First-principles study of crystal and electronic structure of rare-earth cobaltites

Using density functional theory plus self-consistent Hubbard $U$ (DFT$+U_{sc}$) calculations, we have investigated the structural and electronic properties of the rare-earth cobaltites \textit{R}CoO$_3$ (\textit{R} = Pr -- Lu). Our calculations show the evolution of crystal and electronic structure of the insulating low-spin (LS) \textit{R}CoO$_3$ with increasing rare-earth atomic number (decreasing ionic radius), including the invariance of the Co-O bond distance ($d_{Co-O}$), the decrease of the Co-O-Co bond angle ($\Theta$), and the increase of the crystal field splitting ($\Delta_{CF}$) and band gap energy ($E_g$). Agreement with experiment for the latter improves considerably with the use of DFT$+U_{sc}$ and all trends are in good agreement with experimental data. These trends enable a direct test of prior rationalizations of the trend in spin-gap associated with the spin crossover in this series, which is found to expose significant issues with simple band based arguments. We also examine the effect of placing the rare-earth \textit{f}-electrons in the core region of the pseudopotential. The effect on lattice parameters and band structure is found to be small, but distinct for the special case of \textit{Pr}CoO$_3$ where some \textit{f}-states populate the middle of the gap, consistent with recent reports of unique behavior in Pr-containing cobaltites. Overall, this study establishes a foundation for future predictive studies of thermally induced spin excitations in rare-earth cobaltites and similar systems.