Computational Study of the Hydrolysis Reactions of Small MO₂ (M = Zr and Hf) Nanoclusters with Water

Density functional theory (DFT) has been used to study the hydrolysis reaction of (MO₂)_<i>n</i> (M = Zr, Hf, <i>n</i> = 1–4) nanoclusters in the ground singlet and first triplet states. The reactions for singlet <i>n</i> = 1 were benchmarked at the CCSD­(T) level of theory. The reactions of H₂O with the metal site having an MO bond and/or M–O bonds as well as H transfer to both terminal O atoms and bridge −O atoms have been studied. The partial charge on M increases as the MO bonds are replaced with M–OH bonds. The first H₂O adsorption (physisorption) energies for these MO₂ nanoclusters are calculated to be −20 to −30 kcal/mol for the singlet state and −15 to −48 kcal/mol for the triplet state. These physisorption energies depend on the cluster size and the adsorption site, consistent with existing experimental and computational studies. The first hydrolysis (dissociative chemisorption) reaction energies of the MO₂ nanoclusters are calculated to have a much broader range, −30 to −80 kcal/mol for the singlet states and −30 to −100 kcal/mol for the triplet states. Steric effects play an important role in determining the physisorption and chemisorption energies, especially for the trimers and tetramers. The potential energy surfaces for hydrolysis in both the singlet and triplet states are calculated. The calculated Lewis acidities (fluoride affinities) correlate with the hydrolysis properties of the nanoclusters. Our calculations show that H₂O readily reacts with both the singlet and triplet states of the MO₂ nanoclusters to form the hydroxides. The reaction barriers are generally less than 10 kcal/mol for the singlet states, and because the H₂O physisorption energies are large, the barriers occur below the (MO₂)_<i>n</i> asymptote