Extended Data Fig. 9: Tip model for the AFM calculations.
From: Direct assessment of the acidity of individual surface hydroxyls
a, Relaxed structure of an In8O12 cluster cut out of an In2O3(111) slab. The cut is centred around the high-symmetry B site of the surface and its depth is four In2O3(111) trilayers. The In2O3(111) trilayers are all equivalent but they are shifted such that the high-symmetry sites with a three-fold symmetry axis (see Fig. 1a) form a stacking sequence of BCAB. The cluster consists of an In atom at the B site together with three O atoms, and six-membered In3O3 rings around the A and C sites. The cluster is stoichiometric and stable upon geometry optimization, it has a three-fold symmetry axis and its HOMO–LUMO gap is 1.62 eV (PBE). b, Cluster after dissociative adsorption of six water molecules to saturate the broken In–O bonds. The OH groups were added to the six In atoms in the two central planes, and the protons were placed on top of the two-fold bridging O atoms. This increased the HOMO–LUMO gap to 2.57 eV. In the next step, the upper In(OH)3 cap was removed (dashed circle). This was done to eliminate the top three-fold coordinated In atom and to reduce the height of the tip model. This saves some computer time in the AFM calculations, as the thickness of the vacuum region can be reduced. Removing the cap increases the HOMO–LUMO gap to 2.68 eV. At this point, the cluster still has a three-fold symmetry axis. c, Structure of the final tip. One additional water molecule is added to the cluster (b). The OH group is adsorbed at the In apex atom of the tip and the proton is added to one of the remaining O atoms. This breaks the three-fold symmetry of the tip. Careful test calculations showed that the specific choice for the adsorption site of the proton is not important. All tips gave basically the same F(z) curves. In the end, the proton was split into three parts, and three pseudo-hydrogen atoms with nuclear charge of +1/3 were added to the three O atoms closest to the tip apex indicated by arrows. The HOMO–LUMO gap of the final cluster calculated with the PBE functional is 2.64 eV.
