Machine Learning simulations reveal oxygen’s phase diagram and thermal properties at conditions relevant to white dwarfs

Introduction

Oxygen is one of the most abundant elements in the universe, possessing fascinating properties. Under pressures exceeding 96 GPa^1,2, molecular oxygen transitions into a metallic phase and transforms into the ζ phase at around 100 GPa^3,4. Sun et al. thoroughly investigated oxygen at pressures up to 10 TPa⁵. They predicted a transition from the molecular phase to a tetragonal phase with polymerized helical chains at 1.9 TPa, followed by a layered monoclinic phase known as the chain-molecular phase (space group Fmmm) at 9.3 TPa. Moreover, they demonstrated that oxygen maintains a superconducting temperature of 0.6 K to 2.1 K at TPa pressures. Building upon the work of Sun et al., Cogollo-Olivo et al. re-examined the oxygen phase boundaries at finite temperatures within the 1–10 TPa pressure range⁶. These studies comprehensively demonstrate oxygen’s properties and states below 10 TPa. However, even under such extreme pressures, the lone pair electrons in oxygen structures persist, and the polymerization process of oxygen remains incompletely elucidated.

With increasing pressure, diatomic molecules such as oxygen, hydrogen, fluorine and nitrogen gradually aggregate from the molecular phase into the polymeric phase. Hydrogen may exhibit an alternately interlayered structure^{7, 8–9}, while nitrogen, due to its unique outer electron configuration, possesses highly stable nitrogen-nitrogen triple bonds. Beyond 100 GPa, nitrogen transforms into the cubic-gauche phase^10,11, and there are many metastable polymeric nitrogen structures realized. Only fluorine and oxygen are known to remain undissociated and form polymeric phases under TPa pressure^5,12. Fluorine undergoes multi-step dissociation under TPa pressures. Surprisingly, it is at 30 TPa that fluorine finally breaks down its molecular structure to form a polymeric phase¹². Intermediate structures during this transition exhibit superconducting behaviour, affirming fluorine as a superconducting element despite its critical temperature (T_c) of only several Kelvin. This has sparked interest in the electronic properties of TPa pressure structure states.

However, current studies on the high-pressure polymerization of diatomic molecules have predominantly focused on static-pressure structure calculations and have not addressed finite-temperature dynamics. On the one hand, pressures exceeding the TPa regime require the use of pseudopotentials with small cutoff radius to achieve convergence, with the necessity for higher energy cutoffs further increasing computational costs; on the other hand, conventional force fields fail to...