A study published in Nature Physics provides new molecular-level evidence from simulations that liquid water is not a single uniform substance, but a constantly shifting mixture of two distinct microscopic structures.

The idea that water might exist in two distinct structural states is not new. For decades, scientists have theorized that liquid water is composed of two interconvertible local structures—one denser and more disordered, the other less dense and more ordered.

This "two-state model" has been invoked to explain water's many anomalous properties, including why it becomes easier to compress as it cools and why it reaches maximum density at 4°C (39°F) rather than at its freezing point. But the model has remained controversial because direct molecular-level evidence for the two structures has been elusive.

Phys.org spoke to corresponding author Prof. Xiao Cheng Zeng from City University of Hong Kong about the study and its findings.

"I have been very interested in the topic of phase transitions since I was a graduate student," said Zeng. "I started theoretical research on freezing of liquids when I was a postdoc, but I was always hoping to study freezing of water one day. Since then, I have been particularly interested in the topic of liquid-liquid transition in water."

Yet despite decades of theoretical work, direct molecular-level evidence for the two structures has remained out of reach.

Molecular-level proof

Central to the two-state model is a hypothesized phenomenon known as the liquid-liquid phase transition (LLPT). The idea is that in the deeply supercooled regime, water splits into two macroscopically distinct liquid phases: a high-density liquid and a low-density liquid.

The boundary between them is thought to terminate at a "second critical point." This deeply supercooled region is so hard to study experimentally because water crystallizes rapidly. Much of the evidence for the LLPT has therefore come from computational studies.

Previously, a 2025 Nature Physics study made progress by using a deep neural network to map the location of this critical point.

"According to the two-state hypothesis, liquid water can be viewed as a mixture of two distinct structures, A and B. But no one has ever seen a genuine 'pure A' or 'pure B' liquid water. Indeed, due to the lack of direct molecular-level evidence, this model has been a subject of debate," said Zeng.

The problem is not just experimental, according to the researchers. Even in simulations, traditional methods that measure local density and energy differences between molecules failed to cleanly separate the two structures. What was needed was a way to let the data reveal the hidden molecular fingerprint of each structure—without any human assumptions about what that fingerprint should look like.

Unsupervised learning

To find this fingerprint, the team turned to an unsupervised deep learning approach—one that could extract hidden structural information from the data without any predefined assumptions about what the two structures should look like.

"It is practically impossible for humans to intuitively guess or manually construct such complex, nonlinear, and nearly orthogonal physical parameters," said Zeng. "We need AI's help to learn and [then] uncover these hidden physical characteristics."

The model was trained on approximately 74 million local water-molecule configurations drawn from massive molecular dynamics simulations using the TIP4P/Ice water model. This is a widely used and accurate computational model of water across a broad range of temperatures and pressures. Roughly 17% of the training data came from the liquid-liquid phase transition region, while the rest came from outside it to ensure the model learned from diverse conditions.

The architecture was an autoencoder. The encoder took the local structure of each water molecule as input and learned to predict two physically meaningful quantities: local density and local potential energy. The decoder then took these outputs and searched for hidden physical characteristics, mathematical values the model assigned to each molecule that went beyond what density and energy alone could capture.

To guide this search without introducing bias, the researchers set two loose mathematical constraints. Alpha controlled the linear correlation of the hidden characteristic with local density, and phi controlled the geometric angle of that relationship.

By systematically varying these, they effectively rotated their viewing angle of the data, searching for the configuration at which the two structures—if they existed—would reveal themselves most clearly.

Two structures and interconversion

When the model found the optimal configuration, two distinct clusters emerged, suggesting two local structures: Structure A, denser and more disordered, and Structure B, less dense and more ordered. The simulations found these patterns across a broad range of temperatures and pressures, including some close to room-temperature conditions.

But the study revealed something beyond support for the existence of the two structures. The way Structure A and Structure B interconvert depends on where the system sits in the phase diagram. In the high-density liquid phase, the interconversion proceeds via an "upper semi-loop" pathway through a single transition state. In the low-density liquid phase, it follows a different "lower semi-loop" pathway through a different transition state.

Near the liquid-liquid phase boundary, where the two liquid phases compete most intensely, these two pathways combine into a complex three-dimensional "full-loop" reaction pathway involving three transition states. As the system moves away from the boundary and one phase begins to dominate, this full loop degenerates back into a simpler single-pathway semi-loop.

"The transformation between Structure A and Structure B is not a simple 'back-and-forth' process," said Zeng. "The interconversion pathways of the two structures are different under different states of water. This microscopic dynamic process is extremely difficult to identify using traditional theoretical methods."

Future work

The findings provide strong molecular-level evidence for the two-state model of water, with the bimodal feature in the data offering a structural signature of the two distinct local states. But questions remain.

"A crucial immediate step is to decode the physical interpretability of the two hidden physical characteristics revealed by the AI, and to seek their experimental verification," said Zeng.

Beyond fundamental physics, the researchers suggest the findings could have broader implications, from understanding how water behaves in biological cells and membranes to shedding light on geological processes in confined environments.

Who's behind this story?

Tejasri Gururaj

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