Published: August 16, 2011 r2011 American Chemical Society 18494 dx.doi.org/10.1021/jp206183x | J. Phys. Chem. C 2011, 115, 18494–18499 ARTICLE pubs.acs.org/JPCC Role of Symmetry in the Stability and Electronic Structure of Titanium Dioxide Nanowires B  alint Aradi,* ,† Peter De  ak, † Huynh Anh Huy, † Andreas Rosenauer, ‡ and Thomas Frauenheim † † Bremen Center for Computational Materials Science, University of Bremen, Am Fallturm 1, 28359 Bremen, Germany ‡ Institute of Solid State Physics, University of Bremen, Otto-Hahn-Alle 1, 28359 Bremen, Germany ’ INTRODUCTION Titanium dioxide (TiO 2 ) is a versatile material with a wide range of applications. Nanostructures of TiO 2 in various crystal modifications are used among others for photocatalytic and photo- voltaic applications, for water splitting and hydrogen storage, in electrochromic devices, and in various sensing applications. 1 Recently, Liu and Yang synthesized TiO 2 nanowires with dia- meters on the Ångstr€ om scale. 2 Structures on the subnano scale may show effects not present in the bulk material, opening the way for new applications. The first step in investigating such effects is to study the equilibrium structure and (opto)electronic properties of ultrathin wires. Only a few theoretical studies on atomic-scale TiO 2 nanowires have been published so far. Zhang et al. studied the energy of formation of TiO 2 wires assembled from Ti 2 O 4 building blocks (with tetrahedral coordination of the Ti atoms instead of the usual octahedral one) 3 and found them extremely stable. Peng and Li investigated quantum confinement effects in [001] rutile nanowires and found that the gap varies strongly when choosing different central axes (parallel to the [001] direction) and side walls. 4 Iacomino et al. investigated the structure and electronic properties of anatase wires, with different orientations and various surface terminations as a function of diameter. 5 In particular, [001]-oriented wires were cut along a central axis passing through Ti atoms (resulting in mirror symmetry but no screw axis in the wires). Their thinnest model had the structure proposed by Liu and Yang for the experimentally observed atomic-scale nanowire. 2 The calculations resulted in a relaxed geometry where the anatase-type bonding environment of the atoms was partially lost. This seems to be in contradiction with the fact that the observed Raman spectrum of these very thin wires was practically the same as for bulk anatase. 2 As Ångstr€ om-scaled TiO 2 nanowires consist of a few atomic layers only, even small differences in their geometry can have a significant impact on their stability or electronic properties. We investigated bare anatase and rutile nanowires of varying dia- meter cut from their respective bulk crystals along the [001] direction. The investigated nanowires differ in the choice of their central axis and therefore in their symmetry. We show that nanowires cut by keeping the screw symmetry of the original bulk structure are consistently lower in energy than similarly oriented nanowires in which this symmetry is destroyed. We also show that wires with screw symmetry have a consistently larger gap. Furthermore, our results indicate that in rutile wires the direct or indirect character of the band structure is coupled to the abscence or presence of the screw axis. ’ METHODS We carried out ab initio density functional theory (DFT) based calculations with the generalized gradient approximation (GGA) using the VASP 6À8 package. For exchange and correla- tion the PerdewÀBerkeÀEnzerhof 9 functional was used. The effect of the core electrons has been described via the projector- augmented-wave method 10 with the 3p electrons of titanium being explicitly treated as valence electrons. Plane wave bases with energy cutoffs of 420 and 840 eV have been used for the wave functions and the augmentation charges, respectively. During optimization of the lattice constants the two cutoffs had been increased by 30% in order to minimize the influence of the Pulay forces on the equilibrium lattice constants obtained. Received: June 30, 2011 Revised: August 11, 2011 ABSTRACT: The stability and electronic structure of bare [001] nanowires of anatase and rutile have been investigated using ab initio density functional calculations. It was found that symmetry plays an important role in both properties below a critical diameter. Up to 2.1 nm in anatase and 3.7 nm in rutile, those {100}-walled anatase and {110}-walled rutile wires are most stable, which retain the nonsymmorphic character of the bulk space group. Our results explain the observed properties of atomic size anatase nanowires. The wires with screw symmetry also show a consistently larger gap in their electronic structures compared to similarly walled wires without it. Additionally, in rutile the indirect or direct character of the band structure is coupled to the presence or absence of the screw axis.