Temperature-Independent Nuclear Quantum Effects on the Structure of Water

Nuclear quantum effects (NQEs) have a significant influence on the hydrogen bonds in water and aqueous solutions and have thus been the topic of extensive studies. However, the microscopic origin and the corresponding temperature dependence of NQEs have been elusive and still remain the subject of ongoing discussion. Previous x-ray scattering investigations indicate that NQEs on the structure of water exhibit significant temperature dependence [Phys. Rev. Lett. 94, 047801 (2005)]. Here, by performing wide-angle x-ray scattering of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ droplets at temperatures from 275 K down to 240 K, we determine the temperature dependence of NQEs on the structure of water down to the deeply supercooled regime. The data reveal that the magnitude of NQEs on the structure of water is temperature independent, as the structure factor of ${\mathrm{D}}_2\mathrm{O}$ is similar to ${\mathrm{H}}_2\mathrm{O}$ if the temperature is shifted by a constant 5 K, valid from ambient conditions to the deeply supercooled regime. Analysis of the accelerated growth of tetrahedral structures in supercooled ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ also shows similar behavior with a clear 5 K shift. The results indicate a constant compensation between NQEs delocalizing the proton in the librational motion away from the bond and in the OH stretch vibrational modes along the bond. This is consistent with the fact that only the vibrational ground state is populated at ambient and supercooled conditions.

Figure 1

(a) Schematic diagram of wide-angle x-ray scattering of supercooled ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ droplets under evaporative cooling condition. (b) Temperature-dependent scattering structure factor $S(q)$ of ${\mathrm{H}}_2\mathrm{O}$ (top) and ${\mathrm{D}}_2\mathrm{O}$ (bottom). Water temperature decreases from bottom to top, and the temperature of each $S(q)$ curve is indicated on the right-hand side. A constant offset has been introduced between the curves.

Figure 2

(a) Scattering structure factor $S(q)$ of ${\mathrm{H}}_2\mathrm{O}$ (red) and ${\mathrm{D}}_2\mathrm{O}$ (blue) at the same temperature ($\sim 249\mathrm{K}$). The vertical dotted lines indicate the positions of the $S_1$ and $S_2$ peaks. (b) The difference scattering curve $\mathrm{\Delta }{S}_{{\mathrm{H}}_2{\mathrm{O}\text{−}\mathrm{D}}_2\mathrm{O}}(q,T)$, calculated by taking the difference between the $S(q)$ of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ at the same temperature ($\sim 249\mathrm{K}$, black), is compared with the temperature derivative $\mathrm{\Delta }S/\mathrm{\Delta }T$, calculated by taking the difference between the $S(q)$ of ${\mathrm{H}}_2\mathrm{O}$ at two different temperatures (249.1 and 243.3 K, red). (c) Direct comparison of the scattering structure factor $S(q)$ between ${\mathrm{H}}_2\mathrm{O}$ (red) and ${\mathrm{D}}_2\mathrm{O}$ (blue) at three different temperature points. The $\sim 5\mathrm{K}$ warmer temperatures for ${\mathrm{D}}_2\mathrm{O}$ are selected to test the 5 K shift model (241.0 versus 246.6 K, 246.8 versus 251.9 K, and 253.6 versus 258.3 K are shown in the top, middle, and bottom panels, respectively).

Figure 3

(a) Isobaric temperature derivative ${[\partial S_{H_{2}O}(q,T)/\partial T]}_P$ of ${\mathrm{H}}_2\mathrm{O}$ at three different temperatures (243.3, 253.6, and 265.5 K). (b) To obtain a $q$-independent measure of the variation in the magnitude of the ITD of ${\mathrm{H}}_2\mathrm{O}$ (red squares) and ${\mathrm{D}}_2\mathrm{O}$ (blue triangles) with temperature, the ITD for different $q$ values are summed into single values and plotted as a function of temperature. The data points from ${\mathrm{D}}_2\mathrm{O}$ are shifted by 5 K in the graph, and the temperature for ${\mathrm{D}}_2\mathrm{O}$ is indicated at the top axis. The temperature-dependent magnitude of the ITD of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ is indicated by the common fit (black solid line) that has a functional form of $[A/(T-T_0)+B]$.