Michael Yao

Two states of water, made visible

Is liquid water one continuum, or a mixture of two local structures? A century-old debate, because both pictures fit the same bulk data. Unsupervised clustering decides — validated against an observable the clustering never saw.

Is liquid water one continuum, or a mixture of two local structures?

Flowchart from molecular-dynamics trajectories through feature extraction, GMM fitting, and likelihood-ratio classification into LFTS, transitional, and DNLS water structures
From molecular-dynamics trajectories to an unsupervised classification of locally favoured tetrahedral and disordered normal-liquid structures.

The method

I ran molecular dynamics on TIP4P/2005 and TIP5P1 water and described each molecule by four order parameters — tetrahedral order q, LSI, Sk, and translational order ζ. A hybrid density-denoising pipeline (DBSCAN → GMM)2 gave the clearest split: two structurally distinct populations — locally favoured tetrahedral structures (LFTS) and disordered normal-liquid structures (DNLS) — emerge on their own.

Order-parameter density resolved into LFTS and DNLS clusters
One diffuse cloud of molecules (left) resolves into two clean populations across every order parameter (right). No labels were given; the split is the data's own.
Each population as its own 3D density surface — the low-density LFTS cluster (left) and the higher-density DNLS cluster (right). Drag to rotate, scroll to zoom.

The validation

Clusters are easy to draw and hard to trust. So I tested them against something the clustering never saw: the per-cluster oxygen–oxygen structure factor S(k), computed straight from atomic coordinates. The LFTS cluster peaks at kT1 ≈ 0.81, the DNLS cluster at kD1 ≈ 1.05 — exactly where two-state theory predicts. Since clustering and validation share no descriptor, the agreement is model-independent.3

Per-cluster structure factors with distinct first diffraction peaks that superpose into the total
Each cluster carries its own first diffraction peak; together they superpose into the total S(k) of real water.

Generality

The two-state signature is not an artefact of one model or temperature. It holds from deep supercooling to ambient conditions, and across three independent water models.

Structure factors and population fractions across temperature and across water models
The LFTS fraction shifts smoothly with temperature and the peaks persist across TIP4P/2005, TIP5P, and SWM4-NDP.
  1. TIP4P/2005 and TIP5P are rigid, point-charge parameterizations of the water molecule built for molecular-dynamics simulation — along with SWM4-NDP, the third model used in the generality check below, these are three independently developed descriptions of the same substance.
  2. DBSCAN is a density-based clustering step that strips out sparse, ambiguous points without requiring a fixed cluster count in advance; the GMM (Gaussian mixture model) that follows then fits soft, probabilistic memberships to whatever populations DBSCAN leaves behind.
  3. “Model-independent” here means the same two-population split shows up whether you look at the four order parameters used to build the clusters or at S(k) computed straight from atomic coordinates — since the clustering step and the validation step never share a descriptor, one can't have quietly leaked into the other.
  4. The two-state framing tested here follows the Shi & Tanaka hypothesis for structural heterogeneity in liquid water.
  5. Code and analysis: github.com/OhhMoo/Water_Clustering
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