Molecular structures and energetics of the (ZrO(2))(n) and (HfO(2))(n) (n = 1-4) clusters and their anions.

The group IVB transition-metal dioxide clusters and their anions, (MO(2))(n) and (MO(2))(n)(-) (M = Zr, Hf; n = 1-4), are studied with coupled cluster (CCSD(T)) theory and density functional theory (DFT). Similar to the results for M = Ti, these oxide clusters have a number of low-lying isomeric structures, which can make it difficult to predict the ground electronic state especially for the anion. Electron affinities for the low-lying structures are calculated and compared with those for M = Ti. Electron affinities of these clusters depend strongly on the cluster structures. Anion photoelectron spectra are calculated for the monomer and dimer and demonstrate the possibility for structural identification at a spectral line width of <or=0.05 eV. Electron excitation energies from the low-lying states to the singlet and triplet excited states are calculated self-consistently, as well as by the time-dependent DFT and equation-of-motion coupled cluster (EOM-CCSD) methods. The calculated excitation energies are compared to the band energies of bulk oxides, indicating that the excitation energy is not yet converged for n = 4 for these clusters. The excitation energies of the low-lying isomeric clusters are less than the bulk metal oxide band gaps and suggest that these clusters could be useful photocatalysts with a visible light source.