Investigating the Energetic Ordering of Stable and Metastable TiO₂ Polymorphs Using DFT+U and Hybrid Functionals

Prediction of transition metal oxide BO₂ (B = Ti, V, etc.) polymorph energetic properties is critical to tunable material design and identifying thermodynamically accessible structures. Determining procedures capable of synthesizing particular polymorphs minimally requires prior knowledge of their relative energetic favorability. Information concerning TiO₂ polymorph relative energetic favorability has been ascertained from experimental research. In this study, the consistency of first-principles predictions and experimental results involving the relative energetic ordering of stable (rutile), metastable (anatase and brookite), and unstable (columbite) TiO₂ polymorphs is assessed via density functional theory (DFT). Considering the issues involving electron–electron interaction and charge delocalization in TiO₂ calculations, relative energetic ordering predictions are evaluated over trends varying Ti Hubbard U_3d or exact exchange fraction parameter values. Energetic trends formed from varying U_3d predict experimentally consistent energetic ordering over U_3d intervals when using GGA-based functionals, regardless of pseudopotential selection. Given pertinent linear response calculated Hubbard U values, these results enable TiO₂ polymorph energetic ordering prediction. Hybrid functional calculations involving rutile–anatase relative energetics, though demonstrating experimentally consistent energetic ordering over exact exchange fraction ranges, are not accompanied by predicted fractions, for a first-principles methodology capable of calculating exact exchange fractions precisely predicting TiO₂ polymorph energetic ordering is not available.