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 H2O and D2O 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 D2O is similar to H2O 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 H2O and D2O 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.

Femtosecond x-ray laser pulses were used to probe micrometer-sized water droplets that were cooled down to 227 kelvin in vacuum. Isothermal compressibility and correlation length were extracted from x-ray scattering at the low-momentum transfer region. The temperature dependence of these thermodynamic response and correlation functions shows maxima at 229 kelvin for water and 233 kelvin for heavy water. In addition, we observed that the liquids undergo the fastest growth of tetrahedral structures at similar temperatures. These observations point to the existence of a Widom line, defined as the locus of maximum correlation length emanating from a critical point at positive pressures in the deeply supercooled regime. The difference in the maximum value of the isothermal compressibility between the two isotopes shows the importance of nuclear quantum effects.

The dynamics of liquid water feature a variety of time scales, ranging from extremely fast ballistic-like thermal motion, to slower molecular diffusion and hydrogen-bond rearrangements. Here, we utilize coherent X-ray pulses to investigate the sub-100 fs equilibrium dynamics of water from ambient conditions down to supercooled temperatures. This novel approach utilizes the inherent capability of X-ray speckle visibility spectroscopy to measure equilibrium intermolecular dynamics with lengthscale selectivity, by measuring oxygen motion in momentum space. The observed decay of the speckle contrast at the first diffraction peak, which reflects tetrahedral coordination, is attributed to motion on a molecular scale within the first 120 fs. Through comparison with molecular dynamics simulations, we conclude that the slowing down upon cooling from 328 K down to 253 K is not due to simple thermal ballistic-like motion, but that cage effects play an important role even on timescales over 25 fs due to hydrogen-bonding.

The isothermal compressibility and correlation length of supercooled water obtained from small-angle X-ray scattering (SAXS) were analyzed by fits based on an apparent power-law in the temperature range from 280 K down to the temperature of maximum compressibility at 229 K. Although the increase in thermodynamic response functions is not towards a critical point, it is still possible to obtain an apparent power law all the way to the maximum values with best-fit exponents of gamma = 0.40 +/- 0.01 for the isothermal compressibility and nu = 0.26 +/- 0.03 for the correlation length. The ratio between these exponents is close to a value of approximate to 0.5, as expected for a critical point, indicating the proximity of a potential second critical point. Comparison of gamma obtained from experiment with molecular dynamics simulations on the iAMOEBA water model shows that it would be located at pressures in the neighborhood of 1 kbar. The high value and sharpness of the compressibility maximum observed in the experiment are not reproduced by any of the existing classical water models, thus inviting further development of simulation models of water.

Wide angle x-ray scattering of supercooled water down to 234.8 K was studied using high energy x rays at the European Synchrotron Radiation Facility. The oxygen-oxygen pair distribution function (PDF) was calculated from the scattering pattern out to the 5th peak at an intermolecular distance, r approximate to 11 angstrom. We observe that the 4th peak and the 5th peak in the PDF increase in height upon supercooling. We also observe that the 4th peak position (r(4)) shifts to shorter distances upon supercooling consistent with previous studies, but we see a more rapid change at the lowest temperature. The running oxygen-oxygen coordination number is calculated for 5 different temperatures, and an isosbestic point at r(iso) = 3.31 +/- 0.05 angstrom was found corresponding to a coordination number of 4.39 +/- 0.15. The comparison of the PDF of the coldest water with that of amorphous ice shows distinct differences. We propose that there are 5-member pentamer rings in low density liquid-like structures giving rise to the sharp correlations at r approximate to 9 angstrom and r approximate to 11 angstrom.

Here we report on the temperature dependence of the anomalous behaviour of water in terms of (i) its growth in tetrahedral structures, (ii) instantaneous spatial correlations from small angle x-ray scattering (SAXS) data, (iii) estimates of thermodynamic response functions of isothermal compressibility and (iv) thermal expansion coefficient. Water's thermal expansion coefficient is estimated for the first time at supercooled conditions from liquid water's structure factor. We used previously published data from classical force-fields of TIP4P/2005 and iAMOEBA to compare experimental data with molecular dynamics simulations and observe that these force-fields underestimate water's anomalous behaviour but perform better upon increasing pressure. We demonstrate that the molecular dynamics simulations can describe better the temperature dependent anomalous behaviour of ambient pressure water if simulated at 1 kbar. The deviation in anomalous fluctuations in the simulations is not restricted to approximate to 228 K but extends all the way to ambient temperatures.