Comment on "First-principles study of the influence of (110)-oriented strain on the ferroelectric properties of rutile TiO2" [arXiv:1106.2820]

TL;DR

This paper clarifies discrepancies in previous DFT studies of TiO2's ferroelectric properties by identifying errors in pseudopotential treatment and discussing numerical limitations affecting the detection of phonon instabilities.

Contribution

It demonstrates that previous disagreements were due to pseudopotential errors and highlights the importance of appropriate numerical methods for detecting phonon instabilities.

Findings

Erroneous treatment of semi-core electrons caused previous discrepancies.

Frozen semi-core pseudopotentials can cancel out certain phonon instabilities.

Numerical optimization methods may fail to detect shallow double well potential instabilities.

Abstract

In a recent article, Gr\"{u}nebohm et al. [Phys. Rev. B 84 132105 (2011), arXiv:1106.2820] report that they fail to reproduce the A2u ferroelectric instability of TiO2 in the rutile structure calculated with density functional theory within the PBE-GGA approximation by Montanari et al. [Chem. Phys. Lett 364, 528 (2002)]. We demonstrate that this disagreement arises from an erroneous treatment of Ti 3s and 3p semi-core electrons as core in their calculations. Fortuitously the effect of the frozen semi-core pseudopotential cancels the phonon instability of the PBE exchange-correlation, and the combination yields phonon frequencies similar to the LDA harmonic values. Gr\"{u}nebohm et al. also attempted and failed to reproduce the soft acoustic phonon mode instability under (110) strain reported by Mitev et al. [Phys. Rev. B 81 134303 (2010)]. For this mode the combination of PBE-GGA and frozen semi-core yields a small imaginary frequency of 9.8i. The failure of Gr\"{u}nebohm et al. to find this mode probably arose from numerical limitations of the geometry optimization approach in the presence of a shallow double well potential; the optimization method is not suitable for locating such instabilities.