Study of the Structural and Electronic Properties of Rh N and Ru N Clusters (N < 20) within the Density Functional Theory F. Aguilera-Granja* Instituto de Fı ´sica, UniVersidad Auto ´noma de San Luis Potosı ´, San Luis Potosı ´, Me ´xico L. C. Balba ´s and A. Vega Departamento de Fı ´sica Teo ´rica, Ato ´mica y O ´ ptica, UniVersidad de Valladolid, Spain ReceiVed: June 2, 2009; ReVised Manuscript ReceiVed: September 29, 2009 Using the density-functional theory (DFT) with the generalized gradient approximation to exchange and correlation, we compute the geometries, electronic structure, and related properties of free-standing rhodium and ruthenium atomic clusters with sizes below 20 atoms. We explore different structural and spin isomers per size, for which we determine the interatomic distances, binding energy, magnetic moment, HOMO-LUMO gap, and electric dipole moment. For many sizes, different implementations of DFT predict different properties for the lowest-energy isomers, thus illustrating the complex nature of these 4d transition metal elements at the nanoscale. We discuss our results for rhodium clusters in the context of recent electric deflection measurements. I. Introduction Free-standing transition-metal (TM) atomic clusters are a matter of intense research with the goal of understanding the geometrical and electronic properties at the nanoscale as well as their interplay. This knowledge is of great relevance if those systems will be used in nanotechnology to design magnetic or catalytic devices in which the morphology plays a fundamental role. The production of size-selected, free-standing clusters in cluster beams is well-controlled at present, and the magnetic properties as a function of cluster size can be investigated through Stern-Gerlach techniques. 1-3 Molecular beam electric deflection measurements have also been carried out to character- ize the electric dipole and polarizabilities of several TM clusters. 4-6 However, the geometrical structures of free-standing clusters are more difficult to characterize, since most of the techniques used in bulk-like systems are not suitable if the cluster is not supported on a host. Therefore, in the free-standing environment, alternative techniques have emerged to find plausible geometries. In this respect, and closely related to catalysis, it is possible to take advantage of the structural dependency on the adsorption of light molecules on the surface of the cluster. 7 Other types of experiments, such as trapped ion electron diffraction 8 and infrared spectroscopy, 9 have shed light on the geometrical structure of metal clusters when combined with density func- tional theory (DFT) total energy calculations. From the theoretical side, the coexistence of itinerant d electrons with delocalized sp electrons in the electronic valence of transition metals makes it difficult to treat them within simple models. If the determination of both the geometry and electronic structure is being achieved at the same level, which is desirable due to the strong interdependence of both kind of properties, DFT has been demonstrated to be a very efficient and reliable approach for many elements. The electronic structure and magnetic properties of clusters of the non magnetic 4d elements Rh and Ru have been widely investigated from the theoretical side after the pioneering experimental work of Cox and co-workers. 2 The early theoretical studies using both semiempirical approaches and DFT did not consider full structural relaxation (due to the huge computational cost), despite interesting general trends being predicted, such as the magnetic character of small Rh and Ru clusters, in contrast with the nonmagnetic character of their bulk counterparts. 10-18 Later DFT studies, carried out considering structural relaxations, provided further details on the growth patterns and electronic properties, although the wide dispersion in results depending on the DFT flavor did not allow unambiguously proposing geometric and total spin patterns as a function of the cluster size. 19-24 In the present work, we have calculated, using the DFT SIESTA code (Spanish Initiative for Electronic Simulation of Thousands of Atoms) 25 in the generalized gradient approxima- tion (GGA) approximation, the geometries, electronic structure, and related properties of different isomers of Rh and Ru atomic clusters with less than 20 atoms. We have focused on the previous DFT-GGA studies that considered full structural relaxation, 19-24 against which we have benchmarked our results. We also provide results for properties that were not calculated before, such as the electric dipole and polarizability (only for some particular clusters), which we have tried to correlate, in the case of Rh, with recent electric deflection measurements 6 to finally illustrate the complex nature of these 4d TM elements at the nanoscale and the difficulty in reaching an overall agreement at the DFT level. Thus, the present work reports results obtained using another DFT-GGA implementation which we believe will be of interest for the scientific community. Since the problem still remains open, in our opinion, we hope that our work will contribute to the enrichment of the scientific discussion and to the motivation of further experimental and theoretical efforts. * Corresponding author. E-mail: faustino@ifisica.uaslp.mx. J. Phys. Chem. A 2009, 113, 13483–13491 13483 10.1021/jp905188t CCC: $40.75  2009 American Chemical Society Published on Web 10/26/2009