DFT Variants for Mixed-Metal Oxides. Benchmarks Using Multi-Center Cluster Models

Mixed-metal oxides, e.g., V-Mo and Bi-Mo, are promising selective oxidation catalysts. Yet, their intricate chemical composition and electronic structure often confound DFT methods. This study addresses problems arising from the simultaneous presence of two kinds of transition metals, by probing eight functionals-five hybrid functionals (MN15, M06, PBE0-D3, B3LYP-D3, and TPSSh-D3), the meta-GGA functional M06-L-D3, the range-separated functional ωB97XD, and the GGA functional PBE-D3. We examine the ability of these functionals to localize reducing electrons, and to reproduce reaction energies from CCSD(T) calculations. Accordingly, hybrid functionals containing 20% or more exact exchange perform considerably better in both tests. The B3LYP-D3 approach exhibits the lowest overall mean absolute deviation of reaction energies (OMAD), 21 kJ mol^-1, and gave electron distributions as expected from the local lattice structure according to the pseudo-Jahn-Teller effect. MN15 and PBE0-D3 reproduced the electron distributions, but bore slightly higher OMAD values, at 31 and 32 kJ mol^-1. Despite acceptable OMAD values, M06 (28 kJ mol^-1) and TPSSh (23 kJ mol^-1) in some cases did not yield the expected electron distributions. The range-separated functional ωB97XD experienced the opposite problem, yielding correct electron distributions but a poor OMAD of 41 kJ mol^-1. M06-L-D3 and PBE-D3 performed relatively poorly, regarding the electron distribution and the OMAD values, 39 and 65 kJ mol^-1, respectively.