  In order to design clusters with desired properties, we have implemented a
suite of genetic algorithms tailored to optimize for low total energy, high
vertical electron affinity (VEA), and low vertical ionization potential (VIP).
Applied to (TiO$_2$)$_n$ clusters, the property-based optimization reveals the
underlying structure-property relations and the structural features that may
serve as active sites for catalysis. High VEA and low VIP are correlated with
the presence of several dangling-O atoms and their proximity, respectively. We
show that the electronic properties of (TiO$_2$)$_n$ up to n=20 correlate more
strongly with the presence of these structural features than with size.
