HOMOMO Energy Gap Analysis

The HOMO-LUMO energy gap is an important parameter that characterizes the chemical activity of small clusters. It represents the ability of a cluster to participate in chemical reactions to some degree. In general, a large HOMO-LUMO energy gap indicates a weaker chemical reactivity. The calculated values of HOMO-LUMO gaps for Rhn clusters are given in Table 3. From this table, the HOMO-LUMO energy gaps are in the range of (0.018-0.297 eV), indicating that the metallic behaviour can appear in these clusters. Thus, these clusters can be applied to a lot of catalytic reactions. Unfortunately, there are no experimental data for these clusters to compare our theoretical results.
In cluster physics, the ionization potential (IP) and electron affinity
Figure 4 exhibits the size dependence of the total magnetic moments for the lowest-energy Rhn clusters. As shown in Figure 4, the curve of magnetic moments shows irregular oscillating behaviour, and the calculated magnetic moments are in the range of 3-13 μB. Higher magnetic moment was observed for the Rh11 clusters (13 μB). The results exhibit also that the magnetic moment of Rhn clusters depend on their geometries and spin states (see Table 2). For example, the tetrahedron (4b) and octahedron (6c) geometries are nonmagnetic, while the planar square (4c) and prism (6b) structures have a magnetic moment of 5 and 6 μB, respectively. To explore the origin of peculiar magnetic properties, we have performed a detailed analysis of the molecular orbitals by examining the partial density of states (PDOS) from the contribution of different orbital components (4d, 5s and 5p). Figure 5 provides the total and partial of densities of states of some Rhn (n = 2,4,7-12) clusters as representatives. We choose the spin-up states as positive value and spin-down states as negative one. The Fermi level of cluster is presented as a dashed vertical line and shifted to zero. As can be seen from Figure 5, the total density of states (DOS) shows that the Rhn clusters have metallic behavior, except the Rh2 and Rh4 clusters. For both clusters, we observe the same