Stability and Reactivity of TiO2n(TiO₂)ₙ, n = 1–10, Clusters and Their Interactions With CO2CO₂

Small titanium dioxide clusters TiO2n(TiO₂)ₙ (with nn = 1-10) are promising photocatalysts for CO2CO₂ conversion; however, their size-dependent stability and reactivity are not fully characterized. This study uses density functional theory (M06/def2-TZVP) and global and local reactivity descriptors to identify "magic number" clusters that exhibit high stability. The stability function ( ε3ε³ ), reveals nn = 2, 4, and 8 as magic numbers. Electrophilicity analysis ( ΔωΔ ω ) shows moderate electrophilicity for nn = 1-5 and strong electrophilicity for nn = 7-10, while the magic numbers display reduced reactivity. Fukui functions and fractional occupation number-weighted density ( NFODNFOD ) highlight localized reactivity. Notably, they reveal nn = 6 to be highly electrophilic, with distinct "hot" electron sites. CO2CO₂ interaction energies inversely correlate with cluster stability: unstable clusters ( nn = 3, 5, and 9) strongly bind CO2CO₂ (up to 0.72 eV), while magic numbers weakly physisorb it (e.g., 0.45 eV for nn = 8). Non-covalent interaction (NCI) analysis confirms Ti-OCO attraction and C-repulsive sites. Together, these results establish design principles for TiO2TiO₂ cluster catalysts that balance stability with tailored reactivity for CO2CO₂ activation.