Machine-learned interatomic potentials for water-methane mixtures under extreme thermodynamic conditions

The extreme conditions reigning in the interiors of icy giants —Uranus, Neptune—, with pressures up to millions of atmospheres and temperatures reaching thousands of kelvins, make direct exploration impossible. Beneath their atmospheres lies a dense fluid composed of water, methane, and ammonia; understanding the chemical transformations occurring in this mixture could shed light on these planets' physical properties. The "diamonds in the sky" hypothesis suggests that the formation of diamond and superionic water within this mixture can explain the unusual magnetic field and luminosity of icy giants. Evidence from laser-heated diamond anvil cell experiments supports this explanation. Additionally, ab initio molecular dynamics simulations have provided insights into the physical properties of planetary mixtures, such as chemical bond lifetimes, bandgap, and Hugoniot curves. However, the limited accessible timescales in ab initio molecular dynamics and the challenges in experimentally characterizing the process in situ have hindered the exploration of the mechanisms and free energies underlying the transition from planetary mixtures to nanodiamonds. Here we report the parameterization of machine-learned interatomic potentials (MLIPs) based on ab initio molecular dynamics data of water/methane mixtures at 3000 K and above 10 GPa. Our aim is to reproduce the thermodynamics and kinetics of chemical reactions involved in the early stages of diamond formation, ideally in an unsupervised fashion regarding training data selection. We devise an iterative training strategy involving data selection using random sampling in early iterations, and farthest point sampling in a molecular composition space in its final stages. We compare various modern equivariant MLIPs in their ability to reproduce the kinetics of proton transfer reactions, their stability, and free energy profiles of targeted hydrocarbon chain elongation reactions. We also investigate the influence of exchange-correlation functionals, highlighting in particular differences obtained with MLIPs trained either on generalized gradient approximation or hybrid functionals.