Computational Investigation of the Size Evolution of (La₂ B ₂O₇) _n Nanoclusters (B = Ce, Ti, Zr)

Mixed-oxide particles are commonly used to promote chemical reactions in catalysis. However, our atomistic understanding of how particle size and oxygen vacancies influence their physicochemical characteristics remains limited. To address this issue, we use density functional theory calculations to investigate (La₂ B ₂O₇) _n nanoclusters, where B = Ti, Zr, Ce, and n = 2, 4, 6, 8, 10. Our findings and analysis reveal the following: (i) particle size plays a critical role in determining structural motifs, with all atoms in small particles (n = 2, 4) being entirely surface-exposed and exhibiting structural diversity, whereas larger clusters (n ≥ 6) develop bulk-like features in the core region with B cations located in the core and La segregating to the surface region; (ii) binding energy per atom increases with size, indicating enhanced stability resultant from diminished surface effects and compact structural motifs, with Zr-based nanoclusters demonstrating the strongest bonding; (iii) electronic band gaps decrease with increasing size, consistent with quantum confinement, although Ti- and Zr-based nanoclusters exhibit anomalies at intermediate sizes due to structural rearrangements; (iv) electrostatic potential analysis highlights highly positive cores in larger nanoclusters, elucidating their increased stability, while regions of low potential on the surface emerge as preferential sites for defect formation; (v) the formation of oxygen vacancy energetics follow to the hierarchy La₂Ce₂O₇ < La₂Ti₂O₇ < La₂Zr₂O₇, with surface vacancies generally more stable than core ones, particularly in Ce-based nanoclusters; and (vi) vacancy-induced electronic and magnetic responses are significantly influenced by the B cation: Ce-based nanoclusters exhibit localized f-electron reduction and stable magnetic moments, Ti-based systems exhibit a mix of itinerant and polaronic behavior, and Zr-based clusters remain nonreducible and nonmagnetic.