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

In order to explain over 70 unusual properties of water,¹1. M. F. Chaplin, http://www1.lsbu.ac.uk/water/, 2015. it has been proposed that there are fluctuations in water at ambient conditions between two local environments that have distinctly different structures. The dominating local motifs at ambient pressures have been proposed to consist mostly of close-packed, high-density liquid (HDL) local structures,^2,3–62. A. Nilsson and L. G. M. Pettersson, “The structural origin of anomalous properties of liquid water,” Nat. Commun. 6, 8998 (2015). https://doi.org/10.1038/ncomms99983. C. Huang et al., “The inhomogeneous structure of water at ambient conditions,” Proc. Natl. Acad. Sci. U. S. A. 106, 15214–15218 (2009). https://doi.org/10.1073/pnas.09047431064. O. Mishima and H. E. Stanley, “The relationship between liquid, supercooled and glassy water,” Nature 396, 329–335 (1998). https://doi.org/10.1038/245405. A. K. Soper and M. A. Ricci, “Structures of high-density and low-density water,” Phys. Rev. Lett. 84, 2881–2884 (2000). https://doi.org/10.1103/physrevlett.84.28816. M. C. Bellissent-Funel, “Is there a liquid-liquid phase transition in supercooled water?,” Europhys. Lett. 42, 161–166 (1998). https://doi.org/10.1209/epl/i1998-00223-5 also denoted normal, thermally excited structures,⁷7. J. Russo and H. Tanaka, “Understanding water’s anomalies with locally favoured structures,” Nat. Commun. 5, 3556 (2014). https://doi.org/10.1038/ncomms4556 where some hydrogen bonds (H-bonds) are strongly modified to allow higher coordination. Upon cooling from high temperatures, patches of tetrahedrally coordinated molecules, often denoted low-density liquid (LDL),^2,82. A. Nilsson and L. G. M. Pettersson, “The structural origin of anomalous properties of liquid water,” Nat. Commun. 6, 8998 (2015). https://doi.org/10.1038/ncomms99988. A. Nilsson and L. G. M. Pettersson, “Perspective on the structure of liquid water,” Chem. Phys. 389, 1–34 (2011). https://doi.org/10.1016/j.chemphys.2011.07.021 symmetrical^9,109. T. D. Kühne and R. Z. Khaliullin, “Electronic signature of the instantaneous asymmetry in the first coordination shell of liquid water,” Nat. Commun. 4, 1450 (2013). https://doi.org/10.1038/ncomms245910. M. Leetmaa et al., “Diffraction and IR/Raman data do not prove tetrahedral water,” J. Chem. Phys. 129, 084502 (2008). https://doi.org/10.1063/1.2968550 or locally favored structures,⁷7. J. Russo and H. Tanaka, “Understanding water’s anomalies with locally favoured structures,” Nat. Commun. 5, 3556 (2014). https://doi.org/10.1038/ncomms4556 begin to appear as fluctuations in the HDL random structure. The number of such LDL patches and their size and lifetime would increase with decreasing temperature^2,32. A. Nilsson and L. G. M. Pettersson, “The structural origin of anomalous properties of liquid water,” Nat. Commun. 6, 8998 (2015). https://doi.org/10.1038/ncomms99983. C. Huang et al., “The inhomogeneous structure of water at ambient conditions,” Proc. Natl. Acad. Sci. U. S. A. 106, 15214–15218 (2009). https://doi.org/10.1073/pnas.0904743106 and make the properties of water deviate from the simple liquid behavior at high temperatures.^2,7,11,122. A. Nilsson and L. G. M. Pettersson, “The structural origin of anomalous properties of liquid water,” Nat. Commun. 6, 8998 (2015). https://doi.org/10.1038/ncomms99987. J. Russo and H. Tanaka, “Understanding water’s anomalies with locally favoured structures,” Nat. Commun. 5, 3556 (2014). https://doi.org/10.1038/ncomms455611. P. Gallo et al., “Water: A tale of two liquids,” Chem. Rev. 116, 7463–7500 (2016). https://doi.org/10.1021/acs.chemrev.5b0075012. V. Holten and M. A. Anisimov, “Entropy-driven liquid–liquid separation in supercooled water,” Sci. Rep. 2, 713 (2012). https://doi.org/10.1038/srep00713

It is essential to provide experimental evidence of the existence of the two HDL-LDL environments in water and how these change as a function of temperature, pressure, and presence of solutes. The electronic structure probe of the occupied orbitals, x-ray emission spectroscopy (XES) or also often denoted resonant inelastic x-ray scattering (RIXS), shows for water that the highest occupied orbital 1b₁ is split into two components 1b₁′ and 1b₁″;^13,1413. O. Fuchs et al., “Isotope and temperature effects in liquid water probed by x-ray absorption and resonant x-ray emission spectroscopy,” Phys. Rev. Lett. 100, 027801 (2008). https://doi.org/10.1103/physrevlett.100.02780114. T. Tokushima et al., “High resolution x-ray emission spectroscopy of liquid water: The observation of two structural motifs,” Chem. Phys. Lett. 460, 387–400 (2008). https://doi.org/10.1016/j.cplett.2008.04.077 see Fig. 1. The origin of the split has been discussed as due to two different instantaneous structural environments giving different electronic emission energies in the spectroscopic process^14–1614. T. Tokushima et al., “High resolution x-ray emission spectroscopy of liquid water: The observation of two structural motifs,” Chem. Phys. Lett. 460, 387–400 (2008). https://doi.org/10.1016/j.cplett.2008.04.07715. A. Nilsson et al., “Resonant inelastic x-ray scattering of liquid water,” J. Electron Spectrosc. Relat. Phenom. 188, 84–100 (2013). https://doi.org/10.1016/j.elspec.2012.09.01116. T. Tokushima et al., “High resolution x-ray emission spectroscopy of water and its assignment based on two structural motifs,” J. Electron Spectrosc. Relat. Phenom. 177, 192–205 (2010). https://doi.org/10.1016/j.elspec.2010.02.008 where the low energy peak 1b₁′ is related to LDL and the high energy peak 1b₁″ as the HDL structural motifs.³3. C. Huang et al., “The inhomogeneous structure of water at ambient conditions,” Proc. Natl. Acad. Sci. U. S. A. 106, 15214–15218 (2009). https://doi.org/10.1073/pnas.0904743106 However, the intensity variation of the two peaks in the 1b₁ region between H₂O and D₂O is significantly larger than any structural dependence between the isotopes, indicating that there are important core hole induced vibrational effects affecting the spectra.^13,1413. O. Fuchs et al., “Isotope and temperature effects in liquid water probed by x-ray absorption and resonant x-ray emission spectroscopy,” Phys. Rev. Lett. 100, 027801 (2008). https://doi.org/10.1103/physrevlett.100.02780114. T. Tokushima et al., “High resolution x-ray emission spectroscopy of liquid water: The observation of two structural motifs,” Chem. Phys. Lett. 460, 387–400 (2008). https://doi.org/10.1016/j.cplett.2008.04.077 This core hole dynamics effect was included by applying an asymmetric Gaussian tail to higher loss energy of the 1b₁″ peak by considering gradual energy shift of the emission line during the lifetime of the core hole. The 1b₁′ peak would then reside on top of the asymmetry from the 1b₁″ peak, and since the level of 1b₁″ asymmetry would be isotope dependent, this would cause the two peaks to have different intensities.^15–1715. A. Nilsson et al., “Resonant inelastic x-ray scattering of liquid water,” J. Electron Spectrosc. Relat. Phenom. 188, 84–100 (2013). https://doi.org/10.1016/j.elspec.2012.09.01116. T. Tokushima et al., “High resolution x-ray emission spectroscopy of water and its assignment based on two structural motifs,” J. Electron Spectrosc. Relat. Phenom. 177, 192–205 (2010). https://doi.org/10.1016/j.elspec.2010.02.00817. M. P. Ljungberg, L. G. M. Pettersson, and A. Nilsson, “Vibrational interference effects in x-ray emission of a model water dimer: Implications for the interpretation of the liquid spectrum,” J. Chem. Phys. 134, 044513 (2011). https://doi.org/10.1063/1.3533956 We note that recent RIXS calculations of different structural environments in the liquid give rise to the shift between the two lone pair peaks.¹⁸18. I. Zhovtobriukh et al., “Relationship between x-ray emission and absorption spectroscopy and the local H-bond environment in water,” J. Chem. Phys. 148, 144507 (2018). https://doi.org/10.1063/1.5009457

The alternative picture is that the core hole dynamics is considered more dominating and gives rise not only to asymmetrical line shape differences but also to a separate peak. Then, the two peaks in the 1b₁ region are related to the extreme case with a fully dissociated OH lone pair state corresponding to the 1b₁′ position due to faster dissociation of the hydrogen atom than the lifetime of the core hole and the 1b₁ state of intact water at the 1b₁″ position in Fig. 1.¹³13. O. Fuchs et al., “Isotope and temperature effects in liquid water probed by x-ray absorption and resonant x-ray emission spectroscopy,” Phys. Rev. Lett. 100, 027801 (2008). https://doi.org/10.1103/physrevlett.100.027801

A validation of this interpretation was given based on molecular dynamics simulations of water followed with core hole dynamics calculations.^19–2219. V. V. Cruz et al., “Probing hydrogen bond strength in liquid water by resonant inelastic x-ray scattering,” Nat. Commun. 10, 1013 (2019). https://doi.org/10.1038/s41467-019-08979-420. J. Niskanen et al., “Compatibility of quantitative x-ray spectroscopy with continuous distribution models of water at ambient conditions,” Proc. Natl. Acad. Sci. U. S. A. 116, 4058–4063 (2019). https://doi.org/10.1073/pnas.181570111621. M. Odelius, “Molecular dynamics simulations of fine structure in oxygen K-edge x-ray emission spectra of liquid water and ice,” Phys. Rev. B 79, 144204 (2009). https://doi.org/10.1103/physrevb.79.14420422. M. Odelius, “Information content in O[1s] K-edge X-ray emission spectroscopy of liquid water,” J. Phys. Chem. A 113, 8176–8181 (2009). https://doi.org/10.1021/jp903096k A peak appears in the simulated 1b₁′ region that was assigned to dissociated fragments of a₁ symmetry. This interpretation was discussed in a review on RIXS applied to water¹⁵15. A. Nilsson et al., “Resonant inelastic x-ray scattering of liquid water,” J. Electron Spectrosc. Relat. Phenom. 188, 84–100 (2013). https://doi.org/10.1016/j.elspec.2012.09.011 and found to be inconsistent based on two different experimental independent observations. First, polarization-dependent RIXS measurements show that this peak is not of a₁ but of b₁ symmetry.²³23. T. Tokushima et al., “Polarization dependent resonant x-ray emission spectroscopy of D₂O and H₂O water: Assignment of the local molecular orbital symmetry,” J. Chem. Phys. 136, 044517 (2012). https://doi.org/10.1063/1.3678443 Second, in the simulation, 1b₁″ is kept at fixed energy position during the dynamics^20–2220. J. Niskanen et al., “Compatibility of quantitative x-ray spectroscopy with continuous distribution models of water at ambient conditions,” Proc. Natl. Acad. Sci. U. S. A. 116, 4058–4063 (2019). https://doi.org/10.1073/pnas.181570111621. M. Odelius, “Molecular dynamics simulations of fine structure in oxygen K-edge x-ray emission spectra of liquid water and ice,” Phys. Rev. B 79, 144204 (2009). https://doi.org/10.1103/physrevb.79.14420422. M. Odelius, “Information content in O[1s] K-edge X-ray emission spectroscopy of liquid water,” J. Phys. Chem. A 113, 8176–8181 (2009). https://doi.org/10.1021/jp903096k and this would imply that there is no shift or change in line shape of the 1b₁″ peak between the two isotopes. Indeed, there is a significant shift to lower emission energy and broader peak in H₂O in comparison with D₂O^14,1714. T. Tokushima et al., “High resolution x-ray emission spectroscopy of liquid water: The observation of two structural motifs,” Chem. Phys. Lett. 460, 387–400 (2008). https://doi.org/10.1016/j.cplett.2008.04.07717. M. P. Ljungberg, L. G. M. Pettersson, and A. Nilsson, “Vibrational interference effects in x-ray emission of a model water dimer: Implications for the interpretation of the liquid spectrum,” J. Chem. Phys. 134, 044513 (2011). https://doi.org/10.1063/1.3533956 showing that the lone pair peak should shift down in energy during the core hole dynamics. This is the basis for the asymmetry of the 1b₁″ peak.¹⁷17. M. P. Ljungberg, L. G. M. Pettersson, and A. Nilsson, “Vibrational interference effects in x-ray emission of a model water dimer: Implications for the interpretation of the liquid spectrum,” J. Chem. Phys. 134, 044513 (2011). https://doi.org/10.1063/1.3533956 The simulations, proposing the a₁ symmetry peak, lead to that 3a₁ intensity moves up in energy and appears in the lone pair region. Indeed, with a correct energy scale, the 3a₁ emission peak should broaden and stay in the a₁ region separated by 2 eV from the 1b₁″ peak.¹⁷17. M. P. Ljungberg, L. G. M. Pettersson, and A. Nilsson, “Vibrational interference effects in x-ray emission of a model water dimer: Implications for the interpretation of the liquid spectrum,” J. Chem. Phys. 134, 044513 (2011). https://doi.org/10.1063/1.3533956 Since this interpretation considering a₁ contribution to the lone pair region is not consistent with two previous experimental observations, we will no longer include it in the following discussion.

Here, we provide additional information on the debate of the two different interpretations shown in Fig. 1 using combined analysis of vibrational excitations in the elastic scattering region and valence band emissions in resonant inelastic x-ray scattering (RIXS) spectra. The high spectral resolution enables us to observe the vibrational losses going into the continuum of full OH bond breaking in the RIXS spectra upon selective excitation. This allows us to determine the amount of extremely enlarged O–H bond length states contributing to the 1b₁ region of the RIXS spectra, which can be associated with a faint spectral plateau at the higher part of the 1b₁′ peak. The latter is also shown to be consistent with the energy position of the OH⁻ ion in water. This means that the actual effect of core hole dynamics appears not only as the asymmetric tail to higher loss energy of the 1b₁″ peak but also as a faint plateau that was not considered in the previous studies.^14–1914. T. Tokushima et al., “High resolution x-ray emission spectroscopy of liquid water: The observation of two structural motifs,” Chem. Phys. Lett. 460, 387–400 (2008). https://doi.org/10.1016/j.cplett.2008.04.07715. A. Nilsson et al., “Resonant inelastic x-ray scattering of liquid water,” J. Electron Spectrosc. Relat. Phenom. 188, 84–100 (2013). https://doi.org/10.1016/j.elspec.2012.09.01116. T. Tokushima et al., “High resolution x-ray emission spectroscopy of water and its assignment based on two structural motifs,” J. Electron Spectrosc. Relat. Phenom. 177, 192–205 (2010). https://doi.org/10.1016/j.elspec.2010.02.00817. M. P. Ljungberg, L. G. M. Pettersson, and A. Nilsson, “Vibrational interference effects in x-ray emission of a model water dimer: Implications for the interpretation of the liquid spectrum,” J. Chem. Phys. 134, 044513 (2011). https://doi.org/10.1063/1.353395618. I. Zhovtobriukh et al., “Relationship between x-ray emission and absorption spectroscopy and the local H-bond environment in water,” J. Chem. Phys. 148, 144507 (2018). https://doi.org/10.1063/1.500945719. V. V. Cruz et al., “Probing hydrogen bond strength in liquid water by resonant inelastic x-ray scattering,” Nat. Commun. 10, 1013 (2019). https://doi.org/10.1038/s41467-019-08979-4 We assign three spectral features in the 1b₁ region providing an important additional piece of information where the 1b₁′ feature has two contributions, LDL structural environments and dissociative component coming from the dominated HDL environment where the latter is slightly shifted to higher energy. The 1b₁″ peak is then associated with the mostly intact HDL.

O 1s RIXS spectra of pure liquid H₂O water were collected with the high resolution soft X-ray emission spectrometer HORNET station at SPring-8 BL07LSU,²⁴24. S. Yamamoto et al., “New soft x-ray beamline BL07LSU at SPring-8,” J. Synchrotron Radiat. 21, 352–365 (2014). https://doi.org/10.1107/s1600577513034796 which is equipped with a high resolution soft x-ray RIXS spectrometer²⁵25. Y. Harada et al., “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012). https://doi.org/10.1063/1.3680559 perpendicular to the light path of the incident x-rays. The O 1s x-ray absorption spectrum (XAS) spectra were recorded with partial fluorescence yield mode using a 10 mm² Silicon Drift Detector (SDD, Ourstex, Co. Ltd.). The energy resolution for the O 1s XAS and XES measurements was 0.1 eV and 0.15 eV, respectively. A custom-made liquid flow-through cell equipped with a 150 nm thick SiC membrane (NTT-AT Corporation, Japan) was used to flush liquid water at a speed of 100 mm/s in the horizontal direction. The details of the experimental setup and operating condition are described elsewhere.¹⁶16. T. Tokushima et al., “High resolution x-ray emission spectroscopy of water and its assignment based on two structural motifs,” J. Electron Spectrosc. Relat. Phenom. 177, 192–205 (2010). https://doi.org/10.1016/j.elspec.2010.02.008 All measurements were done at room temperature.

It has been demonstrated that it is possible to resolve vibrational spectra using high resolution RIXS at the O K-edge as an energy-loss process from the elastic line^26–2926. R. C. Couto et al., “Selective gating to vibrational modes through resonant x-ray scattering,” Nat. Commun. 8, 14165 (2017). https://doi.org/10.1038/ncomms1416527. F. Hennies et al., “Resonant inelastic scattering spectra of free molecules with vibrational resolution,” Phys. Rev. Lett. 104, 193002 (2010). https://doi.org/10.1103/physrevlett.104.19300228. A. Pietzsch et al., “Snapshots of the fluctuating hydrogen bond network in liquid water on the sub-femtosecond timescale with vibrational resonant inelastic x-ray scattering,” Phys. Rev. Lett. 114, 088302 (2015). https://doi.org/10.1103/physrevlett.114.08830229. J. E. Rubensson, “Resonant inelastic soft x-ray scattering applied to molecular materials,” J. Electron Spectrosc. Relat. Phenom. 200, 239–246 (2015). https://doi.org/10.1016/j.elspec.2015.05.004 and OH stretch vibrational spectra of water could be measured with RIXS.^28,30,3128. A. Pietzsch et al., “Snapshots of the fluctuating hydrogen bond network in liquid water on the sub-femtosecond timescale with vibrational resonant inelastic x-ray scattering,” Phys. Rev. Lett. 114, 088302 (2015). https://doi.org/10.1103/physrevlett.114.08830230. Y. Harada et al., “Selective probing of the OH or OD stretch vibration in liquid water using resonant inelastic soft-x-ray scattering,” Phys. Rev. Lett. 111, 193001 (2013). https://doi.org/10.1103/physrevlett.111.19300131. Y. Harada et al., “Probing the OH stretch in different local environments in liquid water,” J. Phys. Chem. Lett. 8, 5487–5491 (2017). https://doi.org/10.1021/acs.jpclett.7b02060 Figure 2(a) shows the excitation-dependent vibrationally-resolved RIXS spectra of water related to the OH stretch. In the core-excited state, the potential energy surface is different from that of the ground state, and since the lifetime of the O 1s core-hole state is around 4 fs,³²32. M. Neeb et al., “Coherent excitation of vibrational wave functions observed in core hole decay spectra of O₂, N₂ and CO,” J. Electron Spectrosc. Relat. Phenom. 67, 261–274 (1994). https://doi.org/10.1016/0368-2048(93)02050-v there is sufficient time for the vibrational wave packet to evolve along the internal O–H bond resulting in a large number of overtones. In water, it has been possible to detect excitations into v = 7 while beyond a continuum is seen, meaning that the decay is into the ground state above the dissociation limit where the OH bond is broken.³⁰30. Y. Harada et al., “Selective probing of the OH or OD stretch vibration in liquid water using resonant inelastic soft-x-ray scattering,” Phys. Rev. Lett. 111, 193001 (2013). https://doi.org/10.1103/physrevlett.111.193001

Figure 2(a) shows how the amount of overtones depends strongly on the excitation energy. This is connected to the elongation of the OH bond in water during the 4 fs lifetime of the core hole. If the excited electron is not trapped in a bound state and is above the ionization limit, the excited electron could access the continuum of core-ionized states and delocalize into the liquid far from the core excited atom.³³33. D. Nordlund et al., “Probing the electron delocalization in liquid water and ice at attosecond time scales,” Phys. Rev. Lett. 99, 217406 (2007). https://doi.org/10.1103/physrevlett.99.217406 This process would then strongly affect the lifetime of the excited state at the core hole atom and will become much shorter than the core hole lifetime resulting in that the OH bond would not have time to elongate. We can thereby separate two contributions that will affect the amount of overtones in the spectra in terms of degree of OH elongation and lifetime of the excited electron compared to the existence of the core hole. The latter contribution will only become essential when the excitation energy is at or above the core ionization energy of water at around 538 eV.³⁴34. B. Winter et al., “Hydrogen bonds in liquid water studied by photoelectron spectroscopy,” J. Chem. Phys. 126, 124504 (2007). https://doi.org/10.1063/1.2710792

The x-ray absorption spectrum (XAS) of water is shown in Fig. 2(b) and has been categorized into three major spectral features in terms of the pre- (534–535 eV), main- (537–538 eV) and post-edge (540–541 eV) resonances.^35–3735. T. Fransson et al., “X-ray and electron spectroscopy of water,” Chem. Rev. 116, 7551–7569 (2016). https://doi.org/10.1021/acs.chemrev.5b0067236. A. Nilsson et al., “X-ray absorption spectroscopy and x-ray Raman scattering of water and ice; an experimental view,” J. Electron Spectrosc. Relat. Phenom. 177, 99–129 (2010). https://doi.org/10.1016/j.elspec.2010.02.00537. P. Wernet et al., “The structure of the first coordination shell in liquid water,” Science 304, 995–999 (2004). https://doi.org/10.1126/science.1096205 In Fig. 2(b), we also show the integrated intensity of the plateau region of the vibrational loss between 4.0 eV and 4.5 eV taken from Fig. 2(a) as a function of excitation energy. This is similar to the study in liquid methanol,³⁸38. S. Schreck et al., “Dynamics of the OH group and the electronic structure of liquid alcohols,” Struct. Dyn. 1, 054901 (2014). https://doi.org/10.1063/1.4897981 but in this case, we are beyond any vibrational fine structure and thereby above the dissociation limit. By integrating 200 points included between 4.0 and 4.5 eV, the statistical error is fully minimized, which is indicated by the absence of the error bar masked by the marker of the tail intensity in Fig. 2(b).

We see at the pre-edge feature around 535 eV in the XAS process that we have a maximum of the intensity and thereby large number of dissociation events. This is expected since the pre-edge corresponds to excitation into strongly OH antibonding molecular orbitals of the water molecule causing large OH distortions, not only from the presence of the core hole but also due to the excited electron.^30,33,36,3730. Y. Harada et al., “Selective probing of the OH or OD stretch vibration in liquid water using resonant inelastic soft-x-ray scattering,” Phys. Rev. Lett. 111, 193001 (2013). https://doi.org/10.1103/physrevlett.111.19300133. D. Nordlund et al., “Probing the electron delocalization in liquid water and ice at attosecond time scales,” Phys. Rev. Lett. 99, 217406 (2007). https://doi.org/10.1103/physrevlett.99.21740636. A. Nilsson et al., “X-ray absorption spectroscopy and x-ray Raman scattering of water and ice; an experimental view,” J. Electron Spectrosc. Relat. Phenom. 177, 99–129 (2010). https://doi.org/10.1016/j.elspec.2010.02.00537. P. Wernet et al., “The structure of the first coordination shell in liquid water,” Science 304, 995–999 (2004). https://doi.org/10.1126/science.1096205 When we excite into resonances around the main-edge at 536–537 eV, the tail intensity rapidly decreases by a factor of 5 in comparison with the pre-edge. In this case, the excited electron is populating much less antibonding molecular character and the OH elongation is mostly driven by the core hole. From an inspection of Fig. 2(a), we observe that the intensities are more in the lower overtones in comparison with the pre-edge excitation.

As the excitation energy is further increased above 537.5 eV, the tail intensity completely diminishes as we are reaching the ionization limit. When the ionization channel opens, there is a possibility for a decay of the core excited state to the core ionized state, where the excited electron will be lost into the surrounding water. Such a process becomes possible when the core ionized state is at lower energy than the excited state. If the decay process into the core ionized state is faster than the core hole lifetime, this channel will dominate and no vibrational excitations will be seen close to the elastic line. Such a fast decay of the core excited state has been previously observed in resonant Auger studies when the excitation energy is above the ionization limit through a loss of spectator shift from the excited electron.³³33. D. Nordlund et al., “Probing the electron delocalization in liquid water and ice at attosecond time scales,” Phys. Rev. Lett. 99, 217406 (2007). https://doi.org/10.1103/physrevlett.99.217406

A consistency test of our overall interpretation can be seen in Fig. 2(a) by going far below the pre-edge at 532.7 eV where the scattering duration time becomes extremely short³⁹39. R. Feifel et al., “Generalization of the duration-time concept for interpreting high-resolution resonant photoemission spectra,” Phys. Rev. A 69, 022707 (2004). https://doi.org/10.1103/physreva.69.022707 and the overtones completely vanish similar to as for excitation energies above the core ionization limit where instead the decay into the core ionized state becomes faster. This is fully in line with what was observed for liquid methanol.³⁸38. S. Schreck et al., “Dynamics of the OH group and the electronic structure of liquid alcohols,” Struct. Dyn. 1, 054901 (2014). https://doi.org/10.1063/1.4897981

In order to be as quantitative as possible, we have taken self-absorption effects for the plateau region into account but found them to be negligible in this case because at excitation energies under the ionization limit (538 eV excitation), the plateau energy is below 534 eV, which is prior to the absorption edge. Thus, we have now a direct measurement of the relative amount of dissociation events if we stay below the core ionized limit and this varies by a factor of 5 between excitation energies at the pre-edge and just below the ionization limit.

Since the tail intensity would point to the existence of a small component of a dissociated fragment or molecular species with a significantly elongated O–H bond, it is essential to discuss if this can be seen in the electronic transitions of the RIXS spectra. Here, we present new measurements that are similar to previous work^14,23,3514. T. Tokushima et al., “High resolution x-ray emission spectroscopy of liquid water: The observation of two structural motifs,” Chem. Phys. Lett. 460, 387–400 (2008). https://doi.org/10.1016/j.cplett.2008.04.07723. T. Tokushima et al., “Polarization dependent resonant x-ray emission spectroscopy of D₂O and H₂O water: Assignment of the local molecular orbital symmetry,” J. Chem. Phys. 136, 044517 (2012). https://doi.org/10.1063/1.367844335. T. Fransson et al., “X-ray and electron spectroscopy of water,” Chem. Rev. 116, 7551–7569 (2016). https://doi.org/10.1021/acs.chemrev.5b00672 but with improved energy resolution and better control of the emission energy scale in order to see small shifts. We will introduce the hypothesis of an additional component in the excitation energy spectra and see if this is consistent with the tail intensity in Fig. 2(b).

Figure 3 shows the excitation-dependent RIXS spectra of the 1b₁ region. The dissociative component is labeled 1b₁″^*. If we start with the spectra at the onset of the pre-edge XAS resonance at 534.9 eV, there are two peaks. In the gas phase, RIXS spectra excited to the 4a₁ state and also two peaks are observed where there is a large isotope effect in the relative intensity.⁴⁰40. L. Weinhardt et al., “Nuclear dynamics and spectator effects in resonant inelastic soft x-ray scattering of gas-phase water molecules,” J. Chem. Phys. 136, 144311 (2012). https://doi.org/10.1063/1.3702644 This has been proposed to be due to a dissociative peak at low energy and an intact water molecule,⁴⁰40. L. Weinhardt et al., “Nuclear dynamics and spectator effects in resonant inelastic soft x-ray scattering of gas-phase water molecules,” J. Chem. Phys. 136, 144311 (2012). https://doi.org/10.1063/1.3702644 which is fully consistent with a resonant Auger study of gas phase water excited to the same resonance where dissociative fragments have been detected⁴¹41. I. Hjelte et al., “Evidence for ultra-fast dissociation of molecular water from resonant Auger spectroscopy,” Chem. Phys. Lett. 334, 151–158 (2001). https://doi.org/10.1016/s0009-2614(00)01434-2 and theoretically simulated.⁴²42. O. Takahashi et al., “Auger decay calculations with core-hole excited-state molecular-dynamics simulations of water,” J. Chem. Phys. 124, 064307 (2006). https://doi.org/10.1063/1.2166234 This is not surprising since the 4a₁ molecular orbital is strongly antibonding along the OH bonds in the water molecule.⁴²42. O. Takahashi et al., “Auger decay calculations with core-hole excited-state molecular-dynamics simulations of water,” J. Chem. Phys. 124, 064307 (2006). https://doi.org/10.1063/1.2166234 What is interesting is that for the pre-edge excited liquid water and 4a₁ excited gas phase water, RIXS spectra closely resemble each other with the two peaks of similar intensity ratio and dependence between the isotopes.¹⁵15. A. Nilsson et al., “Resonant inelastic x-ray scattering of liquid water,” J. Electron Spectrosc. Relat. Phenom. 188, 84–100 (2013). https://doi.org/10.1016/j.elspec.2012.09.011 These observations point to that the low-energy peak in the pre-edge excited RIXS spectrum of liquid water corresponds to a dissociative peak.¹⁵15. A. Nilsson et al., “Resonant inelastic x-ray scattering of liquid water,” J. Electron Spectrosc. Relat. Phenom. 188, 84–100 (2013). https://doi.org/10.1016/j.elspec.2012.09.011 Another evidence for this can be derived from the lower part of the RIXS spectra between the 3a₁ and 1b₂ spectral feature where the 4a₁ excited gas phase spectrum shows a sharp feature at 522 eV that is much stronger for H₂O than for D₂O corresponding to the σ bonding state of the remaining OH fragment after dissociation by core hole dynamics.⁴⁰40. L. Weinhardt et al., “Nuclear dynamics and spectator effects in resonant inelastic soft x-ray scattering of gas-phase water molecules,” J. Chem. Phys. 136, 144311 (2012). https://doi.org/10.1063/1.3702644 Such a spectral feature is also observed in the pre-edge excited water spectrum that has less intensity in D₂O showing also the existence of dissociation during the core hole lifetime.¹⁵15. A. Nilsson et al., “Resonant inelastic x-ray scattering of liquid water,” J. Electron Spectrosc. Relat. Phenom. 188, 84–100 (2013). https://doi.org/10.1016/j.elspec.2012.09.011

This observation of clear dissociation in pre-edge excited RIXS spectra is fully consistent with the discussion of Fig. 2 where strong tail intensity is seen in the vibrationally resolved spectra. Then, we use the pre-edge excited RIXS spectrum as a starting point to the apparent hypothesized dissociative (light blue) water component. Curve fitting of the pre-edge excited water spectrum is shown in panel A in Fig. 4(a) into two components, dissociative (light blue) and intact (green) water components.

We follow the energy position of these components as the excitation energy is changed, as shown in Fig. 3 where lines indicate their position. The 1b₁′ peak (green, here assigned to intact HDL water) disperses strongly with photon energy between 533.9 eV and 535.3 eV and then much less up to 537.9 eV where it becomes constant at higher excitation energies. It is well known for many systems that for electrons excited into bound states, the spectra shift down in energy due to the difference in the screening of the core hole and valence hole by the additional electron.^29,43,4429. J. E. Rubensson, “Resonant inelastic soft x-ray scattering applied to molecular materials,” J. Electron Spectrosc. Relat. Phenom. 200, 239–246 (2015). https://doi.org/10.1016/j.elspec.2015.05.00443. F. Gel’mukhanov and H. Ågren, “Resonant x-ray Raman scattering,” Phys. Rep. 312, 87–330 (1999). https://doi.org/10.1016/s0370-1573(99)00003-444. J.-E. Rubensson, “RIXS dynamics for beginners,” J. Electron Spectrosc. Relat. Phenom. 110-111, 135 (2000). https://doi.org/10.1016/s0368-2048(00)00161-4 Furthermore, varying the excitation energy involves variation of the population of the vibrational states in the excited pre-edge state that also can give different population of the vibrational states in the final 1b₁ state of the intact molecule peak. For the dissociative component (light blue), we see even a smaller dispersion, and this can be understood as an additional degree of freedom to give a part of the excitation energy to the repelled hydrogen atom, and since we are only detecting the OH fragment in the RIXS process, there are smaller spectator shifts and vibrational excitations coupled to the valence emission for this fragment.⁴²42. O. Takahashi et al., “Auger decay calculations with core-hole excited-state molecular-dynamics simulations of water,” J. Chem. Phys. 124, 064307 (2006). https://doi.org/10.1063/1.2166234

In order to further assist in the spectra interpretation and test the consistency with the additional hypothesized dissociative component, together with the results from the tail intensity variation, we test if the spectra could be fitted using these 3 components. This is not a completely unique fit since more input would be required but is rather meant to test our hypothesis. Taking the reasonable variation of the three peak positions, we performed three component fittings to the XES spectra at all excitation energies, which are summarized in Fig. S1 along with the detailed procedure in the supplementary material, and results for three selected excitation energies are shown in Fig. 4(a). For the 1b₁″ peak, we have introduced an asymmetry parameter¹⁶16. T. Tokushima et al., “High resolution x-ray emission spectroscopy of water and its assignment based on two structural motifs,” J. Electron Spectrosc. Relat. Phenom. 177, 192–205 (2010). https://doi.org/10.1016/j.elspec.2010.02.008 to describe the effect that core hole dynamics have on the line shape. It resembles closely the line shape of the almost exact solution to the Kramers-Heisenberg description of the water dimer.¹⁷17. M. P. Ljungberg, L. G. M. Pettersson, and A. Nilsson, “Vibrational interference effects in x-ray emission of a model water dimer: Implications for the interpretation of the liquid spectrum,” J. Chem. Phys. 134, 044513 (2011). https://doi.org/10.1063/1.3533956

As the excitation energy increases above the pre-edge [Fig. 4(a) and Fig. S1], the dissociative component becomes much smaller in intensity, consistent with drop in tail intensity, seen in Fig. 2. It is interesting to note that this is almost opposite to what was found in the case of liquid methanol, where instead the tail intensity increased at higher excitation energy well above the pre-edge.³⁸38. S. Schreck et al., “Dynamics of the OH group and the electronic structure of liquid alcohols,” Struct. Dyn. 1, 054901 (2014). https://doi.org/10.1063/1.4897981

In the lower part of Fig 4(b), we show the intensity of the fitted dissociative component (light blue) together with the tail intensity (black) from Fig. 2(b) as a function of excitation energy. We observe a close agreement indicating the consistency between the two. We can thereby conclude that a fitted third dissociative component that follows the tail intensity is consistent with the spectra. In particular, at excitation energies above the pre-edge, it decreases by almost a factor of 5 in contribution to the spectral profile. We note that the asymmetry parameter α also varies with excitation energy being higher at the pre-edge, fully consistent with the argument that this is related to core hole dynamics. Higher amount of the dissociative component gives higher asymmetry reflecting states with elongated O–H bond distances. It is this asymmetry that gives rise to the isotope effect at high excitation energies since it is much smaller for D₂O than for H₂O.^14–1714. T. Tokushima et al., “High resolution x-ray emission spectroscopy of liquid water: The observation of two structural motifs,” Chem. Phys. Lett. 460, 387–400 (2008). https://doi.org/10.1016/j.cplett.2008.04.07715. A. Nilsson et al., “Resonant inelastic x-ray scattering of liquid water,” J. Electron Spectrosc. Relat. Phenom. 188, 84–100 (2013). https://doi.org/10.1016/j.elspec.2012.09.01116. T. Tokushima et al., “High resolution x-ray emission spectroscopy of water and its assignment based on two structural motifs,” J. Electron Spectrosc. Relat. Phenom. 177, 192–205 (2010). https://doi.org/10.1016/j.elspec.2010.02.00817. M. P. Ljungberg, L. G. M. Pettersson, and A. Nilsson, “Vibrational interference effects in x-ray emission of a model water dimer: Implications for the interpretation of the liquid spectrum,” J. Chem. Phys. 134, 044513 (2011). https://doi.org/10.1063/1.3533956 We see in Fig. 4(b) also how the 1b₁′ spectral intensity (red) increases rapidly above the pre-edge, and this can be directly understood in terms of LDL related tetrahedral structures since it is expected that these lack pre-edge intensity as seen in XAS measurements of ice with minimum beam induced effects.⁴⁵45. J. A. Sellberg et al., “Comparison of x-ray absorption spectra between water and ice: New ice data with low pre-edge absorption cross-section,” J. Chem. Phys. 141, 034507 (2014). https://doi.org/10.1063/1.4890035

It has been proposed that the lone pair state in the OH spectrum from sodium hydroxide (NaOH) solution would match the 1b₁′ spectral peak in the non-resonant RIXS spectrum of water as a support of the picture that this feature is entirely due to a dissociation event.¹³13. O. Fuchs et al., “Isotope and temperature effects in liquid water probed by x-ray absorption and resonant x-ray emission spectroscopy,” Phys. Rev. Lett. 100, 027801 (2008). https://doi.org/10.1103/physrevlett.100.027801 The question is if the reference OH group should be the OH⁻ ion or the OH radical state. In the ionization process, when an O 1s electron is removed, we are left with a H₂O⁺ molecule and with the equivalent core approximation; it means that the molecule is close to a H₂F⁺ species. Since F is extremely electronegative, the dissociation event will keep electrons on the fluorine atom with H⁺ leaving to the other hydrogen bonded molecule. We are then left with an OH group that has a completely filled valence shell as an OH⁻ plus an O 1s hole. O 1s ionization of the OH⁻ will thereby lead to a similar electronic state. The only deviation from the simplicity of this comparison can be if the solvation of the remaining OH⁻ group is dramatically different between NaOH and water, but we assume the difference in the bond length between OH⁻ and solvating water for these two cases is only less than a tenth of an angstrom and, therefore, this bond length adjustment should occur on similar time scales as a 1.8 Å transfer of a proton to neighboring water molecule.

In order to enhance the OH contribution, selective excitation was used on a pre-pre-edge feature at 533.5 eV. However, since selective excitation was used, we may expect also, as in the case of pure water, that there will be a spectator shift and the absolute energy position of the OH spectral component in the RIXS spectrum will depend on the exact excitation energy. In the bottom of Fig. 5, we demonstrate that the OH feature shifts with excitation energy in the RIXS spectra of NaOH illustrating the spectator shift. In order to establish the RIXS position of the OH lone pair state, it is essential to use nonresonant excitation. In the top part of Fig. 5, we compare pure water and 2M NaOH solution at nonresonant conditions with the excitation energy of 539.6 eV. We observe that the 1b₁′ position shifts to higher energy and broadens in the NaOH solution indicating the appearance of another component. The difference between the spectra of NaOH and pure water reveals the spectral component of the OH lone pair state, as shown in the middle of Fig. 5. We find the position to be shifted by 0.22 eV from the 1b₁′ position of pure water. It resides almost exactly at the same position, as the fitted dissociative component in Fig. 4(b). This shows consistency with the picture that indeed there is a dissociative OH related component in liquid water at 526.0 eV indicated by an arrow in Fig. 5.

In a special interface layer of water in contact with a hydrophilic brush, there is indeed a spectrum of the 1b₁′ component present with only a small tail toward the 1b₁″ position indicating that this component can be seen without the high energy spectral peak.⁴⁶46. K. Yamazoe et al., “Enhancement of the hydrogen-bonding network of water confined in a polyelectrolyte brush,” Langmuir 33, 3954–3959 (2017). https://doi.org/10.1021/acs.langmuir.7b00243 The IR spectrum shows a vibrational OH stretch frequency of 3200 cm⁻¹⁴⁶46. K. Yamazoe et al., “Enhancement of the hydrogen-bonding network of water confined in a polyelectrolyte brush,” Langmuir 33, 3954–3959 (2017). https://doi.org/10.1021/acs.langmuir.7b00243 consistent with that the sample with a sole 1b₁′ position consists of fully H-bonded coordinated water similar to LDL. It is very unlikely that an almost sole 1b₁′ spectral peak would only be assigned to a fully dissociative OH component without spectral intensity for an intact water peak. Instead this is related to the spectral feature of a unique structural environment.

In conclusion, we find that supporting evidence for both pictures, the one of two structural environments and the one of a dissociative component, contributes to the interpretation of high resolution RIXS data of liquid water. In particular, from the usage of the vibrationally resolved spectra, seen as losses from the elastic line, and inspecting the tail intensity, corresponding to the decay to an almost dissociated state, we can determine the spectral amount of such a component. At pre-edge excitation, the dissociative component is almost of equal intensity as the intact water component, but at higher excitation energies, it diminishes and is observed as a weak component on the high energy tail of the 1b₁′ spectral peak. Based on these observations, we can confirm that the main part of the 1b₁′ peak intensity is related to water in a tetrahedral structural environment.