Four recent x-ray diffraction measurements of ambient liquid water are reviewed here. Each of these measurements represents a significant development of the x-ray diffraction technique applied to the study of liquid water. Sources of uncertainty from statistical noise, Q-range, Compton scattering, and self-scattering are discussed. The oxygen-hydrogen contribution to the measured x-ray scattering pattern was subtracted using literature data to yield an experimental determination, with error bars, of the oxygen-oxygen pair-distribution function, g_OO(r), which essentially describes the distribution of molecular centers. The extended Q-range and low statistical noise of these measurements has significantly reduced truncation effects and related errors in the g_OO(r) functions obtained. From these measurements and error analysis, the position and height of the nearest neighbor maximum in g_OO(r) were found to be 2.80(1) Å and 2.57(5) respectively. Numerical data for the coherent differential x-ray scattering cross-section I_X(Q), the oxygen-oxygen structure factor S_OO(Q), and the derived g_OO(r) are provided as benchmarks for calibrating force-fields for water.

The structures of heavy and light water at ambient conditions are investigated with the combined techniques of x-ray diffraction, neutron diffraction, and computer simulation. It is found that heavy water is a more structured liquid than light water. We find the OH bond length in ${\mathrm{H}}_2\mathrm{O}$ is $\sim 3\%$ longer than the OD bond length in ${\mathrm{D}}_2\mathrm{O}$. This is a much larger change than current predictions. Corresponding to this, the hydrogen bond in light water is $\sim 4\%$ shorter than in heavy water, while the intermolecular HH distance is $\sim 2\%$ longer.

Calcium silicate hydrate (CSH) is the major volume phase in the matrix of Portland cement concrete. Total x-ray scattering measurements with synchrotron x rays on synthetic CSH(I) shows nanocrystalline ordering with a particle diameter of 3.5(5) nm, similar to a size-broadened 1.1 nm tobermorite crystal structure. The CSH component in hydrated tricalcium silicate is found to be similar to CSH(I). Only a slight bend and additional disorder within the CaO sheets is required to explain its nanocrystalline structure.

Structural changes during annealing of high-density amorphous ice were studied with both neutron and x-ray diffraction. The first diffraction peak was followed from the high- to the low-density amorphous form. Changes were observed to occur through a series of intermediate forms that appear to be metastable at each anneal temperature. Five distinct amorphous forms were studied with neutron scattering, and many more forms may be possible. Radial distribution functions indicate that the structure evolves systematically between 4 and 8 angstroms. The phase transformations in low-temperature liquid water may be much more complex than currently understood.

An accurate and computationally efficient molecular level description of mesoscopic behavior of ice-water systems remains a major challenge. Here, we introduce a set of machine-learned coarse-grained (CG) models (ML-BOP, ML-BOP_dih, and ML-mW) that accurately describe the structure and thermodynamic anomalies of both water and ice at mesoscopic scales, all at two orders of magnitude cheaper computational cost than existing atomistic models. In a significant departure from conventional force-field fitting, we use a multilevel evolutionary strategy that trains CG models against not just energetics from first-principles and experiments but also temperature-dependent properties inferred from on-the-fly molecular dynamics (~ 10’s of milliseconds of overall trajectories). Our ML BOP models predict both the correct experimental melting point of ice and the temperature of maximum density of liquid water that remained elusive to-date. Our ML workflow navigates efficiently through the high-dimensional parameter space to even improve upon existing high-quality CG models (e.g. mW model).

Here we present diffraction data that yield the oxygen-oxygen pair distribution function, g_OO(r) over the range 254.2–365.9 K. The running O-O coordination number, which represents the integral of the pair distribution function as a function of radial distance, is found to exhibit an isosbestic point at 3.30(5) Å. The probability of finding an oxygen atom surrounding another oxygen at this distance is therefore shown to be independent of temperature and corresponds to an O-O coordination number of 4.3(2). Moreover, the experimental data also show a continuous transition associated with the second peak position in g_OO(r) concomitant with the compressibility minimum at 319 K.