Selective gating to vibrational modes through resonant X-ray scattering

Deconvolution of the X-ray absorption spectrum of trans-1,3-butadiene with resonant Auger spectroscopy

High-resolution carbon K-edge X-ray photoelectron, X-ray absorption, non-resonant and resonant Auger spectra are presented of gas phase trans-1,3-butadiene alongside a detailed theoretical analysis utilising nuclear ensemble approaches and vibronic models to simulate the spectroscopic observables. The resonant Auger spectra recorded across the first pre-edge band reveal a complex evolution of different electronic states which remain relatively well-localised on the edge or central carbon sites. The results demonstrate the sensitivity of the resonant Auger observables to the weighted contributions from multiple electronic states. The gradually evolving spectral features can be accurately and feasibly simulated within nuclear ensemble methods and interpreted with the population analysis.

Quantifying vibronic coupling with resonant inelastic X-ray scattering

Electron–phonon interactions are fundamental to the behavior of chemical and physical systems.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory for Accurate X-ray Absorption Spectroscopy

It is demonstrated that the challenging core-hole particle (CHP) orbital relaxation for core electron spectra can be readily achieved by the mixed-reference spin-flip (MRSF)-time-dependent density functional theory (TDDFT). With the additional scalar relativistic effects on K-edge excitation energies of 24 second- and 17 third-row molecules, the particular ΔCHP-MRSF(R) exhibited near perfect predictions with RMSE ∼0.5 eV, featuring a median value of 0.3 and an interquartile range of 0.4. Overall, the CHP effect is 2-4 times stronger than relativistic ones, contributing more than 20 eV in the cases of sulfur and chlorine third-row atoms. Such high precision allows to explain the splitting and spectral shapes of O, N, and C atom K-edges in the ground state of thymine with atom as well as orbital specific accuracy. The same protocol with a double hole particle relaxation also produced remarkably accurate K-edge spectra of core to valence hole excitation energies from the first (n_O8π*) and second (ππ*) excited states of thymine, confirming the assignment of 1s → n excitation for the experimentally observed 526.4 eV peak. Regarding both accuracy and practicality, therefore, MRSF-TDDFT provides a promising protocol for core electron spectra of both ground and excited electronic states alike.

X-ray absorption of molecular cations-a new challenge for electronic structure theory

In this paper we put forward some historical notes on the development of computational chemistry toward applications of x-ray spectroscopies. We highlight some of the important contributions by Enrico Clementi as method and program developer and as a supporter of this branch of computational research. We bring up a modern example based on the very recent experimental development of x-ray absorption of cationic molecules. As we show this spectroscopy poses new challenges for electronic structure theory and the electron correlation problem.

Cuts through the manifold of molecular H2O potential energy surfaces in liquid water at ambient conditions

Liquid water at ambient conditions is ubiquitous in chemistry and biology as well as in technology, energy, and atmospheric processes. Since parts of the phase diagram of water are unsettled—most notably the supercooled liquid homogeneous nucleation region—repercussions thereof on our molecular-level understanding for even the common ambient conditions remain. Breathtaking advances in X-ray–based approaches over the last decade give us now the tools to derive molecular potential energy surfaces as a quantitative view on the molecular manifold within the fluctuating hydrogen bonding network. With selective cuts along the local asymmetric O–H bond coordinate and the symmetric normal mode excitations an experimental foundation to benchmark competing molecular-level models of water has been achieved.

The fluctuating hydrogen bridge bonded network of liquid water at ambient conditions entails a varied ensemble of the underlying constituting H₂O molecular moieties. This is mirrored in a manifold of the H₂O molecular potentials. Subnatural line width resonant inelastic X-ray scattering allowed us to quantify the manifold of molecular potential energy surfaces along the H₂O symmetric normal mode and the local asymmetric O–H bond coordinate up to 1 and 1.5 Å, respectively. The comparison of the single H₂O molecular potentials and spectroscopic signatures with the ambient conditions liquid phase H₂O molecular potentials is done on various levels. In the gas phase, first principles, Morse potentials, and stepwise harmonic potential reconstruction have been employed and benchmarked. In the liquid phase the determination of the potential energy manifold along the local asymmetric O–H bond coordinate from resonant inelastic X-ray scattering via the bound state oxygen 1s to 4a1 resonance is treated within these frameworks. The potential energy surface manifold along the symmetric stretch from resonant inelastic X-ray scattering via the oxygen 1s to 2b2 resonance is based on stepwise harmonic reconstruction. We find in liquid water at ambient conditions H₂O molecular potentials ranging from the weak interaction limit to strongly distorted potentials which are put into perspective to established parameters, i.e., intermolecular O–H, H–H, and O–O correlation lengths from neutron scattering.

Ultrafast dissociation of ammonia: Auger Doppler effect and redistribution of the internal energy

We study vibrationally-resolved resonant Auger (RAS) spectra of ammonia recorded in coincidence with the NH₂⁺ fragment, which is produced in the course of dissociation either in the core-excited 1s^-14a11 intermediate state or the first spectator 3a^-24a11 final state. Correlation of the NH₂⁺ ion flight times with electron kinetic energies allows directly observing the Auger-Doppler dispersion for each vibrational state of the fragment. The median distribution of the kinetic energy release E_KER, derived from the coincidence data, shows three distinct branches as a function of Auger electron kinetic energy E_e: E_e + 1.75E_KER = const for the molecular band; E_KER = const for the fragment band; and E_e + E_KER = const for the region preceding the fragment band. The deviation of the molecular band dispersion from E_e + E_KER = const is attributed to the redistribution of the available energy to the dissociation energy and excitation of the internal degrees of freedom in the molecular fragment. We found that for each vibrational line the dispersive behavior of E_KERvs. E_e is very sensitive to the instrumental uncertainty in the determination of E_KER causing the competition between the Raman (E_KER + E_e = const) and Auger (E_e = const) dispersions: increase in the broadening of the finite kinetic energy release resolution leads to a change of the dispersion from the Raman to the Auger one.

Capturing Atom-Specific Electronic Structural Dynamics of Transition-Metal Complexes with Ultrafast Soft X-Ray Spectroscopy

The atomic specificity of X-ray spectroscopies provides a distinct perspective on molecular electronic structure. For 3 d metal coordination and organometallic complexes, the combination of metal- and ligand-specific X-ray spectroscopies directly interrogates metal–ligand covalency—the hybridization of metal and ligand electronic states. Resonant inelastic X-ray scattering (RIXS), the X-ray analog of resonance Raman scattering, provides access to all classes of valence excited states in transition-metal complexes, making it a particularly powerful means of characterizing the valence electronic structure of 3 d metal complexes. Recent advances in X-ray free-electron laser sources have enabled RIXS to be extended to the ultrafast time domain. We review RIXS studies of two archetypical photochemical processes: charge-transfer excitation in ferricyanide and ligand photodissociation in iron pentacarbonyl. These studies demonstrate femtosecond-resolution RIXS can directly characterize the time-evolving electronic structure, including the evolution of the metal–ligand covalency.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Extended quasiparticle approach to non-resonant and resonant X-ray emission spectroscopy

The initial state of X-ray emission spectroscopy (XES) and resonant inelastic X-ray emission spectroscopy (RIXS) is a highly excited eigenstate with a deep core hole after a X-ray photoelectron spectroscopy...

Analytical gradients for core-excited states in the algebraic diagrammatic construction (ADC) framework

Expressions for analytical molecular gradients of core-excited states have been derived and implemented for the hierarchy of algebraic diagrammatic construction (ADC) methods up to extended second-order within the core-valence separation (CVS) approximation. We illustrate the use of CVS-ADC gradients by determining relaxed core-excited state potential energy surfaces and optimized geometries for water, formic acid, and benzene. For water, our results show that in the dissociative lowest core-excited state, a linear configuration is preferred. For formic acid, we find that the O K-edge lowest core-excited state is non-planar, a fact that is not captured by the equivalent core approximation where the core-excited atom with its hole is replaced by the "Z + 1" neighboring atom in the periodic table. For benzene, the core-excited state gradients are presented along the Jahn-Teller distorted geometry of the 1s → π* excited state. Our development may pave a new path to studying the dynamics of molecules in their core-excited states.

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

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

Development of an Electron-Atom Compton Scattering Apparatus Using a Picosecond Pulsed Electron Gun

An apparatus has been developed for electron-atom Compton scattering experiments that can employ a pulsed laser and a picosecond pulsed electron beam in a pump-and-probe scheme. The design and technical details of the apparatus are described. Furthermore, experimental results on the Xe atom in its ground state are presented to illustrate the performance of the pulsed electron gun and the detection and spectrometric capabilities for scattered electrons. The scope of future application is also discussed, involving real-time measurement of intramolecular force acting on each constituent atom with different mass numbers, in a transient, evolving system during a molecular reaction.

Vibrational resonant inelastic X-ray scattering in liquid acetic acid: a ruler for molecular chain lengths

Quenching of vibrational excitations in resonant inelastic X-ray scattering (RIXS) spectra of liquid acetic acid is observed. At the oxygen core resonance associated with localized excitations at the O-H bond, the spectra lack the typical progression of vibrational excitations observed in RIXS spectra of comparable systems. We interpret this phenomenon as due to strong rehybridization of the unoccupied molecular orbitals as a result of hydrogen bonding, which however cannot be observed in x-ray absorption but only by means of RIXS. This allows us to address the molecular structure of the liquid, and to determine a lower limit for the average molecular chain length.

Role of Dopants on the Local Electronic Structure of Polymeric Carbon Nitride Photocatalysts

Polymeric carbon nitride (PCN) is a promising class of materials for solar-to-chemical energy conversion. The increase of the photocatalytic activity of PCN is often achieved by the incorporation of heteroatoms, whose impact on the electronic structure of PCN remains poorly explored. This work reveals that the local electronic structure of PCN is strongly altered by doping with sulfur and iron using X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS). From XAS at the carbon and nitrogen K-edges, sulfur atoms are found to mostly affect carbon atoms, in contrast to iron doping mostly altering nitrogen sites. In RIXS at the nitrogen K-edge, a vibrational progression, affected by iron doping, is evidenced, which is attributed to a vibronic coupling between excited electrons in nitrogen atoms and C-N stretching modes in PCN heterocycling rings. This work opens new perspectives for the characterization of vibronic coupling in polymeric photocatalysts.

Probing the Electronic Structure of Warm Dense Nickel via Resonant Inelastic X-Ray Scattering

The development of bright free-electron lasers (FEL) has revolutionized our ability to create and study matter in the high-energy-density (HED) regime. Current diagnostic techniques have been successful in yielding information on fundamental thermodynamic plasma properties, but provide only limited or indirect information on the detailed quantum structure of these systems, and on how it is affected by ionization dynamics. Here we show how the valence electronic structure of solid-density nickel, heated to temperatures of around 10 of eV on femtosecond timescales, can be probed by single-shot resonant inelastic x-ray scattering (RIXS) at the Linac Coherent Light Source FEL. The RIXS spectrum provides a wealth of information on the HED system that goes well beyond what can be extracted from x-ray absorption or emission spectroscopy alone, and is particularly well suited to time-resolved studies of electronic-structure dynamics.

Observation of Double Excitations in the Resonant Inelastic X-ray Scattering of Nitric Oxide

The nitrogen K-edge resonant inelastic X-ray scattering (RIXS) map of nitric oxide (NO) has been measured and simulated to provide a detailed analysis of the observed features. High-resolution experimental RIXS maps were collected using an in situ gas flow cell and a high-transmission soft X-ray spectrometer. Accurate descriptions of the ground, excited, and core-excited states are based upon restricted active space self-consistent-field calculations using second order multiconfigurational perturbation theory. The nitrogen K-edge RIXS map of NO shows a range of features that can be assigned to intermediate states arising from 1s → π* and 1s → Rydberg excitations; additional bands are attributed to doubly excited intermediate states comprising 1s → π* and π → π* excitations. These results provide a detailed picture of RIXS for an open-shell molecule and an extensive description of the core-excited electronic structure of NO, an important molecule in many chemical and biological processes.

Disparate Exciton-Phonon Couplings for Zone-Center and Boundary Phonons in Solid-State Graphite

The exciton-phonon coupling in highly oriented pyrolytic graphite is studied using resonant inelastic x-ray scattering (RIXS) spectroscopy. With ∼70  meV energy resolution, multiple low energy excitations associated with coupling to phonons can be clearly resolved in the RIXS spectra. Using resonance dependence and the closed form for RIXS cross section without considering the intermediate state mixing of phonon modes, the dimensionless coupling constant g is determined to be 5 and 0.35, corresponding to the coupling strength of 0.42  eV+/-20  meV and 0.20  eV+/-20  meV, for zone center and boundary phonons, respectively. The reduced g value for the zone-boundary phonon may be related to its double resonance nature.

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.

Characterization of the soft X-ray spectrometer PEAXIS at BESSY II

The performance of the recently commissioned spectrometer PEAXIS for resonant inelastic soft X-ray scattering (RIXS) and X-ray photoelectron spectroscopy and its hosting beamline U41-PEAXIS at the BESSY II synchrotron are characterized. The beamline provides linearly polarized light from 180 eV to 1600 eV allowing for RIXS measurements in the range 200-1200 eV. The monochromator optics can be operated in different configurations to provide either high flux with up to 1012 photons s-1 within the focal spot at the sample or high energy resolution with a full width at half maximum of <40 meV at an incident photon energy of ∼400 eV. The measured total energy resolution of the RIXS spectrometer is in very good agreement with theoretically predicted values obtained by ray-tracing simulations. PEAXIS features a 5 m-long RIXS spectrometer arm that can be continuously rotated about the sample position by 106° within the horizontal photon scattering plane, thus enabling the study of momentum-transfer-dependent excitations. Selected scientific examples are presented to demonstrate the instrument capabilities, including measurements of excitations in single-crystalline NiO and in liquid acetone employing a fluid cell sample manipulator. Planned upgrades of the beamline and the RIXS spectrometer to further increase the energy resolution to ∼100 meV at 1000 eV incident photon energy are discussed.

The carbon and oxygen K-edge NEXAFS spectra of CO+

We present and analyze high resolution near edge X-ray absorption fine structure (NEXAFS) spectra of CO⁺ at the carbon and oxygen K-edges.

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.

Compatibility of quantitative X-ray spectroscopy with continuous distribution models of water at ambient conditions

The phase diagram of water harbors controversial views on underlying structural properties of its constituting molecular moieties, its fluctuating hydrogen-bonding network, as well as pair-correlation functions. In this work, long energy-range detection of the X-ray absorption allows us to unambiguously calibrate the spectra for water gas, liquid, and ice by the experimental atomic ionization cross-section. In liquid water, we extract the mean value of 1.74 ± 2.1% donated and accepted hydrogen bonds per molecule, pointing to a continuous-distribution model. In addition, resonant inelastic X-ray scattering with unprecedented energy resolution also supports continuous distribution of molecular neighborhoods within liquid water, as do X-ray emission spectra once the femtosecond scattering duration and proton dynamics in resonant X-ray-matter interaction are taken into account. Thus, X-ray spectra of liquid water in ambient conditions can be understood without a two-structure model, whereas the occurrence of nanoscale-length correlations within the continuous distribution remains open.

Valence orbitals and local bond dynamics around N atoms of histidine under X-ray irradiation

The valence orbitals of aqueous histidine under basic, neutral and acidic conditions and their X-ray induced transformations have been monitored through N 1s resonant inelastic X-ray scattering. Using density functional ab initio molecular dynamics simulations in the core-hole state within the Z + 1 approximation, core-excitation-induced molecular transformations are quantified. Spectroscopic evidence for a highly directional X-ray-induced local N-H dissociation within the scattering duration is presented for acidic histidine. Our report demonstrates a protonation-state and chemical-environment dependent propensity for a molecular dissociation, which is induced by the absorption of high energy photons. This case study indicates that structural deformations in biomolecules under exposure to ionizing radiation, yielding possible alteration or loss of function, is highly dependent on the physiological state of the molecule upon irradiation.

Ultrafast dissociation features in RIXS spectra of the water molecule

The “pseudo-atomic” peak is formed significantly faster than the atomic-like peak in water RIXS.

Probing the OH Stretch in Different Local Environments in Liquid Water

We use resonant inelastic X-ray scattering (RIXS) to resolve vibrational losses corresponding to the OH stretch where the X-ray absorption process allows us to selectively probe different structural subensembles in liquid water. The results point to a unified interpretation of X-ray and vibrational spectroscopic data in line with a picture of two classes of structural environments in the liquid at ambient conditions with predominantly close-packed high-density liquid (HDL) and occasional local fluctuations into strongly tetrahedral low-density liquid (LDL).

Polarization landscape effects in soft X-ray-induced surface chemical decomposition of lead zirco-titanate, evidenced by photoelectron spectromicroscopy

The stability of thin films of lead zirco-titanate (PZT) under intense soft X-ray beams is investigated by time-resolved photoelectron spectromicroscopy with a lateral resolution below 1 micrometer. Surface dissociation is observed when samples are irradiated with intense (5 × 10²³ photons per s per m²) soft X-rays, with promotion of reduced lead on the surface. On areas exhibiting outwards polarization (P⁽⁺⁾), the reduced lead is formed at the expense of P⁽⁺⁾-PZT. On areas presenting co-existing P⁽⁺⁾ states with areas without out-of-plane polarization (P⁽⁰⁾), the reduced lead is formed at the expense of the P⁽⁰⁾-PZT component, while the P⁽⁺⁾-PZT remains constant. The main dissociation mechanism was found to be triggered by 'hot' electrons in the conduction band, with energies exceeding the surface dissociation energies. Dissociation occurs basically when the electron affinity is larger than the dissociation energy of PbO (for P⁽⁺⁾ areas) or PbO^- (for P⁽⁰⁾ areas). Such mechanisms may be adapted for dissociation of other molecules on surfaces of ferroelectric thin films or for quantifying the stability of ferroelectric surfaces interacting with other radiation, with applications in the fields of photocatalysis or photovoltaic devices.

Gradual collapse of nuclear wave functions regulated by frequency tuned X-ray scattering

As is well established, the symmetry breaking by isotope substitution in the water molecule results in localisation of the vibrations along one of the two bonds in the ground state. In this study we find that this localisation may be broken in excited electronic states. Contrary to the ground state, the stretching vibrations of HDO are delocalised in the bound core-excited state in spite of the mass difference between hydrogen and deuterium. The reason for this effect can be traced to the narrow “canyon-like” shape of the potential of the state along the symmetric stretching mode, which dominates over the localisation mass-difference effect. In contrast, the localisation of nuclear motion to one of the HDO bonds is preserved in the dissociative core-excited state . The dynamics of the delocalisation of nuclear motion in these core-excited states is studied using resonant inelastic X-ray scattering of the vibrationally excited HDO molecule. The results shed light on the process of a wave function collapse. After core-excitation into the state of HDO the initial wave packet collapses gradually, rather than instantaneously, to a single vibrational eigenstate.

Nuclear Dynamical Correlation Effects in X-ray Spectroscopy from a Theoretical Time-Domain Perspective

To date X-ray spectroscopy has become a routine tool that can reveal highly local and element-specific information on the electronic structure of atoms in complex environments. Here, we focus on nuclear dynamical correlation effects in X-ray spectra and develop a rigorous time-correlation function method employing ground state classical molecular dynamics simulations. The importance of nuclear correlation phenomena is demonstrated by comparison against the results from the conventional sampling approach performed on the same data set for gas phase water. In contrast to the first-order absorption, second-order resonant inelastic scattering spectra exhibit pronounced fingerprints of nuclear motions. The developed methodology is not biased to a particular electronic structure method and, owing to its generality, can be applied to, e.g., X-ray photoelectron and Auger spectroscopies.

A study of the water molecule using frequency control over nuclear dynamics in resonant X-ray scattering

We report a full analysis of the resonant inelastic X-ray scattering spectra of H₂O, D₂O and HDO.