Quantum Monte Carlo study of the energetics of the rutile, anatase, brookite, and columbite TiO$_2$ polymorphs

TL;DR

This study uses advanced quantum Monte Carlo methods to accurately compare the energies of TiO₂ polymorphs, revealing the importance of vibrational effects and predicting a phase transition at around 630 K.

Contribution

It demonstrates the effectiveness of diffusion quantum Monte Carlo combined with vibrational analysis in accurately determining phase stability of TiO₂ polymorphs.

Findings

Rutile is stabilized over anatase when vibrational effects are included.

A phase transition from anatase to rutile is predicted at approximately 630 K.

Anharmonic vibrational energies significantly influence polymorph energetics.

Abstract

The relative energies of the low-pressure rutile, anatase, and brookite polymorphs and the high-pressure columbite polymorph of TiO$_2$ have been calculated as a function of temperature using the diffusion quantum Monte Carlo (DMC) method and density functional theory (DFT). The vibrational energies are found to be important on the scale of interest and significant quartic anharmonicity is found in the rutile phase. Static-lattice DFT calculations predict that anatase is lower in energy than rutile, in disagreement with experiment. The accurate description of electronic correlations afforded by DMC calculations and the inclusion of anharmonic vibrational effects contribute to stabilizing rutile with respect to anatase. Our calculations predict a phase transition from anatase to rutile TiO$_2$ at $630 \pm 210$ K.