Entropic stabilized ABO₃ perovskite oxides promise novel applications, including solid oxide fuel cells, catalysts, and two-step solar thermochemical hydrogen (STCH) production. While mixing multiple cations offers a new compositional space with vast tunability, it also introduces new computational challenges. These challenges include how to sample the structures within the size scale of Density functional theory (DFT) calculations; whether the structures are fully random or with local order; and how to define oxygen vacancy and its distributions in CCPO.  

We calibrated our DFT-based predictive models with experiments in two CCPO systems, multiple A-site mixed {A}FeO₃ and B-site mixed (La_0.75Sr_0.25){Mn_0.25Fe_0.25Co_0.25Al_0.25}O₃ (MFCA).  DFT was combined with the Metropolis Monte Carlo method (DFT-MC) to efficiently sample the possible cation configurations in CCPO materials. By comparing four different DFT-informed statistical models with experiments, we show that both the oxygen vacancy formation energy distribution (E_v^f) and the vacancy interactions must be considered to predict the oxygen non-stoichiometry (δ) accurately. Similar to experiments, the predicted δ can be used to extract the enthalpy and entropy of reduction through the Van't Hoff method, providing direct comparisons with experimental results. This procedure provides a full predictive workflow using DFT-MC to obtain possible local ordering or fully random structures, understand the redox activity of each element, and predict the thermodynamic properties of CCPOs, for computational screening and design of these CCPO materials at STCH conditions.

Our calculations also revealed several important characteristics of CCPO. First, as more cation types, especially above four, are mixed, the cell lattice becomes more cubic-like but the local cation-O octahedrons are more distorted. The oxygen vacancy did not show preferred site preference in the A-site {A}FeO₃, but it is very sensitive to the B-sites. In the B-site mixed MFCA, the DFT-MC simulations predicted a significant increase in the local site preference of the cations (short-range ordering) in the presence of oxygen vacancies (V_O), compared to a more random mixing without V_O.  Co is found to be the redox active element among other species (e.g. Mn, Fe), agreeing with experiments. In MFCA_, Mn is the element that takes a 4+ oxidation state to compensate for the charge neutrality, while others are 3+. In the locally deformed lattice, the Fe-O are compassed, while Co-O bonds hold the most elongation, followed by Al, which provides extra mixing entropy that stabilizes the system. Thus, it was concluded that the V_O prefers to be generated next to Co due to stretched Co-O bonds.

For ideal STCH applications with higher hydrogen production levels, the E_v^f distribution enabled positive Δδ (difference of δ between the two-step conditions) in the lower E_v^f and higher temperature range, where the traditional dilute and no-distribution model often misinterprets. This suggests the efficiency of water splitting and hydrogen production can be thermodynamically improved by mixing cations in CCPO and tunning both the average E_v^f and its distribution.