Density functional theory assessment of molecular structures and energies of neutral and anionic Al_n (n = 2-10) clusters

We report the results of a benchmarking study on hybrid, hybrid-meta, long-range-corrected, meta-generalized gradient approximation (meta-GGA), and GGA density functional theory (DFT) methods for aluminum (Al) clusters. A range of DFT functionals, such as B3LYP, B1B95, PBE0, mPW1PW91, M06, M06-2X, ωB97X, ωB97XD, TPSSh, BLYP, PBE, mPWPW91, M06-L, and TPSS, have been used to optimize the molecular structures and calculate the vibrational frequencies and four energetic parameters for neutral and anionic Al_n (n = 2-10) clusters. The performances of these functionals are assessed systematically by calculating the vertical ionization energy for neutral Al clusters and the vertical electron detachment energy for anionic Al clusters, along with the cohesive energy and dissociation energy. The results are compared with the available experimental and high-level ab initio calculated results. The calculated results showed that the PBE0 and mPW1PW91 functionals generally provide better results than the other functionals studied. TPSS can be a good choice for the calculations of very large Al clusters. On the other hand, the B3LYP, BLYP, and M06-L functionals are in poor agreement with the available experimental and theoretical results. The calculated results suggest that the hybrid DFT functionals like B3LYP do not always provide better performance than GGA functionals.