Molecular Structures, Acid−Base Properties, and Formation of Group 6 Transition Metal Hydroxides

Density functional theory (DFT) and coupled cluster theory (CCSD(T)) were used to study the group 6 metal (M = Cr, Mo, W) hydroxides: MO 3− m (OH) 2 m ( m = 1−3), M 2 O 6− m (OH) 2 m ( m = 1−5), M 3 O 9− m (OH) 2 m ( m = 1, 2), and M 4 O 11 (OH) 2 . The calculations were done up to the complete basis set (CBS) limit for the CCSD(T) method. Molecular structures of many low-energy conformers/isomers were located. Brønsted acidities in the gas phase and p K a values in aqueous solution were predicted for MO 3− m (OH) 2 m ( m = 1−3) and M n O 3 n −1 (OH) 2 ( n = 2−4). In addition, Brønsted basicities and Lewis acidities (fluoride affinities) were predicted for MO 3− m (OH) 2 m ( m = 1−3) as well as the metal oxide clusters M n O 3 n ( n = 1−3). The metal hydroxides were predicted to be strong Brønsted acids and weak to modest Brønsted bases and Lewis acids. The p K a values can have values as negative as −31. Potential energy surfaces for the hydrolysis of the M n O 3 n ( n = 1−4) clusters were calculated. Heats of formation of the metal hydroxides were predicted from the calculated reaction energies, and the agreement with the limited available experimental data is good. The first hydrolysis step leading to the formation of M n O 3 n −1 (OH) 2 was predicted to be exothermic, with the exothermicity becoming less negative as n increases and essentially converged at n = 3. Reaction rate constants for the hydrogen transfer steps were calculated using transition state theory and RRKM theory. Further hydrolysis of M n O 3 n −1 (OH) 2 tends to be endothermic especially for M = Cr. Fifty-five DFT exchange-correlation functionals were benchmarked for the calculations of the reaction energies, complexation energies, and reaction barriers by comparing to our CCSD(T) results. Overall, the DFT results for the potential energy surfaces are semiquantitatively correct, but no single functional works for all processes and all three metals. Among the functionals benchmarked, the wB97, wB97X, B1B95, B97-1, mPW1LYP, and X3LYP functionals have the best performance. Linear correlations between the calculated reaction barrier and reaction energy for hydrogen transfer reactions to the terminal ═O atom and to the bridge O atom were found to be quite different, indicating their different reaction properties. The calculated Lewis acidity (fluoride affinity) was found to best correlate with the calculated adsorption energy, the dissociative adsorption energy, and the reaction barrier for hydrogen transfer reactions to the terminal ═O atom.