The physical properties of small rhodium clusters, Rh${}_n$, have been in debate due to the shortcomings of density functional theory (DFT). To help in the solution of those problems, we obtained a set of putative lowest energy structures for small Rh${}_n$ $(n=$ 2–15) clusters employing hybrid-DFT and the generalized gradient approximation (GGA). For $n=$ 2–6, both hybrid and GGA functionals yield similar ground-state structures (compact), however, hybrid favors compact structures for $n=7$–15, while GGA favors open structures based on simple cubic motifs. Thus, experimental results are crucial to indicate the correct ground-state structures, however, we found that a unique set of structures (compact or open) is unable to explain all available experimental data. For example, the GGA structures (open) yield total magnetic moments in excellent agreement with experimental data, while hybrid structures (compact) have larger magnetic moments compared with experiments due to the increased localization of the $4d$ states. Thus, we would conclude that GGA provides a better description of the Rh${}_n$ clusters, however, a recent experimental-theoretical study [Harding et al., J. Chem. Phys. 133, 214304 (2010)] found that only compact structures are able to explain experimental vibrational data, while open structures cannot. Therefore, it indicates that the study of Rh${}_n$ clusters is a challenging problem and further experimental studies are required to help in the solution of this conundrum, as well as a better description of the exchange and correlation effects on the Rh${}_n$ clusters using theoretical methods such as the quantum Monte Carlo method.

• Received 17 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.125430