Stability and Reactivity of TiO 2 n $$ {\left({\mathrm{TiO}}_2\right)}_n $$ , n = 1–10, Clusters and Their Interactions With CO 2 $$ {\mathrm{CO}}_2 $$

Small titanium dioxide clusters ${\left({\mathrm{TiO}}_2\right)}_n$ (with $n$ = 1–10) are promising photocatalysts for ${\mathrm{CO}}_2$ 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 (${\epsilon }^3$), reveals $n$ = 2, 4, and 8 as magic numbers. Electrophilicity analysis ($\Delta \omega$) shows moderate electrophilicity for $n$ = 1–5 and strong electrophilicity for $n$ = 7–10, while the magic numbers display reduced reactivity. Fukui functions and fractional occupation number-weighted density ($N_{\mathrm{FOD}}$) highlight localized reactivity. Notably, they reveal $n$ = 6 to be highly electrophilic, with distinct “hot” electron sites. ${\mathrm{CO}}_2$ interaction energies inversely correlate with cluster stability: unstable clusters ($n$ = 3, 5, and 9) strongly bind ${\mathrm{CO}}_2$ (up to 0.72 eV), while magic numbers weakly physisorb it (e.g., 0.45 eV for $n$ = 8). Non-covalent interaction (NCI) analysis confirms Ti–OCO attraction and C-repulsive sites. Together, these results establish design principles for ${\mathrm{TiO}}_2$ cluster catalysts that balance stability with tailored reactivity for ${\mathrm{CO}}_2$ activation.