Accurate Thermochemistry for Transition Metal Oxide Clusters

Total atomization energies (TAEs) and normalized clustering energies (NCEs) of group IVB (MO<sub>2</sub>)<sub><i>n</i></sub> (M = Ti, Zr, Hf) and VIB (MO<sub>3</sub>)<sub><i>n</i></sub> (M = Cr, Mo, W) transition metal oxide clusters up to <i>n</i> = 4 were calculated at the coupled cluster [CCSD(T)] and density functional theory (DFT) levels. For all the clusters studied, the TAEs calculated at the CCSD(T) level were found to be strongly basis set dependent, whereas the NCEs were significantly less basis set dependent. Here we further develop an efficient strategy for calculating accurate thermodynamic properties of large clusters based on those of the cluster unit and the NCEs. The calculated TAEs, NCEs, and heats of formations for these clusters were compared with available experimental data. We also benchmarked the performance of popular DFT exchange−correlation functionals for the calculations of the TAEs and NCEs. The performance of many DFT functionals for the calculation of the TAEs strongly depends on the choice of the electronic state for the transition metal atom. Hybrid functionals were found to generally outperform pure functionals in the calculation of NCEs, and the PBE1PBE functional has the best performance with average deviations of ∼1 kcal/mol for the dimers and ∼2 kcal/mol for the trimers and tetramers. The benchmarked functionals all display gradual degradation in performance with increasing cluster size.