State-dependent electron delocalization dynamics at the solute-solvent interface: soft-x-ray absorption spectroscopy and ab initio calculations

Unveiling Hidden Shake-Up Features in the Uranyl M4-Edge Spectrum

The M4,5-edge high energy resolution X-ray absorption near-edge structure (HR-XANES) spectra of actinyls offer valuable insights into the electronic structure and bonding properties of heavy-element complexes. To conduct a comprehensive spectral analysis, it is essential to employ computational methods that accurately account for relativistic effects and electron correlation. In this work, we utilize variational relativistic multireference configurational interaction methods to compute and analyze the X-ray M4-edge absorption spectrum of uranyl. By employing these advanced computational techniques, we achieve excellent agreement between the calculated spectral features and experimental observations. Moreover, the calculations unveil significant shake-up features, which arise from the intricate interplay between strongly correlated 3d core-electron and ligand excitations. This research provides important theoretical insights into the spectral characteristics of heavy-element complexes. Furthermore, it establishes the foundation for utilizing M4,5-edge spectroscopy as a means to investigate the chemical activities of such complexes. By leveraging this technique, we can gain a deeper understanding of the bonding behavior and reactivity of heavy-element compounds.

Interpreting the Cu-O2 Antibonding Nature in Two Cu-O2 Complexes from Cu L-Edge X-ray Absorption Spectra

Cu-O2 structures play important roles in bioinorganic chemistry and enzyme catalysis, where the bonding between the Cu and O2 parts serves as a fundamental research concern. Here, we performed a multiconfigurational study on the copper L2,3-edge X-ray absorption spectra (XAS) of two copper enzyme model complexes to gain a better understanding of the antibonding nature from the clearly interpreted structure-spectroscopy relation. We obtained spectra in good agreement with the experiments by using the restricted active space second-order perturbation theory (RASPT2) method, which facilitated reliable chemical analysis. Spectral feature interpretations were supported by computing the spin-orbit natural transition orbitals. All major features were assigned to be mainly from Cu 2p to antibonding orbitals between Cu 3d and O2 π*, Cu 3d-πO-O* (type A), and a few also to mixed antibonding/bonding orbitals between Cu 3d and O2 π, Cu 3d ± πO-O (type M). Our calculations provided a clear illustration of the interactions between Cu 3d and O2 π*/π orbitals that are carried in the metal L-edge XAS.

Electronic Structure of the Complete Series of Gas-Phase Manganese Acetylacetonates by X-ray Absorption Spectroscopy

Metal centers in transition metal-ligand complexes occur in a variety of oxidation states causing their redox activity and therefore making them relevant for applications in physics and chemistry. The electronic state of these complexes can be studied by X-ray absorption spectroscopy, which is, however, due to the complex spectral signature not always straightforward. Here, we study the electronic structure of gas-phase cationic manganese acetylacetonate complexes Mn(acac)1-3+ using X-ray absorption spectroscopy at the metal center and ligand constituents. The spectra are well reproduced by multiconfigurational wave function theory, time-dependent density functional theory as well as parameterized crystal field and charge transfer multiplet simulations. This enables us to get detailed insights into the electronic structure of ground-state Mn(acac)1-3+ and extract empirical parameters such as crystal field strength and exchange coupling from X-ray excitation at both the metal and ligand sites. By comparison to X-ray absorption spectra of neutral, solvated Mn(acac)2,3 complexes, we also show that the effect of coordination on the L3 excitation energy, routinely used to identify oxidation states, can contribute about 40-50% to the observed shift, which for the current study is 1.9 eV per oxidation state.

X-ray absorption spectra of f-element complexes: insight from relativistic multiconfigurational wavefunction theory

X-ray absorption near edge structure (XANES) spectroscopy, coupled with ab initio calculations, has emerged as the state-of-the-art tool for elucidating the metal-ligand bonding in f-element complexes. This highlight presents recent efforts in calculating XANES spectra of lanthanide and actinide compounds with relativistic multiconfiguration wavefunction approaches that account for differences in donation bonding in the ground state (GS) versus a core-excited state (ES), multiplet effects, and spin-orbit-coupling. With the GS and ES wavefunctions available, including spin-orbit effects, an arsenal of chemical bonding tools that are popular among chemists can be applied to rationalize the observed intensities in terms of covalent bonding.

Soft x-ray signatures of ionic manganese-oxo systems, including a high-spin manganese(V) complex

Manganese-oxo species catalyze key reactions, including C–H bond activation or dioxygen formation in natural photosynthesis. To better understand relevant reaction intermediates, we characterize electronic states and geometric structures of [MnOn]+...

Covalency in Actinide(IV) Hexachlorides in Relation to Chlorine K­-Edge X­-ray Absorption Structure

Chlorine K-edge X-ray absorption near edge structure (XANES) in actinide^IV hexachlorides, [AnCl₆]²⁻ (An = Th–Pu), is calculated with relativistic multiconfiguration wavefunction theory (WFT). Of particular focus is a 3-peak feature emerging from U toward Pu, and its assignment in terms of donation bonding to the An 5f vs. 6d shells. With or without spin–orbit coupling, the calculated and previously measured XANES spectra are in excellent agreement with respect to relative peak positions, relative peak intensities, and peak assignments. Metal–ligand bonding analyses from WFT and Kohn–Sham theory (KST) predict comparable An 5f and 6d covalency from U to Np and Pu. Although some frontier molecular orbitals in the KST calculations display increasing An 5f–Cl 3p mixing from Th to Pu, because of energetic stabilization of 5f relative to the Cl 3p combinations of the matching symmetry, increasing hybridization is neither seen in the WFT natural orbitals, nor is it reflected in the calculated bond orders. The appearance of the pre-edge peaks from U to Pu and their relative intensities are rationalized simply by the energetic separation of transitions to 6d t_2gversus transitions to weakly-bonded and strongly stabilized a_2u, t_2u and t_1u orbitals with 5f character. The study highlights potential pitfalls when interpreting XANES spectra based on ground state Kohn–Sham molecular orbitals.

Chlorine K-edge XANES of An(iv) hexachlorides, calculated with multiconfiguration wavefunction theory, is interpreted in terms of similar metal–ligand covalency along the An = Th–Pu series.

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.

Theoretical Calculation of Core-Excited States along Dissociative Pathways beyond Second-Order Perturbation Theory

We extend the multireference driven similarity renormalization (MR-DSRG) method to compute core-excited states by combining it with a GASSCF treatment of orbital relaxation and static electron correlation effects. We consider MR-DSRG treatments of dynamical correlation truncated at the level of perturbation theory (DSRG-MRPT2/3) and iterative linearized approximations with one- and two-body operators [MR-LDSRG(2)] in combination with a spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects. This approach is calibrated and tested on a series of 16 core-excited states of five closed- and open-shell diatomic molecules containing first-row elements (C, N, and O). All GASSCF-MR-DSRG theories show excellent agreement with experimental adiabatic transitions energies, with mean absolute errors ranging between 0.17 and 0.35 eV, even for the challenging partially doubly excited states of the N₂⁺ molecule. The vibrational structure of all these transitions, obtained from using a full potential energy scan, shows a mean absolute error as low as 25 meV for DSRG-MRPT2 and 12/13 meV for DSRG-MRPT3 and MR-LDSRG(2). We generally find that a treatment of dynamical correlation that goes beyond the second-order level in perturbation theory improves the accuracy of the potential energy surface, especially in the bond-dissociation region.

Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra

X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structures, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra are complicated by both relativistic effects, including spin-orbit coupling and the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space (RAS) configuration interaction scheme that uses an exact two-component state-averaged complete active space self-consistent-field method, which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a RAS configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron-containing complexes, with results showing key features of the spectrum being reproduced, including ligand-to-metal charge transfer and shake-up excitations.

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.

Origin of core-to-core x-ray emission spectroscopy sensitivity to structural dynamics

Recently, coherent structural dynamics in the excited state of an iron photosensitizer was observed through oscillations in the intensity of Kα x-ray emission spectroscopy (XES). Understanding the origin of the unexpected sensitivity of core-to-core transitions to structural dynamics is important for further development of femtosecond time-resolved XES methods and, we believe, generally necessary for interpretation of XES signals from highly non-equilibrium structures that are ubiquitous in photophysics and photochemistry. Here, we use multiconfigurational wavefunction calculations combined with atomic theory to analyze the emission process in detail. The sensitivity of core-to-core transitions to structural dynamics is due to a shift of the minimum energy metal-ligand bond distance between 1s and 2p core-hole states. A key effect is the additional contraction of the non-bonding 3s and 3p orbitals in 1s core-hole states, which decreases electron-electron repulsion and increases overlap in the metal-ligand bonds. The effect is believed to be general and especially pronounced for systems with strong bonds. The important role of 3s and 3p orbitals is consistent with the analysis of radial charge and spin densities and can be connected to the negative chemical shift observed for many transition metal complexes. The XES sensitivity to structural dynamics can be optimized by tuning the emission energy spectrometer, with oscillations up to ±4% of the maximum intensity for the current system. The theoretical predictions can be used to design experiments that separate electronic and nuclear degrees of freedom in ultrafast excited state dynamics.

Modern quantum chemistry with [Open]Molcas

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

Simulations of valence excited states in coordination complexes reached through hard X-ray scattering

Hard X-ray spectroscopy selectively probes metal sites in complex environments. Resonant inelastic X-ray scattering (RIXS) makes it is possible to directly study metal-ligand interactions through local valence excitations. Here multiconfigurational wavefunction simulations are used to model valence K pre-edge RIXS for three metal-hexacyanide complexes by coupling the electric dipole-forbidden excitations with dipole-allowed valence-to-core emission. Comparisons between experimental and simulated spectra makes it possible to evaluate the simulation accuracy and establish a best-modeling practice. The calculations give correct descriptions of all LMCT excitations in the spectra, although energies and intensities are sensitive to the description of dynamical electron correlation. The consistent treatment of all complexes shows that simulations can rationalize spectral features. The dispersion in the manganese(iii) spectrum comes from unresolved multiple resonances rather than fluorescence, and the splitting is mainly caused by differences in spatial orientation between holes and electrons. The simulations predict spectral features that cannot be resolved in current experimental data sets and the potential for observing d-d excitations is also explored. The latter can be of relevance for non-centrosymmetric systems with more intense K pre-edges. These ab initio simulations can be used to both design and interpret high-resolution X-ray scattering experiments.

Ab Initio Study of Covalency in the Ground versus Core-Excited States and X-ray Absorption Spectra of Actinide Complexes

Relativistic multireference ab initio wave function calculations within the restricted active space (RAS) framework were performed to calculate metal and ligand X-ray absorption (XAS) near-edge spectroscopy (XANES) intensities for the metal M_4,5 edges of [PuO₂(H₂O)₅]²⁺, [An^VIO₂]²⁺ (An = U, Np, Pu), and [AmCl₆]^3- and the Cl K edge of the Am complex. The extent of An(5f)-ligand bonding was determined via natural localized molecular orbital analyses of the relevant spin-orbit coupled multireference states. The calculated spectra are in good agreement with experiments and allow a detailed assignment of the observed spectral features. The XANES M_4,5-edge spectra are representative of the actinide orbital covalency in the probed core-excited states, which may be different from the ground-state covalency. An assignment of ground-state An orbital covalency based on XAS spectra should therefore be made with caution.

Ultrafast Spin-State Dynamics in Transition-Metal Complexes Triggered by Soft-X-Ray Light

Recent advances in attosecond physics provide access to the correlated motion of valence and core electrons on their intrinsic timescales. For valence excitations, processes related to the electron spin are usually driven by nuclear motion. For core-excited states, where the core hole has a nonzero angular momentum, spin-orbit coupling is strong enough to drive spin flips on a much shorter time scale. Here, unprecedented short spin crossover is demonstrated for L-edge (2p→3d) excited states of a prototypical Fe(II) complex. It occurs on a time scale, which is faster than the core-hole lifetime of about 4 fs and can be manipulated by the excitation conditions. A detailed analysis of such phenomena will help to gain a fundamental understanding of spin-crossover processes and establish the basis for their control by light.

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.

Identification of the dominant photochemical pathways and mechanistic insights to the ultrafast ligand exchange of Fe(CO)5 to Fe(CO)4EtOH

We utilized femtosecond time-resolved resonant inelastic X-ray scattering and ab initio theory to study the transient electronic structure and the photoinduced molecular dynamics of a model metal carbonyl photocatalyst Fe(CO)5 in ethanol solution. We propose mechanistic explanation for the parallel ultrafast intra-molecular spin crossover and ligation of the Fe(CO)4 which are observed following a charge transfer photoexcitation of Fe(CO)5 as reported in our previous study [Wernet et al., Nature 520, 78 (2015)]. We find that branching of the reaction pathway likely happens in the (1)A1 state of Fe(CO)4. A sub-picosecond time constant of the spin crossover from (1)B2 to (3)B2 is rationalized by the proposed (1)B2 → (1)A1 → (3)B2 mechanism. Ultrafast ligation of the (1)B2 Fe(CO)4 state is significantly faster than the spin-forbidden and diffusion limited ligation process occurring from the (3)B2 Fe(CO)4 ground state that has been observed in the previous studies. We propose that the ultrafast ligation occurs via (1)B2 → (1)A1 → (1)A' Fe(CO)4EtOH pathway and the time scale of the (1)A1 Fe(CO)4 state ligation is governed by the solute-solvent collision frequency. Our study emphasizes the importance of understanding the interaction of molecular excited states with the surrounding environment to explain the relaxation pathways of photoexcited metal carbonyls in solution.

Undistorted X-ray Absorption Spectroscopy Using s-Core-Orbital Emissions

Detection of secondary emissions, fluorescence yield (FY), or electron yield (EY), originating from the relaxation processes upon X-ray resonant absorption has been widely adopted for X-ray absorption spectroscopy (XAS) measurements when the primary absorption process cannot be probed directly in transmission mode. Various spectral distortion effects inherent in the relaxation processes and in the subsequent transportation of emitted particles (electron or photon) through the sample, however, undermine the proportionality of the emission signals to the X-ray absorption coefficient. In the present study, multiple radiative (FY) and nonradiative (EY) decay channels have been experimentally investigated on a model system, FeCl3 aqueous solution, at the excitation energy of the Fe L-edge. The systematic comparisons between the experimental spectra taken from various decay channels, as well as the comparison with the theoretically simulated Fe L-edge XA spectrum that involves only the absorption process, indicate that the detection of the Fe 3s → 2p partial fluorescence yield (PFY) gives rise to the true Fe L-edge XA spectrum. The two key characteristics generalized from this particular decay channel-zero orbital angular momentum (i.e., s orbital) and core-level emission-set a guideline for obtaining undistorted X-ray absorption spectra in the future.

Joint Analysis of Radiative and Non-Radiative Electronic Relaxation Upon X-ray Irradiation of Transition Metal Aqueous Solutions

L-edge soft X-ray spectroscopy has been proven to be a powerful tool to unravel the peculiarities of electronic structure of transition metal compounds in solution. However, the X-ray absorption spectrum is often probed in the total or partial fluorescence yield modes, what leads to inherent distortions with respect to the true transmission spectrum. In the present work, we combine photon- and electron-yield experimental techniques with multi-reference first principles calculations. Exemplified for the prototypical FeCl2 aqueous solution we demonstrate that the partial yield arising from the Fe3s → 2p relaxation is a more reliable probe of the absorption spectrum than the Fe3d → 2p one. For the bonding-relevant 3d → 2p channel we further provide the basis for the joint analysis of resonant photoelectron and inelastic X-ray scattering spectra. Establishing the common energy reference allows to assign both spectra using the complementary information provided through electron-out and photon-out events.

Multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling

X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due to the multi-configurational and spin-mixed nature of the many-electron wave function. Here, the restricted active space self-consistent field method including spin-orbit coupling is used to cope with this challenge and to calculate valence- and core-level photoelectron spectra. The intensities are estimated within the frameworks of the Dyson orbital formalism and the sudden approximation. Thereby, we utilize an efficient computational algorithm that is based on a biorthonormal basis transformation. The approach is applied to the valence photoionization of the gas phase water molecule and to the core ionization spectrum of the [Fe(H2O)6](2+) complex. The results show good agreement with the experimental data obtained in this work, whereas the sudden approximation demonstrates distinct deviations from experiments.

Synchrotron soft X-ray absorption spectroscopy study of carbon and silicon nanostructures for energy applications

Carbon and silicon materials are two of the most important materials involved in the history of the science and technology development. In the last two decades, C and Si nanoscale materials, e.g., carbon nanotubes, graphene, and silicon nanowires, and quantum dots, have also emerged as the most interesting nanomaterials in nanoscience and nanotechnology for their myriad promising applications such as for electronics, sensors, biotechnology, etc. In particular, carbon and silicon nanostructures are being utilized in energy-related applications such as catalysis, batteries, solar cells, etc., with significant advances. Understanding of the nature of surface and electronic structures of nanostructures plays a key role in the development and improvement of energy conversion and storage nanosystems. Synchrotron soft X-ray absorption spectroscopy (XAS) and related techniques, such as X-ray emission spectroscopy (XES) and scanning transmission X-ray microscopy (STXM), show unique capability in revealing the surface and electronic structures of C and Si nanomaterials. In this review, XAS is demonstrated as a powerful technique for probing chemical bonding, the electronic structure, and the surface chemistry of carbon and silicon nanomaterials, which can greatly enhance the fundamental understanding and also applicability of these nanomaterials in energy applications. The focus is on the unique advantages of XAS as a complementary tool to conventional microscopy and spectroscopy for effectively providing chemical and structural information about carbon and silicon nanostructures. The employment of XAS for in situ, real-time study of property evolution of C and Si nanostructures to elucidate the mechanisms in energy conversion or storage processes is also discussed.

Distinguishing between High- and Low-Spin States for Divalent Mn in Mn-Based Prussian Blue Analogue by High-Resolution Soft X-ray Emission Spectroscopy

We combine Mn L2,3-edge X-ray absorption, high resolution Mn 2p-3d-2p resonant X-ray emission, and configuration-interaction full-multiplet (CIFM) calculation to analyze the electronic structure of Mn-based Prussian blue analogue. We clarified the Mn 3d energy diagram for the Mn(2+) low-spin state separately from that of the Mn(2+) high-spin state by tuning the excitation energy for the X-ray emission measurement. The obtained X-ray emission spectra are generally reproduced by the CIFM calculation for the Mn(2+) low spin state having a stronger ligand-to-metal charge-transfer effect between Mn t2g and CN π orbitals than the Mn(2+) high spin state. The d-d-excitation peak nearest to the elastic scattering was ascribed to the Mn(2+) LS state by the CIFM calculation, indicating that the Mn(2+) LS state with a hole on the t2g orbital locates near the Fermi level.

Incisive probing of intermolecular interactions in molecular crystals: core level spectroscopy combined with density functional theory

The α-form of crystalline para-aminobenzoic acid (PABA) has been examined as a model system for demonstrating how the core level spectroscopies X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine-structure (NEXAFS) can be combined with CASTEP density functional theory (DFT) to provide reliable modeling of intermolecular bonding in organic molecular crystals. Through its dependence on unoccupied valence states NEXAFS is an extremely sensitive probe of variations in intermolecular bonding. Prediction of NEXAFS spectra by CASTEP, in combination with core level shifts predicted by WIEN2K, reproduced experimentally observed data very well when all significant intermolecular interactions were correctly taken into account. CASTEP-predicted NEXAFS spectra for the crystalline state were compared with those for an isolated PABA monomer to examine the impact of intermolecular interactions and local environment in the solid state. The effects of the loss of hydrogen-bonding in carboxylic acid dimers and intermolecular hydrogen bonding between amino and carboxylic acid moieties are evident, with energy shifts and intensity variations of NEXAFS features arising from the associated differences in electronic structure and bonding.