| Abstract
| - As ruthenium plays an important role in heterogeneous catalysis, understanding the structural and electronicproperties of Ru clusters is crucial to advancement of technology. Because of its efficiency, density functionaltheory (DFT) calculations are often utilized in nanoscience, but careful validation is necessary. Recently,small, nonmetallic Run clusters were reported by Zhang et al. [J. Phys. Chem. B2004, 108, 2140] to formunusual 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 thatthe calculated, energetically preferred structures are sensitive to which XC functional is used and whetherrelativistic effects are included. We find that a hybrid XC functional with partially exact exchange, such asPBE0, corrects the Ru2 magnetic moment, bond length, and dissociation energy in agreement with experimentand 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 electronicstructure of a Ru atom, where the relative position of majority spin s level is shifted with respect to eg levels.We also find that standard nonrelativistic DFT-GGA gives similar results to relativistic DFT-PBE0, i.e., relativeshifting of s level, but not for the right reasons. Our results again stress the need to validate an XC functionalbefore application to transition-metal nanoclusters.
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