Theoretical study of the electronic states of Rhn+ (n=3–5)

Abstract

Theoretical study of the electronic states of small cationic niobium clusters, Nb n + (n=3-5) Geometries and energy separations of the various low-lying electronic states of Rh 3 ϩ , Rh 4 ϩ , and Rh 5 ϩ clusters with different structural arrangements have been investigated. The complete active space multiconfiguration self-consistent field method, ͑CASMCSCF͒ followed by large scale multireference singles plus doubles configuration interaction ͑MRSDCI͒ computations that included up to 1.6 million configurations for Rh 3 ϩ , 1.5 million configurations for Rh 4 ϩ , and 2.7 million configurations for Rh 5 ϩ , were used. Four nearly degenerate electronic states were found for Rh 3 ϩ . The 6 AЈ electronic state of the pyramidal structure of Rh 4 ϩ was found to be the ground state. Although the 6 AЉ electronic state of Rh 4 ϩ with the same geometry was found to be close in energy at the CASMCSCF level, it is 0.5 eV higher at the higher level of theory. Two nearly degenerate electronic states ͑ 5 AЉ and 5 AЉ͒ of the distorted edge capped tetrahedron structure of Rh 5 ϩ were found as candidates for the ground state of this cluster. Mulliken population analysis has been carried out on these cationic clusters to investigate their bonding properties.

Structural and electronic study of neutral, positive, and negative small rhodium clusters [Rhn, Rh, and Rh]

“…These values are large when compared with the average near-neighboring distances of 2.67 and 2.6 Å calculated with the GGA method from the Vienna ab initio simulation package [22,23]; for Rh 5 icosahedral and buckled planar structures by Chang et al [13] and Bae et al [14] with pseudopotential calculations using GGA obtain a square pyramid structure with bond lengths 2.42 Å in the base and 2.54 Å from vertex to base, which is lower in energy than a trigonal bipyramid (bond lengths 2.65 Å in the base and 2.50 Å [15]. For multiplicities 4-12, the geometry adopted by the cluster is a distorted edge-capped tetrahedron.…”

“…The occurrence of magnetism in clusters of nonmagnetic TMs such as rhodium [2] has attracted much attention [3]; however, a proper understanding still remains elusive. A clump of 13 atoms of Rh should show the effect; ferromagnetism was particularly strong in clusters of 15,16, and 19 atoms [4].…”

“…Furthermore, this kind of calculations reports different geometries and fundamental states for the same cluster [3,13,14]. Studies at the highest level of theory are scarce; HartreeFock configuration interaction or multiconfiguration self-consistent field calculations have been extended only up to five-atom clusters [15]. Thus, it would be interesting to acquire further knowledge on how to compare the results obtained with HF-SCF methods with those reported in literature, obtained with methods based on DFT theory, with experimental results [16,17], and with theoretical high-quality calculations [15] when available.…”

Communications: The structure of Rh8+ in the gas phase

“…Application of DFT to midsized TM clusters requires caution in the interpretation of results; not only because of the approximations inherent to all contemporary exchange-correlation functionals but also because there is a lack of benchmark data from high-quality multireference electronic structure theory, although data do exist for rhodium clusters as large as the pentamer. 17 Most contemporary functionals were not designed with TM clusters in mind and it is not clear if one single exchange-correlation functional is to be preferred for all TM clusters. Rhodium clusters present many of these challenges and opportunities and, as a consequence, have been studied experimentally in some detail.…”

The Structure of Rh$_8^+$ in the Gas Phase

“…The large size of TM clusters, both in terms of the number of electrons which must be treated and the complexity of the potential energy surfaces (PES), generally restricts practical calculations to the realm of DFT. Application of DFT to mid-sized TM clusters requires caution in the interpretation of results; not only because of the approximations inherent to all contemporary exchange-correlation functionals, but also because there is a lack of benchmark data from high-quality multi-reference electronic structure theory, although data does exist for rhodium clusters as large as the pentamer [17]. Most contemporary functionals were not designed with TM clusters in mind and it is not clear if one single exchange-correlation functional is to be preferred for all TM clusters.…”