Hydrogen’s Hidden Phase:

Machine Learning Unlocks the Secrets of the Universe’s Most Abundant Element

By UNIVERSITY OF ILLINOIS GRAINGER COLLEGE OF ENGINEERING APRIL 23, 2023
https://scitechdaily.com/hydrogens-hidden-phase-machine-learning-unlocks-the-secrets-of-the-universes-most-abundant-element/

New Phase of Solid Hydrogen Predicted


Putting hydrogen on solid ground: simulations with a machine learning model 
predict a new phase of solid hydrogen.

A machine-learning technique developed by University of Illinois 
Urbana-Champaign researchers has revealed a previously undiscovered 
high-pressure solid hydrogen phase, offering insights into hydrogen’s behavior 
under extreme conditions and the composition of gaseous planets like Jupiter 
and Saturn.


Hydrogen, the most abundant element in the universe, is found everywhere from 
the dust filling 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 any element with just one proton and 
one electron.

For David Ceperley, a professor of physics at the University of Illinois 
Urbana-Champaign, this makes hydrogen the natural starting point for 
formulating and testing theories of matter.

Ceperley, also a member of the Illinois Quantum Information Science and 
Technology Center, uses computer simulations to study how hydrogen atoms 
interact and combine to form different phases of matter like solids, liquids, 
and gases.

However, a true understanding of these phenomena requires quantum mechanics, 
and quantum mechanical simulations are costly. 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 Review Letters that their method found a new kind of 
high-pressure solid hydrogen that past theory and experiments missed.

“Machine learning turned out to teach us a great deal,” Ceperley said. “We had 
been seeing signs of new behavior in our previous simulations, but we didn’t 
trust them because we could only accommodate small numbers of atoms. With our 
machine learning model, we could take full advantage of the most accurate 
methods and see what’s really going on.”

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 like quantum Monte Carlo (QMC) can feasibly 
simulate hundreds of atoms, while understanding large-scale phase behaviors 
requires simulating thousands of atoms over long periods of time.

To make QMC more versatile, two former graduate students, Hongwei Niu and Yubo 
Yang, developed a machine learning model trained with QMC simulations capable 
of accommodating many more atoms than QMC by itself.

They then used the model with postdoctoral research associate Scott Jensen to 
study how the solid phase of hydrogen that forms at very high pressures melts.

Molecules change shape

The three of them were surveying 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 normally close-to-spherical and form 
a configuration called hexagonal close packed—Ceperley compared it to stacked 
oranges—the researchers observed a phase where the molecules become oblong 
figures—Ceperley described them as egg-like.  (and looking almost wall-like?)

“We started with the not-too-ambitious goal of refining the theory of something 
we know about,” Jensen recalled. “Unfortunately, or perhaps fortunately, it was 
more interesting than that.

There was this new behavior showing up. In fact, it was the dominant behavior 
at high temperatures and pressures, something there was no hint of in 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 standard 
theory. The researchers concluded that their large-scale, machine 
learning-assisted QMC simulations can account for effects and make predictions 
that standard techniques cannot.

This work has started a conversation between Ceperley’s collaborators and some 
experimentalists. High-pressure measurements of hydrogen are difficult to 
perform, so experimental results are limited. The new prediction has inspired 
some groups to revisit the problem and more carefully explore hydrogen’s 
behavior under extreme conditions.

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

Reference: “Stable Solid Molecular Hydrogen above 900 K from a Machine-Learned 
Potential Trained with Diffusion Quantum Monte Carlo” by Hongwei Niu, Yubo 
Yang, Scott Jensen, Markus Holzmann, Carlo Pierleoni and David M. Ceperley, 17 
February 2023, Physical Review Letters.  DOI: 10.1103/PhysRevLett.130.076102


This work was done in collaboration with Markus Holzmann of Univ. Grenoble 
Alpes and Carlo Pierleoni of the University of L’Aquila. Ceperley’s research 
group is supported by the U.S. Department of Energy, Office of Basic Energy 
Sciences, Computational Materials Sciences program under Award DE-SC0020177.
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