Correlation effects on coupled electronic and structural properties of doped rare-earth trihydrides

Rare-earth trihydride ($R{\mathrm{H}}_{3}$) compounds exhibit intriguing coupled electronic and structural properties as a function of doping, hydrogen vacancies, and thermodynamic conditions. Theoretical studies of these materials typically rely on density functional theory (DFT), including the use of small supercells that may underestimate strong correlation effects and structural distortions which in turn may influence their metallicity. Here, we elucidate the roles of lattice distortions and correlation effects on the electronic properties of pristine and doped $R{\mathrm{H}}_{3}$ compounds by adopting $\mathrm{DFT}+\mathrm{U}$ and quantum Monte Carlo (QMC) methods. Linear-response constrained DFT (LR-cDFT) methods find Hubbard U $\ensuremath{\approx}2$ eV for ${R}_{d}$ orbitals and $\mathrm{U}\ensuremath{\approx}6$ eV for ${\mathrm{H}}_{s}/{\mathrm{N}}_{p}/{\mathrm{O}}_{p}$ orbitals. The small U on ${\mathrm{Lu}}_{d}$ orbitals is consistent with QMC calculations on ${\mathrm{LuH}}_{3}$ and ${\mathrm{LuH}}_{2.875}{\mathrm{N}}_{0.125}$. In pure face-centered-cubic (FCC) $R{\mathrm{H}}_{3}$ ($R=\mathrm{Lu},\mathrm{Y}$) compounds, neither DFT nor $\mathrm{DFT}+\mathrm{U}$ with the self-consistently determined U is enough to create a band gap, however a supercell with hydrogen distortions creates a small gap whose magnitude increases when performing $\mathrm{DFT}+\mathrm{U}$ with self-consistently determined U values. Correlation effects, in turn, have a moderate influence on the coupled structural and electronic properties of doped $R{\mathrm{H}}_{3}$ compounds and may be important when considering the competition between structural distortions and superconductivity.