8 overestimate the experimental gap like B3LYP. This overesti- mation by GW may be attributed to excitonic effects, which are not included in GW, or the role played by oxygen defects [36]. For these reasons, GW and DFT calculations are best used as upper and lower bounds for optical band gaps. Fig. 10 shows that for both 3D and 2D systems, RPBE gaps underestimate the experimental results by approximately 1 eV. For 1D and 0D systems, we find a much larger difference of about 4 eV and 5 eV respectively, between the RPBE gaps and the I$_{p}$ − E$_{a}$ and GW results. We may attribute this increas- ing disparity to the greater quantum confinement and charge localization in the 1D and 0D systems, which yield greater self-interaction effects. We find B3LYP gaps also underesti- mate this effect, simply increasing the RPBE energy gaps for both 0D and 3D systems up by about 1.4 eV. On the other hand, we find the RPBE gaps reproduce qual- itatively the structural dependence of the I$_{p}$ − E$_{a}$ , GW, and experimental results for a given dimensionality, up to a con- stant shift. This is true even for 3D bulk systems, where stan- dard DFT does not predict rutile to be the most stable [29], as shown in Fig. 1. Whether calculated using RPBE, I$_{p}$ − E$_{a}$ or GW, the en- ergy gaps for both boron and nitrogen doped TiO$_{2}$ nanostruc- tures are generally narrowed, as shown in Fig. 10(b) and (c). However, for nitrogen doped (TiO$_{2}$)$_{n}$ clusters where nitrogen acts as an acceptor ( n = 5 , 6 , 9 ), the energy gap is actually increased when spin is conserved, compared to the undoped clusters in RPBE. This effect is not properly described by the N → N +1 transitions of I$_{p}$ − E$_{a}$ , for which spin is not con- served for these nitrogen doped clusters. On the other hand, when nitrogen acts as a donor ( n = 7 , 8 ) the smallest gap between energy levels does conserve spin. The boron doped TiO$_{2}$ nanorods and nanotubes have per- haps the most promising energy gap results of the TiO$_{2}$ struc- tures considered herein, as seen in Fig. 5(b). Boron dopants introduce in the nanorods localized occupied states near the conduction band edge in both RPBE ( cf. Figs. 5 and 6) and GW ( cf. Fig. 7) calculations. On the other hand, nitrogen dop- ing of nanorods and nanotubes introduces well defined mid- gap states, as shown in Fig. 5(c). However, to perform water dissociation, the energy of the excited electron must be above that for hydrogen evolution, with respect to the vacuum level. This is not the case for such a mid-gap state. This opens the possibility of a second excitation from the mid-gap state to the conduction band. However, the cross section for such an excitation may be rather low. For boron doping of 2D and 3D structures, the highest oc- cupied state donates its electron almost entirely to the con- duction band, yielding an n -type semiconductor. Thus at very low temperatures, the RPBE band gap is very small. The same is true for n -type nitrogen doped bulk anatase. For these rea- sons, we also provide the energy gap between the highest fully occupied state and the conduction band, which may be more relevant for photoabsorption. We find these RPBE gaps are still generally smaller than those for their undoped TiO$_{2}$ coun- terparts. In summary, for both boron and nitrogen doped clusters we find RPBE gaps differ from I$_{p}$ − E$_{a}$ by about 3 eV, while for nitrogen doped anatase the RPBE gap differs from experiment by about 0.6 eV. Given the common shift of 1 eV for undoped 2D and 3D structures, this suggests that both boron and ni- trogen doped 2D TiO$_{2}$ structures are promising candidates for photocatalysis. Further, the boron and nitrogen doped 1D nan- otube results also warrant further experimental investigation. In conclusion, we have demonstrated how the electronic properties of TiO$_{2}$ may be “tailored” using nanostructural changes in combination with boron and nitrogen doping. While boron doping tends to produce smaller band gap n - type semiconductors, nitrogen doping produces p -type or n - type semiconductors depending on whether or not nearby oxy- gen atoms occupy surface sites. This suggests that a p -type TiO$_{2}$ semiconductor may be produced using nitrogen doping in conjunction with surface confinement at the nanoscale. We thank S. In, Z.-W. Qu, G.-J. Kroes, T. Jaramillo, and J. K. Nørskov for useful discussions. The authors acknowl- edge financial support from NABIIT and the Danish Cen- ter for Scientific Computing. J.I.M. acknowledges the finan- cial support of the STREP EU APOLLON-B Project through grant No. NMP3-CT-2006-033228. 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