In section 3.1, we use seven of the Si-12Å clusters for a full reactivity study, which includes the evaluation of reactant, transition state (TS), and product structures. For this part, we also consider two smaller models, derived from the Si-12Å clusters, called "Si-10Å" and "Si-Min". The Si-10Å clusters have the same 9 Å relaxed region as the original Si-12Å clusters, but the frozen region was reduced to a single-atom layer past the boundary of the relaxed zone (dangling bonds were capped with H atoms). An example of a Si-10Å cluster is shown in Figure . In the Si-Min clusters, the Nb center and connecting O/Si atoms were extracted from the parent Si-12Å clusters, and dangling Si-O bonds were capped with F atoms. A pseudo-bridging silanol (PBS) was also included in five of the seven Si-Min clusters, as they affect the charge of the metal center and provide steric hindrance for the site. In the reactivity calculations, only Nb, the connecting oxygens, the oxo group, and any PBS were allowed to move, while the F and Si centers were kept frozen. An example of a Si-Min cluster (including a PBS) is shown in Figure .