Performance of the r$^{2}$SCAN functional in transition metal oxides

We assess the accuracy and computational efficiency of the recently developed meta-generalized gradient approximation (metaGGA) functional, the restored regularized strongly constrained and appropriately normed (r$^2$SCAN), in transition metal oxide (TMO) systems and compare its performance against SCAN. Specifically, we benchmark the r$^2$SCAN-calculated oxidation enthalpies, lattice parameters, on-site magnetic moments, and band gaps of binary 3\textit{d} TMOs against the SCAN-calculated and experimental values. Additionally, we evaluate the optimal Hubbard \emph{U} correction required for each transition metal (TM) to improve the accuracy of the r$^2$SCAN functional, based on experimental oxidation enthalpies, and verify the transferability of the \emph{U} values by comparing against experimental properties on other TM-containing oxides. Notably, including the \textit{U}-correction to r$^2$SCAN increases the lattice parameters, on-site magnetic moments and band gaps of TMOs, apart from an improved description of the ground state electronic state in narrow band gap TMOs. The r$^2$SCAN and r$^2$SCAN+\textit{U} calculated oxidation enthalpies follow the qualitative trends of SCAN and SCAN+\emph{U}, with r$^2$SCAN and r$^2$SCAN+\textit{U} predicting marginally larger lattice parameters, smaller magnetic moments, and lower band gaps compared to SCAN and SCAN+\textit{U}, respectively. We observe that the overall computational time (i.e., for all ionic+electronic steps) required for r$^2$SCAN(+\textit{U}) to be lower than SCAN(+\textit{U}). Thus, the r$^2$SCAN(+\textit{U}) framework can offer a reasonably accurate description of the ground state properties of TMOs with better computational efficiency than SCAN(+\textit{U}).