Anomalous Reversal of Stability in Mo-containing Oxides: A Difficult Case Exhibiting Sensitivity to DFT+U and Distortion

Accurate predictions of the properties of transition metal oxides using density functional theory (DFT) calculations are essential for the computational design of energy materials. In this work, we investigate the anomalous reversal of the stability of structural distortions (where distorted structures go from being energetically favorable to sharply unfavorable relative to undistorted ones) induced by DFT+U on Mo d-orbitals in layered AMoO$_2$ (A = Li, Na, K) and rutile-like MoO$_2$. We highlight the significant impact of varying U$_{\text{eff}}$ values on the structural stability, convex hull, and thermodynamic stability predictions, noting that deviations can reach up to the order of 100 meV/atom across these energetic quantities. We find the transitions in stability are coincident with changes in the electron localization and magnetic behavior. The anomalous reversal persists across PBE, r$^2$SCAN functionals, and also with vdW-dispersion energy corrections (PBE+D3). In Mo-containing oxide systems, high U$_{\text{eff}}$ leads to inaccurate descriptions of physical quantities and structural relaxations under artificial symmetry constraints, as demonstrated by the phonon band structures, the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional results, and comparisons with experimental structural data. We conclude that high U$_{\text{eff}}$ values (around 4 eV and above, depending on the specific structures and compositions) might be unsuitable for energetic predictions in A-Mo-O chemical spaces. Our results suggest that the common practice of applying DFT+U to convex hull constructions, especially with high U$_{\text{eff}}$ values derived from fittings, should be carefully evaluated to ensure that ground states are correctly reproduced, with careful consideration of dynamic stability and possible energetically favorable distortions.