Stability and Reactivity of , n = 1-10, Clusters and Their Interactions With .

Small titanium dioxide clusters (with = 1-10) are promising photocatalysts for 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 ( ), reveals = 2, 4, and 8 as magic numbers. Electrophilicity analysis ( ) shows moderate electrophilicity for = 1-5 and strong electrophilicity for = 7-10, while the magic numbers display reduced reactivity. Fukui functions and fractional occupation number-weighted density ( ) highlight localized reactivity. Notably, they reveal = 6 to be highly electrophilic, with distinct "hot" electron sites. interaction energies inversely correlate with cluster stability: unstable clusters ( = 3, 5, and 9) strongly bind (up to 0.72 eV), while magic numbers weakly physisorb it (e.g., 0.45 eV for = 8). Non-covalent interaction (NCI) analysis confirms Ti-OCO attraction and C-repulsive sites. Together, these results establish design principles for cluster catalysts that balance stability with tailored reactivity for activation.