Computational design of nanoclusters by property-based genetic algorithms: Tuning the electronic properties of $({\mathrm{TiO}}_2{)}_n$ clusters

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 ${\left(\mathrm{Ti}{\mathrm{O}}_2\right)}_n$ 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 ${\left(\mathrm{Ti}{\mathrm{O}}_2\right)}_n$ up to $n=20$ correlate more strongly with the presence of these structural features than with size.

Figure 1

Comparison of the three GAs in terms of their ability to find structures with the target properties of (a) high VEA, (b) low VIP, and (c) low energy. Histograms represent the number of isomers found by the respective GA for ${\left(\mathrm{Ti}{\mathrm{O}}_2\right)}_n$ clusters with $n=3,5,10,15,20$.

Figure 2

(a) Cumulative Ti-O PCFs of the ten best ${\left(\mathrm{Ti}{\mathrm{O}}_2\right)}_5$ isomers found by the VEA-GA (left) vs the EGA (right); (b) visualization of the ${\left(\mathrm{Ti}{\mathrm{O}}_2\right)}_5$ isomer with the highest VEA, showing its four dangling-O atoms; (c) the average and maximum VEAs (top) and number of dangling-O atoms (bottom) of the ten isomers with the highest VEA vs the ten isomers with the lowest energy for all cluster sizes.

Figure 3

(a) Bond connectivity of the energy global minimum (EGM) vs the VIP-GM for ${\left(\mathrm{Ti}{\mathrm{O}}_2\right)}_{10}$; (b) the average and minimum VIPs (top) and bond connectivity between dangling-O atoms (bottom) of the ten isomers with the lowest VEA vs the ten isomers with the lowest energy for all cluster sizes.

Figure 4

(a) VIP vs VEA for the best ten structures found in each search for all cluster sizes. The loci of constant fundamental gap are indicated by diagonal lines. (b) The average and minimum gaps of the ten best structures found in each search for all cluster sizes.