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

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.