We analyze the basic structural units of simple reconstructions of the (111) surface of SrTiO3 using density functional calculations. The prime focus is to answer three questions: what is the most appropriate functional to use; how accurate are the energies; what are the dominant low-energy structures and where do they lie on the surface phase diagram. Using test calculations of representative small molecules we compare conventional GGA with higher-order methods such as the TPSS meta-GGA and on-site hybrid methods PBE0 and TPSSh, the later being the most accurate. There are large effects due to reduction of the metal d oxygen sp hybridization when using the hybrid methods which are equivalent to a dynamical GGA+U, which leads to rather substantial improvements in the atomization energies of simple calibration molecules, even though the d-electron density for titanium compounds is rather small. By comparing the errors of the different methods we are able to generate an estimate of the theoretical error, which is about 0.25eV per 1x1 unit cell, with changes of 0.5-1.0 eV per 1x1 cell with the more accurate method relative to conventional GGA. An analysis of the plausible structures reveals an unusual low-energy TiO2-rich configuration with an unexpected distorted trigonal biprismatic structure. This structure can act as a template for layers of either TiO or Ti2O3, consistent with experimental results as well as, in principle, Magnelli phases. The results also suggest that both the fracture surface and the stoichiometric SrTiO3 (111) surface should spontaneously disproportionate into SrO and TiO2 rich domains, and show that there are still surprises to be found for polar oxide surfaces.
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