Linking the polyatomic arrangements of interstitial H2 O and cations to bonding within Prussian blue analogues ab initio using gradient-boosted machine learning

Prussian blue analogues (PBAs) are model host compounds for the intercalation of monovalent cations for electrochemical energy storage and separations. However, the interactions among interstitial species and their effects on atomic arrangements therein are understood mainly at a phenomenological level. Analyzing correlations between electronic interactions and polyatomic arrangements in hydrated Prussian blue analogues is complicated by the nonlocal hydrogen-bonding interactions between zeolitic water and framework lattices. Here, we train machine-learning (ML) models to learn DFT-calculated energy landscapes of nickel hexacyanoferrate PBA lattices with various lattice hydration degrees, oxidation states, and types of intercalated alkali cations based on various three-particle feature parameters. This ML approach is enabled by using gradient-boosted regression trees with features that are rotationally invariant geometric parameters. ML model accuracy is shown to be a cation-specific indicator of correlations between energy and polyatomic arrangements. Overlap population analysis among correlated atoms further confirms that such correlations are caused by the competition for dative bonding between Lewis-acid intercalated cations and Lewis bases (cyanide and oxygen in H2O). Examination of lowest-energy structures reveals that cation hydrophilicity and bare ionic radius determine dative-bonding strength, resulting in cation-H2O ordering in interstitial space. The projected energy landscapes of hydrated PBA lattices is also explored in subspaces spanned by certain many-particle feature parameters inspired by ML analysis. The downhill traces in such landscapes indicate that lattice distortion is accompanied by two kinds of collective movements: (1) rearrangements in the hydration shells around small and hydrophilic cations and (2) collective attack of H2O molecules on nickel-cyanide bonds promoted by large, hydrophobic cations.