0 1 2 3 0 1 2 Total Density of States [eV -1 / TiO 2 ] -1 0 1 2 3 $_{VB}$ [eV] 0 1 2 (a) HexABC Layer (b) Anatase Surface (c) Anatase Bulk [!b] B−doped N−doped Anatase Surface Anatase Bulk HexABC Layer FIG. 8: Total density of states in eV -1 per TiO$_{2}$ functional unit ver- sus energy in eV for undoped (thin black solid line), boron doped (magenta dashed line) and nitrogen doped (blue thick solid line) (a) TiO$_{2}$ HexABC layer, (b) TiO$_{2}$ anatase surface, and (c) bulk anatase, with 5.6%, 3.1%, and 3.1% doping respectively. Energies are mea- sured from the top of the valence bands of anatase TiO$_{2}$ ε$_{VB}$ , and the DOSs are shifted to align the lowest eigenstate with that for anatase TiO$_{2}$. Occupancy is denoted by curve filling for states in the band gap. FIG. 9: Schematics of the boron doped (left) and nitrogen doped (right) HexABC layer, anatase surface, and anatase bulk phases, with 5.6%, 3.1%, and 3.1% doping respectively. The highest occupied states for boron and nitrogen doped TiO$_{2}$ 2D and 3D structures are depicted by isosurfaces of ± 0.05 e/ ˚ A$^{3}$. Note the circled nitrogen- oxygen bonds in the nitrogen doped structures for the bulk phase, where nitrogen acts as a donor [6]. thus yield donor states near the conduction band, which may be photocatalytically active in the visible region. However, the quantum confinement inherent in these 1D structures may stretch these gaps, as found for the GW calculated DOS shown in Fig. 7. On the other hand, we find nitrogen dopants prefer to oc- cupy oxygen sites which are 3-fold coordinated to Ti, as was previously found for the rutile TiO$_{2}$ surface[16, 17]. This yields one occupied state at the top of the valence band and one unoccupied mid-gap state in the same spin channel. Both states are localized on the nitrogen dopant but overlap the va- lence band O 2 p$_{π}$ states, as shown in Fig. 6. Nitrogen dopants thus act as acceptors, providing localized states well above the valence band, as is also found for the GW calculated DOS shown in Fig. 7. Although we find nitrogen dopants act as acceptors in TiO$_{2}$ 1D structures, such large gaps between the valence band and the unoccupied mid-gap states would not yield p -type semi- conductors. This may be attributed to the substantial quantum confinement in these 1D structures. However, for 2D and 3D systems, we find it is possible to produce both p -type and n - type classical semiconductors. To determine the reliability of our DFT and GW electronic structure calculations, we now consider the influence of boron and nitrogen doping on the DOS for 2D and 3D TiO$_{2}$ struc- tures, which may be compared with recent experiments. For the HexABC layer shown in Figs. 8(a) and 9, boron and nitrogen dopants act as donors and acceptors respectively, as was the case for the TiO$_{2}$ nanotubes. However, for these 2D structures the doping states are sufficiently close in en- ergy to the conduction band or valence band to allow charge transfer for classical n -type or p -type doping by boron or ni- trogen dopants respectively. A similar behavior is found for C. DOS of 2D Layers, 3D Surfaces and Bulks 6