Isotope effects in x-ray absorption spectra of liquid water

The isotope effects in x-ray absorption spectra of liquid water are studied by a many-body approach within electron-hole excitation theory. The molecular structures of both light and heavy water are modeled by path-integral molecular dynamics based on the advanced deep-learning technique. The neural network is trained on ab initio data obtained with SCAN density functional theory. The experimentally observed isotope effect in x-ray absorption spectra is reproduced semiquantitatively in theory. Compared to the spectrum in normal water, the blueshifted and less pronounced pre- and main-edge in heavy water reflect that the heavy water is more structured at short- and intermediate-range of the hydrogen-bond network. In contrast, the isotope effect on the spectrum is negligible at post-edge, which is consistent with the identical long-range ordering in both liquids as observed in the diffraction experiment.

Figure 1

(a) XAS spectra of ${\mathrm{H}}_2\mathrm{O}$ (red) and ${\mathrm{D}}_2\mathrm{O}$ (black) from theory (solid and dashed lines) and experiment [28] (circles and triangles). (b) ${\mathrm{D}}_2\mathrm{O}\text{−}{\mathrm{H}}_2\mathrm{O}$ difference of the XAS spectra from theory (line) and experiment [28] (circles). (c) First-order derivatives of the XAS spectra with respect to the energy of ${\mathrm{H}}_2\mathrm{O}$ (red) and ${\mathrm{D}}_2\mathrm{O}$ (black) from theory (solid and dashed lines) and experiment (circles and triangles).

Figure 2

(a) $g_{\mathrm{OO}}\left(r\right)$ of liquids ${\mathrm{H}}_2\mathrm{O}$ (red) and ${\mathrm{D}}_2\mathrm{O}$ (black) from theory (solid and dashed lines) and experiment [9] (circles and triangles). The inset shows definitions of proton transfer coordinate $\nu$ and $\mathrm{O}\mathrm{H}\cdots \mathrm{O}$ angle $\theta$. Joint probability distributions of $\theta$ as a function of $\nu$ for (b) ${\mathrm{H}}_2\mathrm{O}$ and (c) ${\mathrm{D}}_2\mathrm{O}$. The red dot located at ($-0.84$, 161.80) in (b) and the black dot located at ($-0.83$, 163.34) in (c) show the $\theta$ and $\nu$ values with the highest probability.

Figure 3

(a) Joint probability distribution of O-H/O-D covalent bond lengths as a function of excitation energies of states with $4a_1$ character of liquids ${\mathrm{H}}_2\mathrm{O}$ (red shadows) and ${\mathrm{D}}_2\mathrm{O}$ (dashed black lines). (b) Averaged intensities of states with $4a_1$ character as a function of ${\mathrm{A}}_i{\mathrm{D}}_j$ in ${\mathrm{H}}_2\mathrm{O}$. ${\mathrm{A}}_i{\mathrm{D}}_j$ indicates the number of acceptor-type (${\mathrm{A}}_i$) and donor-type (${\mathrm{D}}_j$) H-bonds, respectively. Insets show representative H-bond environments and distributions of quasiparticle wave functions (QWs). The excited oxygen atom is shown in black. QWs with opposite signs are depicted in blue and yellow. (c) Distributions of ${\mathrm{A}}_i{\mathrm{D}}_j$ in liquids ${\mathrm{H}}_2\mathrm{O}$ (red) and ${\mathrm{D}}_2\mathrm{O}$ (grey).

Figure 4

(a) Probability distributions of LSI of liquids ${\mathrm{H}}_2\mathrm{O}$ (solid red line) and ${\mathrm{D}}_2\mathrm{O}$ (dashed black line). The yellow and green shadows divide ${\mathrm{H}}_2\mathrm{O}$ molecules into two parts: $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{L}}$ and $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{H}}$. Insets illustrate molecular configurations schematically, with each dot represents a water molecule. The grey and red areas show the first and second coordination shells, respectively. (b) XAS spectra of liquid ${\mathrm{H}}_2\mathrm{O}$ contributed by water molecules in part $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{L}}$ (solid orange line) and part $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{H}}$ (dashed green line). The XAS spectra of ${\mathrm{D}}_2\mathrm{O}$ contributed by $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{L}}$ and $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{H}}$ molecules have the same trend and are presented in the Supplemental Material [69]. Insets show representative QWs of excited water molecules in part $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{L}}$ (upper panel) and part $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{H}}$ (lower panel). (c) Intensities and excitation energies of excitons in the part $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{L}}$ (yellow circles) and part $\mathrm{L}\mathrm{S}{\mathrm{I}}_{\mathcal{H}}$ (green circles). Colors of the circles show the localization distance of QWs, which is defined as the radial distance from the excited oxygen atom that includes $80\%$ of QWs. Excitons with excitation energy $\in$ [537, 539] eV and intensity larger than 0.5, which contribute to the formation of the main-edge, are presented.