A new phase of solid hydrogen is predicted

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Hydrogen, the most abundant element in the universe, is found everywhere, from the dust that fills most of outer space to the cores of stars to many substances here on Earth. This would be reason enough to study hydrogen, but its individual atoms are also the simplest of all elements with only one proton and one electron. For David Sepperly, a professor of physics at the University of Illinois at Urbana-Champaign, this makes hydrogen the natural starting point for formulating and testing theories of matter.

Ceperley, also a member of the Illinois Center for Quantum Information and Technology, uses computer simulations to study how hydrogen atoms interact and combine to form different phases of matter such as solids, liquids and gases. However, a true understanding of these phenomena requires quantum mechanics, and quantum mechanical simulations are expensive. To simplify the task, Ceperley and his collaborators developed a machine learning technique that allows quantum mechanical simulations to be performed with an unprecedented number of atoms. They reported in Physical examination letters that their method discovered a new type of solid hydrogen under high pressure that previous theory and experiments had missed.

“It turned out that machine learning taught us a lot,” Ceperley said. “We saw signs of new behavior in our previous simulations, but we didn’t believe them because we could only fit a small number of atoms. With our machine learning model, we could take full advantage of the most accurate methods and see what is really happening.”

Hydrogen atoms form a quantum-mechanical system, but capturing their full quantum behavior is very difficult, even on computers. A state-of-the-art technique such as quantum Monte Carlo (QMC) can realistically simulate hundreds of atoms, while understanding the behavior of large-scale phases requires simulating thousands of atoms over long periods of time.

To make QMC more flexible, two former students, Hongwei Niu and Yubo Yang, developed a machine learning model trained with QMC simulations capable of accommodating many more atoms than QMC alone. They then used the model with postdoctoral researcher Scott Jensen to study how the solid phase of hydrogen, which forms at very high pressure, melts.

The three were exploring different temperatures and pressures to form a complete picture when they noticed something unusual in the solid phase. While the molecules in solid hydrogen are usually close to spherical and form a configuration called hexagonal close-packed—Ceperley compares it to stacked oranges—the researchers observed a phase in which the molecules become elongated shapes—Ceperley describes them as egg-like.

“We started out with the not-too-ambitious goal of advancing the theory of something we knew about,” Jensen recalls. “Unfortunately, or perhaps fortunately, it was more interesting than that. This new behavior appeared. In fact, this was the dominant behavior at high temperatures and pressures, something that was not even hinted at in the older theory.

To verify their results, the researchers trained their machine learning model with data from density functional theory, a widely used technique that is less accurate than QMC but can accommodate many more atoms. They found that the simplified machine learning model perfectly reproduced the results of the standard theory. The researchers conclude that their large-scale QMC simulations, aided by machine learning, can account for effects and make predictions that standard techniques cannot.

This work started a conversation between Ceperley’s collaborators and some experimenters. Measurements of hydrogen at high pressure are difficult to perform, so experimental results are limited. The new prediction inspired some groups to revisit the problem and study more closely the behavior of hydrogen under extreme conditions.

Ceperley noted that understanding hydrogen at high temperatures and pressures will improve our understanding of Jupiter and Saturn, gaseous planets made mostly of hydrogen. Jensen added that hydrogen’s “simplicity” makes it an important substance to study. “We want to understand everything, so we have to start with systems we can attack,” he said. “Hydrogen is simple, so it’s worth knowing we can handle it.”

Reference: Niu H, Yang Y, Jensen S, Holzmann M, Pierleoni C, Ceperley DM. Stable solid molecular hydrogen above 900 K from a machine-learned potential trained with diffusion quantum Monte Carlo. Phys Rev Lett. 2023;130(7):076102. do: 10.1103/PhysRevLett.130.076102

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