Symmetry and Stability of the Rutile-Based TiO2 Nanowires: Models and Comparative LCAO-Plane Wave DFT Calculations

The rod symmetry groups for monoperiodic (1D) nanostructures have been applied for construction of models for bulk-like titania nanowires (NWs) cut from a rutile-based 3D crystal along the direction of a chosen crystallographic symmetry axis (in this study we consider only Ti atom-centered axes). The most stable [001]-oriented TiO2 NWs with rhombic cross sections are found to display the energetically preferable {110} facets only, while the nanowires with quasi-square sections across the [110] axis are formed by the alternating {110} and {001} facets. For simulations on rutile-based nanowires possessing four different diameters for each NW type, we have performed comparative large-scale ab initio Density Functional Theory (DFT) calculations with total geometry optimization within the Generalized Gradient Approximation (GGA), using the two different formalisms: (i) linear combination of localized atomic functions (LCAO) and (ii) plane waves (PW). Both approaches have been used for calculations of: (a) the key properties of defectless rutile titania bulk (structure parameters a, c, and u, Ti-O bond lengths, and effective atomic charges q(O) and q(Ti) plus a band gap Delta epsilon(g)) and (b) the structural and electronic properties depending on orientation, shape, and diameter of TiO2 [001]- and [110]-oriented NWs (changes of diameters d(NW) and unit cell lengths l(NW) of nanowires during geometry optimization, correlated with difference of total energies per formula unit in a nanowire and bulk, as well as effective charges and band gaps). Values of d(NW) slightly increase, whereas l(NW) are found to be reduced after optimization, except for the thinnest [110]-NW (d(NW) similar to 3 angstrom) for which the unit cell contains only three formula units, making it similar to a nanofilament. The larger the NW diameter, the closer its structural and electronic parameters are to those of rutile TiO2 bulk. We have obtained the semiquantitative correlation between the results of DFT-LCAO and DFT-PW calculations.