Artifactual Liquid-Liquid Hydrogen Phase Transition from a Machine-Learnt Potential*

Condensed hydrogen is an intrinsically extreme system of great importance.  Cheng et al. [ Nature 585, 217 (2020) ] trained a Hydrogen machine-learning potential (MLP) mostly on small system ab initio MD (AIMD) using DFT. In MD on larger systems (≤ 1728 atoms), the MLP gives a continuous liquid-liquid phase transition and supercriticality,  at odds with all prior conventional  AIMD. They claimed the prior calculations are erroneous because of finite-size  effects exacerbated by use of the NVT ensemble.  Our AIMD NPT simulations up through 2,048 atoms do not sustain that.  Consistent with our earlier NVT work at smaller sizes [ Phys. Rev. Res. 2, 032065(R) (2020) ], we find a first-order transition. We conclude that the MLP-MD results are artifactual, because the MLP-MD does not systematically reproduce the DFT AIMD from which it supposedly comes. Comparison suggests, but does not prove, that the MLP is a smooth interpolation across the phases.