Prussian blue analogs (PBAs) are an important material class for aqueous electrochemical separations and energy storage owing to their ability to reversibly intercalate monovalent cations. However, incorporating interstitial molecules in the ab initio study of PBAs is technically challenging, though essential to understanding the interactions between interstitial water, interstitial cations, and the framework lattice that affect intercalation potential and cation intercalation selectivity. Accordingly, we introduce and use a method that combines the efficiency of machine-learning models with the accuracy of ab initio calculations to elucidate mechanisms of (1) lattice expansion upon intercalation of cations of different sizes, (2) selectivity bias toward intercalating hydrophobic cations of large size, and (3) semiconductor–conductor transitions from anhydrous to hydrated lattices. We analyze the PBA nickel hexacyanoferrate [] due to its structural stability and electrochemical activity in aqueous electrolytes. Here, grand potential analysis is used to determine the equilibrium degree of hydration for a given intercalated cation (Na, K, or Cs) and oxidation state based on pressure-equilibrated structures determined with the aid of machine learning and simulated annealing. The results imply new directions for the rational design of future cation-intercalation electrode materials that optimize performance in various electrochemical applications, and they demonstrate the importance of choosing an appropriate calculation framework to predict the properties of PBA lattices accurately.
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