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In this paper, we have performed a systematic study of the geometries, electronic structures, and magnetic moments of Rhn-1(TM) (n=2-8) (TM=Cr,Mn,Fe,Co,Ni,Cu) clusters using the Density functional theory Semi-core Pseudopots (DSPP) implemented in the DMol package. Via analyzing the average binding energies, the gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO),the fragmentation energies, and the second-order difference of energies (Δ2E) of Rhn-1(TM)(n=2-8),we have learned size-dependence of magnetic and energetic properties.1. Compared to pure Rhn,the TM-doped Rhn-1(TM) (n=2-8) clusters are characterized by structural reconstruction. The overall evolutionary trend shows that TM-doped cluster has the geometry similar to that of Rhn where the TM atom occupies a substitutional site, accompanied by a sight distortion in the cluster.2. From analyzing the fragmentation energies, and the second-order difference of energies (Δ2E) of Rhn-1(TM)(n=2-8), Rh3Cr,Rh5Mn,Rh3Fe,and Rh6Fe,Rh3Co,and Rh5Co,Rh3Ni, and Rh5Ni,Rh5Cu have relatively high stabilities and can be considered as magic clusters.3. From analyzing magnetic properties of Rhn-1(TM)(n=2-8), as comparing that of pure Rhn, for Rhn-1Cr clusters,the magnetic moment of Rh5Cr increases 7μB, as the largest change. For Rhn-1Mn clusters,the magnetic moment of Rh3Mn changes biggest, by increasing 4μB , and by 2μB when n=2,5,6. For Rhn-1Fe clusters, the magnetic moment changes extraordinary remarkable, and the magnetic moment of Rh6Fe increases 11μB. The magnetic moment of Rhn-1Co also changes markedly, and by increasing 10μB for Rh6Co. For Rhn-1Ni clusters, the magnetic moment of Rh6Ni increases 5μB, otherwise by 1μB or 3μB. When n=4、6、8, the magnetic moment of Rhn-1Cu is larger than that of Rhn by 2μB. The magnetism of Rhn-1(TM)(n=2-8)( TM=Cr,Mn,Fe,Co,Ni,Cu ) shows strong isomerization dependence, and the magnetic moment increases remarkably by doping transition metal atoms like Fe,Co or Ni.4. From analyzing the HOMO-LUMO energy gaps of Rhn-1(TM)(n=2-8), it was shown that in general the chemical activity of Rhn clusters can be increased by doping of a transition metal atom.
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