Benchmarking the Fundamental Electronic Properties of small TiO 2 Nanoclusters by GW and Coupled Cluster Theory Calculations.

We study the vertical and adiabatic ionization potentials and electron affinities of bare and hydroxylated TiO ₂ nanoclusters, as well as their fundamental gap and exciton binding energy values, to understand how the clusters' electronic properties change as a function of size and hydroxylation. In addition, we have employed a range of many-body methods; including G ₀ W ₀ , qsGW, EA/IP-EOM-CCSD, and DFT (B3LYP, PBE), to compare the performance and predictions of the different classes of methods. We demonstrate that, for bare clusters, all many-body methods predict the same trend with cluster size. The highest occupied and lowest unoccupied DFT orbitals follow the same trends as the electron affinity and ionization potentials predicted by the many-body methods, but are generally far too shallow and deep respectively in absolute terms. In contrast, the ΔDFT method is found to yield values in the correct energy window. However, its predictions depend upon the functional used and do not necessarily follow trends based on the many-body methods. Adiabatic potentials are predicted to be similar to their vertical counterparts and holes found to be trapped more strongly than excess electrons. The effect of hydroxylation on the clusters is to open up both the optical and fundamental gap. Finally, a simple microscopic explanation for the observed trends with cluster size and upon hydroxylation is proposed in terms of the onsite electrostatic potential.