The ternary phase diagram of nitrogen doped lutetium hydrides can not explain its claimed high T c superconductivity

This paper presents the results of an extensive structural search of ternary solids containing lutetium, nitrogen and hydrogen. Based on thousands of thermodynamically stable structures the convex hull of the formation enthalpies is constructed. To obtain the correct energetic ordering, the highly accurate RSCAN DFT functional is used in high quality all-electron calculations, eliminating possible pseudopotential errors. In this way, a novel lutetium hydride structure (HLu 2 ) is found that is on the convex hull. An electron phonon analysis however shows that it is not a candidate structure for near ambient superconductivity. Besides this structure, which appears to have been missed in previous searches, possibly due to different DFT methodologies, our results agree closely with the results of previously published structure search efforts. This shows, that the field of crystal structure prediction has matured to a state where independent methodologies produce consistent and reproducible results, underlining the trustworthiness of modern crystal structure predictions. Hence it is quite unlikely that a structure, that would give rise within standard BCS theory to the superconducting properties, claimed to have been observed by Dasenbrock-Gammon et al (2023 Nature 615 244), exists. This solidifies the evidence that structures with high T c conventional superconductivity, that could give rise to the experimental claims, do not exist in this material.