Structural Evolution and Chemical Bonding in Rare-Earth Encapsulated Magnesium Clusters: A CALYPSO-Guided DFT Study of La₂Mg_n and Lu₂Mg_n (<i>N</i> = 1–20)

The initial geometric configurations of gas-phase doped magnesium clusters incorporating rare-earth elements (La₂Mg_<i>n</i> and Lu₂Mg_<i>n</i>, <i>n</i> = 1-20) were systematically explored using the CALYPSO structure prediction software. Subsequent density functional theory (DFT) calculations were performed to conduct a comparative analysis of their structural evolution, stability, electronic properties, vibrational spectra, and chemical bonding characteristics. Key findings reveal that both La₂Mg_<i>n</i> and Lu₂Mg_<i>n</i> clusters adopt cage-like architectures for medium sizes (<i>n</i> ≥ 10), with rare-earth atoms encapsulated within the magnesium framework. Stability analyses identified La₂Mg₁₀, La₂Mg₁₅, Lu₂Mg₁₀, and Lu₂Mg₁₅ as potential ″magic-number″ clusters exhibiting enhanced relative stability. Electronic structure investigations through natural population analysis (NPA) demonstrate consistent electron transfer from Mg to rare-earth atoms, with lutetium exhibiting greater electron affinity than lanthanum. Notably, valence orbital distributions reveal distinct hybridization patterns between 5d/6s (Lu) and 5d/6s/4f (La) atomic orbitals. Theoretical infrared and Raman spectra predictions provide characteristic vibrational fingerprints to guide future experimental identification. Bonding critical point (BCP) analysis via atoms-in-molecules (AIM) theory further elucidates the nature of interatomic interactions in these heterometallic systems.