Unexpected density functional dependence of the antipolar $$\boldsymbol{Pbcn}$$ phase in HfO2

The antipolar Pbcn phase of HfO₂ has been suggested to play a critical role in the phase transitions and polarization switching mechanisms of ferroelectric hafnia. Here, we benchmark density functional theory (DFT) and deep potential molecular dynamics (DPMD) simulations to investigate the thermodynamic stability and phase transition behavior of hafnia, with a particular focus on the relationship between the Pbcn and ferroelectric Pca2₁ phases. Significant discrepancies in phase energetics emerge across exchange-correlation functionals: the PBE and hybrid HSE06 functionals exhibit consistent trends, which diverge from the predictions of the PBEsol and SCAN functionals. Quasi-harmonic free energy calculations show good agreement with finite-temperature DPMD simulations using deep potentials trained on the same functional. We further find that, under fixed mechanical boundary conditions based on the Pca2₁ ground-state structure, all functionals predict consistent relative phase stabilities, polarization switching barriers, and domain wall energies.