TiO₂ nanoparticles

In summary, the global minimum search was conducted with an evolutionary algorithm implemented in the USPEX code to find the most stable (TiO₂)_n nanoparticles with n = 2–20 using the PM6-D3 semi-empirical method, exploring more than 60,000 structures. From the evolutionary algorithm results, the candidate clusters with the lowest energy were re-optimized using density functional theory within the GGA approach. In the last step, the ground state for each cluster size was again optimized with the PBE0/def2-TZVP level of theory to calculate the total energy. Effective core potentials (ECP) for describing the Ti and O core electrons were used through all calculations with the PBE0 functional. The valence electrons of Ti (3s²3p⁶3d²4s²) and O (2s²2p⁴) were described with the def2-TZVP basis set (Triple-Zeta Valence with Polarization).