The Stability of TiO₂ Phases Studied Using r²SCAN in the Hubbard-Corrected Density Functional Theory

Titanium dioxide is a quintessential transition metal oxide with many technologically important applications. With its richness in phases, it has also been a testing ground for numerous theoretical studies including density functional theory. We investigated several phases of TiO₂ using the all-electron density functional theory with a regularized-restored strongly constrained appropriately normed (r²SCAN) exchange-correlation functional, a popular choice of meta-generalized gradient approximation (meta-GGA). Specifically, the equilibrium lattice parameters were more accurate than those predicted by GGA and agreed well overall with the experimental data. With increasing pressure, the order of stability was determined as anatase < columbite < rutile < baddeleyite < orthorhombic I < cotunnite, as in the calculations using GGA. Including the Hubbard correction term, the correct ordering between rutile, anatase, and columbite can be achieved, consistent with experimental observations. The necessary U value using r²SCAN is much smaller than that using GGA+U. In addition, the Hubbard correction method using r²SCAN is substantially less sensitive to the size of the local projection space compared to the GGA+U study reported recently. We attribute these significantly improved results to the reduced self-interaction error in the r²SCAN functional.