DFT investigation of (Ca(OH)₂)n clusters: structural motifs and implications for early-stage aggregation

Understanding the early stages of calcium hydroxide formation is important for applications in cement chemistry, catalysis and thermochemical energy storage. In this work, we present a density functional theory (DFT) study of the structures and stability of (Ca(OH)₂)_n clusters (n = 1-15). The coordination behavior of hydroxide ligands around Ca²⁺ centers reveals a systematic evolution in which terminal η¹-OH groups are progressively replaced by higher-order μ_i (i = 2-5) bridging motifs. These motifs act as fundamental structural units that drive the transformation from planar to three-dimensional cluster geometries and promote increasing structural compactness. Small clusters (n < 2) adopt planar μ₂-bridged motifs, while three-dimensional structures emerge at n = 3 with the appearance of μ₃ coordination. A structural transition occurs at n = 5-6, where μ₄ motifs enable core formation. At larger sizes (n ≥ 7), μ₅ coordination and cooperative hydrogen bonding facilitate inward hydroxide migration and further core densification. Several cluster sizes, including n = 6, 7, 9, 10, 11 and 13, are identified as magic-number clusters. These results provide atomistic insight into intrinsic structural tendencies and possible pre-nucleation motifs in calcium hydroxide aggregation.