Topological contribution to the split first peak of the liquid water structure factor using the MACE machine-learning potential.

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 is captured by 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 and provide a topological perspective on the nature of the split first diffraction peak in tetrahedral materials.