Removing Critical Errors for DFT Applications to Transition-Metal Nanoclusters: Correct Ground-State Structures of Ru Clusters

As ruthenium plays an important role in heterogeneous catalysis, understanding the structural and electronic properties of Ru clusters is crucial to advancement of technology. Because of its efficiency, density functional theory (DFT) calculations are often utilized in nanoscience, but careful validation is necessary. Recently, small, nonmetallic Ru(n) clusters were reported by Zhang et al. [J. Phys. Chem. B 2004, 108, 2140] to form unusual square and cubic ground-state structures within DFT by treating the exchange-correlation (XC) functional at the level of general-gradient-corrected approximation (GGA). For such clusters, we show that the calculated, energetically preferred structures are sensitive to which XC functional is used and whether relativistic effects are included. We find that a hybrid XC functional with partially exact exchange, such as PBE0, corrects the Ru2 magnetic moment, bond length, and dissociation energy in agreement with experiment and high-level quantum chemistry calculations and changes the Ru4 ground-state structure to a tetrahedron, instead of a square. The change in structural preference is explained by the corrections to the electronic structure of a Ru atom, where the relative position of majority spin s level is shifted with respect to e(g) levels. We also find that standard nonrelativistic DFT-GGA gives similar results to relativistic DFT-PBE0, i.e., relative shifting of s level, but not for the right reasons. Our results again stress the need to validate an XC functional before application to transition-metal nanoclusters.