was identified in the polarization-dependent XA spectra.

Radial distribution functions of water: Models vs experiments.

We study the temperature behavior of the first four peaks of the oxygen-oxygen radial distribution function of water, simulated by the TIP4P/2005, MB-pol, TIP5P, and SPC/E models and compare to experimental X-ray diffraction data, including a new measurement which extends down to 235 K [H. Pathak et al., J. Chem. Phys. 150, 224506 (2019)]. We find the overall best agreement using the MB-pol and TIP4P/2005 models. We observe, upon cooling, a minimum in the position of the second shell simulated with TIP4P/2005 and SPC/E potentials, located close to the temperature of maximum density. We also calculated the two-body entropy and the contributions coming from the first, second, and outer shells to this quantity. We show that, even if the main contribution comes from the first shell, the contribution of the second shell can become important at low temperature. While real water appears to be less ordered at short distance than obtained by any of the potentials, the different water potentials show more or less order compared to the experiments depending on the considered length-scale.

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.

X-ray absorption spectrum simulations of hexagonal ice.

We calibrate basis sets and performance of two theoretical approaches to compute X-ray absorption spectra (XAS) of condensed water by comparison to experiments on hexagonal ice Ih. We apply both the transition-potential half-core-hole approach and the complex polarization propagator using four different models of the crystal with increasing oxygen and proton disorder but find poor agreement with experiments. We note that there are large variations in experimental spectra depending on detection mode and how the ice samples were prepared, which leads us to critically investigate what structures were actually prepared and measured in each case. This is done by using a Monte Carlo-based fitting technique which fits the spectra based on a library of precomputed spectra and assigns weights to contributions from different model structures. These are then used to generate O-O and O-H radial distribution functions and tetrahedrality parameters associated with each of the measured spectra. We find that all spectra are associated with sharp peaks at the oxygen positions in the perfect lattice, but with significant disorder around these positions. We suggest that presently available XAS of hexagonal ice are not fully representative of the perfect crystalline lattice, but contain varying amounts of defects and possible contributions from low-density amorphous ice.

Atom-specific activation in CO oxidation.

We report on atom-specific activation of CO oxidation on Ru(0001) via resonant X-ray excitation. We show that resonant 1s core-level excitation of atomically adsorbed oxygen in the co-adsorbed phase of CO and oxygen directly drives CO oxidation. We separate this direct resonant channel from indirectly driven oxidation via X-ray induced substrate heating. Based on density functional theory calculations, we identify the valence-excited state created by the Auger decay as the driving electronic state for direct CO oxidation. We utilized the fresh-slice multi-pulse mode at the Linac Coherent Light Source that provided time-overlapped and 30 fs delayed pairs of soft X-ray pulses and discuss the prospects of femtosecond X-ray pump X-ray spectroscopy probe, as well as X-ray two-pulse correlation measurements for fundamental investigations of chemical reactions via selective X-ray excitation.

Coherent X-rays reveal the influence of cage effects on ultrafast water dynamics.

The dynamics of liquid water feature a variety of time scales, ranging from extremely fast ballistic-like thermal motion, to slower molecular diffusion and hydrogen-bond rearrangements. Here, we utilize coherent X-ray pulses to investigate the sub-100 fs equilibrium dynamics of water from ambient conditions down to supercooled temperatures. This novel approach utilizes the inherent capability of X-ray speckle visibility spectroscopy to measure equilibrium intermolecular dynamics with lengthscale selectivity, by measuring oxygen motion in momentum space. The observed decay of the speckle contrast at the first diffraction peak, which reflects tetrahedral coordination, is attributed to motion on a molecular scale within the first 120 fs. Through comparison with molecular dynamics simulations, we conclude that the slowing down upon cooling from 328 K down to 253 K is not due to simple thermal ballistic-like motion, but that cage effects play an important role even on timescales over 25 fs due to hydrogen-bonding.

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

The connection between specific features in the water X-ray absorption spectrum and X-ray emission spectrum (XES) and the local H-bond coordination is studied based on structures obtained from path-integral molecular dynamics simulations using either the opt-PBE-vdW density functional or the MB-pol force field. Computing the XES spectrum using all molecules in a snapshot results in only one peak in the lone-pair (1b1) region, while the experiment shows two peaks separated by 0.8-0.9 eV. Different H-bond configurations were classified based on the local structure index (LSI) and a geometrical H-bond cone criterion. We find that tetrahedrally coordinated molecules characterized by high LSI values and two strong donated and two strong accepted H-bonds contribute to the low energy 1b1 emission peak and to the post-edge region in absorption. Molecules with the asymmetric H-bond environment with one strong accepted H-bond and one strong donated H-bond and low LSI values give rise to the high energy 1b1 peak in the emission spectrum and mainly contribute to the pre-edge and main-edge in the absorption spectrum. The 1b1 peak splitting can be increased to 0.62 eV by imposing constraints on the H-bond length, i.e., for very tetrahedral structures short H-bonds (less than 2.68 Å) and for very asymmetric structures elongated H-bonds (longer than 2.8 Å). Such structures are present, but underrepresented, in the simulations which give more of an average of the two extremes.