Phase stability of TiO₂polymorphs from diffusion Quantum Monte Carlo

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 longstanding 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.

Phase behavior of empirical potentials of titanium dioxide

“…Such phase diagrams have been reported for empirical potentials using energy minimisation, 14 and more generally, a number of density-functional theory (DFT) and quantum Monte Carlo calculations have been used to approximate the phase diagram at absolute zero. [29][30][31][32][33][34][35] For phases with relatively similar energies, entropy differences between the phases can determine the phase behaviour. 36 Some attempts have been made to determine the phase diagram at finite temperatures from DFT calculations 34,[36][37][38][39] by using e.g.…”

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

“…The variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) algorithms in particular have found wide application where the potential accuracy of a full many-body calculation is preferred over mean field methods [2,3]. Improvements in computational power as well as important technical improvements to the methods are enabling calculations on more complex systems, recently including cerium metal [4], copper oxide based superconductors [5,6], and numerous binary transition metal oxides [7][8][9][10][11][12][13][14].…”

Ti interstitial flows giving rutile TiO2 reoxidation process enhancement in (001) surface

“…Diffusion Monte Carlo (DMC) method is the most reliable method in the sense that such a delicate balance is automatically fulfilled in a numerical implementation of the variational principle. [18] The method was successfully applied to the present TiO 2 system in previous works [4,5,19,20].…”

“…[18,30] Orbital functions used in the Slater determinant are generated by LDA+U method implemented in Quantum Espresso. [31] We used a Hubbard correction value of U=4.86 eV from a previous work, [19] giving the best accessible nodal surface within this formalism, guaranteeing the lowest energy for TiO 2 from the variational principle. Core electrons in both Ti and O atoms were described by the use of a hard norm-conserving pseudopotentials developed to reproduce accurately all electrons results with the context of many-body theory and as described in previous works [19].…”

“…[31] We used a Hubbard correction value of U=4.86 eV from a previous work, [19] giving the best accessible nodal surface within this formalism, guaranteeing the lowest energy for TiO 2 from the variational principle. Core electrons in both Ti and O atoms were described by the use of a hard norm-conserving pseudopotentials developed to reproduce accurately all electrons results with the context of many-body theory and as described in previous works [19]. The orbitals are generated with a 300 Ry energy cutoff and the thermodynamic limit is reached with a 2×2×2 k-mesh size.…”