The structure of the material responsible for the room temperature and near
ambient pressure superconductivity reported in an N-doped lutetium hydride
[Nature, 615, 244 (2023)] has not been conclusively determined. Herein, density
functional theory calculations are performed in an attempt to uncover what it
might be. Guided by a range of strategies including crystal structure
prediction and modifications of existing structure types, we present an array
of Lu-N-H phases that are dynamically stable at experimentally relevant
pressures. Although none of the structures found are thermodynamically stable,
and none are expected to remain superconducting above 17 K at 10 kbar, a number
of metallic compounds with fcc Lu lattices -- as suggested by the experimental
X-ray diffraction measurements of the majority phase -- are identified. The
system whose calculated equation of states matches best with that measured for
the majority phase is fluorite-type LuH2, whose 10 kbar superconducting
critical temperature was estimated to be 0.09 K using the Allen-Dynes modified
McMillan equation.Comment: 11 pages, 8 figure