Topological origin of peak splitting in the structure factor of liquid water

Abstract

The splitting of the principal peak in the structure factor of liquid water is commonly interpreted as evidence of a competition between two distinct local environments. Here, we show that this peak splitting arises from medium-range topological features of the hydrogen-bond network. Using atomistic simulations, we systematically decompose the structure factor into contributions from hydrogen-bonded rings of different sizes. We find that 5-8-membered rings, which dominate the network topology of liquid water at low temperatures, can directly explain the experimentally observed bimodal scattering signal. Among these, 5-membered rings are particularly persistent, maintaining distinct structural signatures even above room temperature. Our findings establish a direct link between the network topology of liquid water and experimentally accessible diffraction features, clarifying the microscopic basis of water's behaviour and suggesting a broader conceptual framework for interpreting the anomalies in tetrahedral network liquids and glasses.

Figures (4)

• Figure 1: Peak splitting in the structure factor, $S(q)$, of liquid water at 1 bar. (a) Simulation results obtained with MACE (solid lines) and ACE (dotted lines) potentials at 240 K (yellow) and 260 K (dark blue), alongside experimental data (dashed lines) from Ref. Skinner-14-12. The corresponding experimental temperatures are indicated to the right of each curve. (b) Magnified view of the low-$q$ (1.2 Å$^{-1}$ to 3.6 Å$^{-1}$) region, highlighting the emergence and divergence of two peaks, $S_1$ and $S_2$, as shown by black dashed lines. Peak positions at each temperature are determined via Gaussian Process (GP) fits to the simulation data. At temperatures above 330 K, the GP fit does not resolve two separate maxima. (c) Temperature dependence of the peak separation $S_2 - S_1$ comparing the current MACE model (black circles) with the classical TIP4P/2005 model (squares), and experimental data from Skinner et al.Skinner-14-12 (triangles), Sellberg et al.Sellberg-14-6 (squares), and Benmore et al.Benmore-19-9 (diamonds).
• Figure 2: Ring statistics and neighbourhood structure in the HBN of liquid water from 260 to 350 K. (a) Probability distribution, $P(n)$, of observing hydrogen-bonded rings consisting of $n$ water molecules, where $n \in [3, 12]$, across a range of temperatures. (b) Expected number of neighboring rings of sizes 5 (blue), 6 (grey), and 7 (pink), conditional on a central ring of size 4 (left), 5 (middle), or 6 (right) as a function of temperature. (c--d) Representative snapshots of the HBN at 300 K, illustrating neighbouring ring structures, hydrogens have been omitted for clarity. Panel (c) shows an example of adjacent 4- and 7-membered rings; panel (d) shows an example of adjacent 5- and 6-membered rings. Insets show full molecular representations of the rings.
• Figure 3: Temperature dependence of dynamic properties of hydrogen-bonded rings in liquid water. (a) Average lifetimes of hydrogen-bonded rings as a function of ring size ($n \in [3, 12]$) and temperature. (b) Self-diffusion coefficient, $D$, of water as a function of temperature. The cartoon illustrates the breaking of a hydrogen-bonded ring via translational motion of a water molecule. (c) Rotational lifetime of water molecules as a function of temperature. The cartoon illustrates the breaking of a hydrogen-bonded ring via rotational motion of a water molecule.
• Figure 4: Ring-resolved decomposition of the structure factor, $S(q)$, of liquid water at 1 bar. (a) Structure factors at 260 K and 330 K, decomposed into contributions from individual ring sizes, $S_n(q)$, where $n \in [3, 12]$. The complete structure factor is shown in black, while colored lines represent contributions from specific ring sizes (blue for smaller rings, red for larger rings). (b) Temperature dependence of the peak separation, $S_2 - S_1$, for different ring sizes. The black curve represents the trend for the complete structure factor as shown in Fig. \ref{['fig:struct-fact-per-temp']}c.