Phase Stability of TiO$_2$ Polymorphs from Diffusion Quantum Monte Carlo

TL;DR

This study uses advanced quantum Monte Carlo methods to analyze the phase stability of TiO$_2$ polymorphs, resolving long-standing disagreements between theory and experiment regarding their energetic ordering.

Contribution

First application of diffusion Quantum Monte Carlo to determine phase stability of TiO$_2$ polymorphs, including temperature effects via phonon calculations.

Findings

Anatase is most stable at zero temperature.

Rutile becomes most stable at higher temperatures.

Brookite remains least stable at all temperatures.

Abstract

Titanium dioxide, TiO$_2$, has multiple applications in catalysis, energy conversion and memristive devices because of its electronic structure. Most of these applications utilize the naturally existing phases: rutile, anatase and brookite. Despite the simple form of TiO$_2$ and its wide uses, there is long-standing disagreement between theory and experiment on the energetic ordering of these phases that has never been resolved. We present the first analysis of phase stability at zero temperature using the highly accurate many-body fixed node diffusion Quantum Monte Carlo (QMC) method. We also include the effects of temperature by calculating the Helmholtz free energy including both internal energy and vibrational contributions from density functional perturbation theory based quasi harmonic phonon calculations. Our QMC calculations find that anatase is the most stable phase at zero temperature, consistent with many previous mean-field calculations. However, at elevated temperatures, rutile becomes the most stable phase. For all finite temperatures, brookite is always the least stable phase.