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

Significance Water is the matrix of life and behaves anomalously in many of its properties. Since Wilhelm Conrad Röntgen, two distinct separate phases have been argued to coexist in ambient water, competing with the alternative view of the single-phase liquid, footing on X-ray scattering experiment and theory. We conducted a quantitative and high-resolution X-ray spectroscopic multimethod investigation and analysis (X-ray absorption, X-ray emission, and resonant inelastic X-ray scattering). We find that all known X-ray spectroscopic observables can be fully and consistently described with continuous-distribution models of near-tetrahedral liquid water at ambient conditions with 1.74 ± 2.1% donated and accepted H-bonds per molecule.

linear approximation is a reasonable one. 23 Indeed, the used linear interpolation is supported by our previous results devoted to the simulation of XAS for 64 water The area of pre-edge intensity (σ) was evaluated as the area integral from the XAS spectra in the range [533,535.5] eV. The 33 spectra and the number of donated H-bonds were evaluated for each snapshot and for each molecule separately, which yielded 34 1344 individual (σ, N d ) pairs, that we here classify with respect to N d for average pre-edge intensity evaluation. For

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Since we compare spectra from different methods (EELS for gas phase and XRS for condensed phases), we must consider 43 the possibility of the mismatch in our total spectral range integrals (Table S1) to originate from the mismatch in experimental 44 techniques. Here, we derive H-bond number error estimate assuming the mismatch in total integrated intensity to originate 45 from the method.

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To arrive in an estimate for error limit, we derive the number of donated H-bonds that would be obtained if the gas-phase spectrum was scaled for its integral to meet the total intensity mean 0.5 × (70.7386 + 70.7064) = 70.7220 of the liquid and ice. We note that these two agree rather well. For the gas spectrum to match this intensity, a scaling factor of g = 70.7220/78.5419 ≈ 0.90044 should be applied to the spectrum, and especially all of its regional integrals. Most notably this yields pre-edge intensity of where the potential V (r) = U (r) + l(l + 1)/r 2 for the l−th harmonic include the centrifugal potential. We model the confinement 57 of an electron inside of a coordination shell at r = R by the following potential [3]

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In spite of the fact that this model with extensive barrier ignores tunnelling, it allows to get the energy of the shape resonance.
Here n is integer. Apparently n * = n when V0 = ∞ while n * = n + 1/2 when the energy E kin approaches V0. Now we are in 66 stage to write equation for the radius of coordination shell In the case of our interest E kin ≈ 4 eV. Thus Therefore, we estimate the radius R of the coordination spheres for the shape resonance near E kin = 4 eV 71 R ≈ 1.53Å, 3.06Å, 4.59Å, 6.12Å for effective quantum numbers n * = 0.5, 1, 1.5, and 2, respectively.

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Eq. 5 shows the general property of the peak position of shape resonance This correlation between the shape resonance and position of the effective barrier is universal and is widely used to extract the 76 bond length from the experimental data (8, 9). One should notice that the constant C is sensitive to the system (diatomic 77 molecule, polyatomic molecules, liquids etc).

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The gas and liquid lines of the phase diagram in Figure 1 are from Refs. 10, 11. For the phase diagram, the gray coexistence 79 curves between the triple points of ices (11-17) were obtained by Clausius equation as a boundary value problem with fixed 80 ∆S/∆V .

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The experimental RIXS spectrum contained sidepeaks due to X-ray optics that were subtracted as follows: (i) a constant to obtain parameters De and a. The position of the minimum r0 is not obtainable from the data and was given the value 0.95 Å, when drawing the potential energy curve for gas.

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The XES simulations were carried out in three steps. First, we obtained a snapshot from ab initio molecular dynamics intervals up to 10 fs, and a broadening with a gaussian of 0.5 eV full-width-at-half-maximum was applied to the spectrum.

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Because the decay-rate (and the relative contribution of XES spectra of later times) follows the same exponential law as the 120 core-hole-state, we computed the XES σ(τ ), accumulated up to time τ as follows The energy scale is relative to the ground state of the ion, and we averaged over all oxygen sites of the simulation box. The 123 results with different upper limit τ for the integral are depicted in Figure 4, where the instantaneous averaged emission spectra 124 are also shown.

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In the analysis of XES, we refer to the structural parameters at the moment of ionization (before the core-ionized dynamics), 126 except for bond lengths that are evaluated at the indicated time. The error limit is based on the standard deviation in 1000-fold 127 bootstrap re-sampling technique.

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Supporting data 129 The short XRS spectra were normalized to the mean value in the range 548-550 eV, and are depicted with f-density normalization 130 and with f-sum rule normalization in Fig. S1. The long spectra were normalized to the mean value in the range 580-585 eV, and 131 are depicted in Fig. S2 and the corresponding intensity integral values are presented in Table S1. The XES spectra recorded 132 photon energies 550 eV and above are shown in full in Figure S3. Tabulated values for the peak positions and heights of the 133 radial distribution functions of water in some condensed phases from Ref. 29 are given in Table S2. The average structural 134 parameters from the XES simulation are given in Table S3. The complete correlation coefficient data of Ref. 2 is presented in 135 Figure S4. Figure S5 shows the relation of the mean pre-peak intensity to N d from simulations (2).