We constructed a cluster model of anatase TiO 2 as follows. Starting from the crystal structure of the bulk material, we extracted a cluster Ti 21 O 70 H 56 that is depicted in Fig. , capping the surface oxygen atoms with hydrogen to maintain charge neutrality. As suggested in Ref. 76, this is the smallest cluster model where the central Ti atom retains its bulk character. The geometry of this cluster model was then relaxed using HF theory but constraining the surface Ti-O and O-H bond lengths to provide some mechanical stability at the surface. These optimizations used the LANL2DZ basis set (and corre-sponding effective core potential) for Ti, 77 with 6-31G* used for the remaining atoms.