Cluster structures optimized at the SIE-free HF and MP2 levels of theory exhibit a single elongated Al-O bond, whereas the remaining three Al-O bonds have nearly identical bond lengths. In contrast, geometries obtained with GGA functionals (BLYP and PBE) exhibit four identical Al-O bond lengths and very little structural distortion. This is consistent with a hole that is delocalized over all four bonds, as shown for BLYP in Fig. , but inconsistent with the EPR spectroscopy. For the hybrid functionals PBE0 and B3LYP, the hole is delocalized over two Al-O bonds rather than four (Fig. ). This is reflected in two elongated Al-O bonds whose bond lengths have intermediate values between the short and long Al-O bond lengths obtained at the MP2 level.