Machine learning helped us calculate the liquid hydrogen phase diagram

Chemists used machine learning to calculate the thermodynamic parameters of the transition of liquid hydrogen from a dielectric to a metallic state. To train the potentials used to calculate these parameters, we used the results of electron density calculations using conventional quantum chemistry methods. The study is published in Nature.

The composition of gas giants and brown dwarfs includes liquid hydrogen, which at high pressures and temperatures acquires the properties of a metallic conductor. Understanding the transition of hydrogen from a dielectric to a metallic state is very important for modelling the structure and evolution of giants like Jupiter, Saturn, and many exoplanets. According to standard models of such planets, this transition is abrupt and accompanied by a noticeable change in density, so the boundary between the inner metallic mantle and the outer dielectric mantle should be fairly clear.

Technical difficulties of conducting experiments to study the transition in extreme conditions lead researchers to different results, so computational methods for studying this process are especially necessary. However, they also have their limitations due to the fact that not all effects are taken into account. The more system parameters are taken into account, the more accurate the calculations are, but their cost and duration are higher.

Bingqing Cheng and colleagues from the University of Cambridge calculated the parameters of the hydrogen phase diagram using machine learning methods. They created three sets of potentials trained on the results of calculations of potential energy surfaces and interatomic forces obtained by methods of electron density functional and quasi-Monte Carlo variation. Based on the calculated energies, the authors created molecular-dynamic simulations of the transition process from the dielectric to the mental state in a wide temperature range and recreated the melting and polymorphism of the solid phase.

Results of one of the calculations and experimental data on the thermodynamic properties of hydrogen at high pressures. Color indicates the proportion of molecular fraction black line corresponds to the points at which the liquid and solid phase coexist. The maximum density and molecular heat capacity are indicated by purple and orange dots, respectively. The dotted green curve corresponds to the parameters under which atomic and molecular liquids coexist, and the green line points out the conditions under which these liquids are separated. The area between the green curves indicated by a star represents the predicted position of the critical point Bingqing Cheng et al. / Nature, 2020

The potential could correctly determine the basic States of crystals in the pressure range from 100 to 400 gigapascals. The accuracy of crystal structure predictions demonstrates the possibility of using the created potentials to search for unknown crystal structures. Simulations of the process indicated that in liquid hydrogen, the transition from molecular to atomic form occurs not in a leap, but smoothly. This means that in gas giants the boundary between the dielectric and metal layers is smooth, and the differences in experimental data can be explained by the behaviour of hydrogen as a supercritical liquid.

Three years ago, American physicists reported that they had synthesized metallic hydrogen, but the study raised questions from some scientists.

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