Structural and electronic properties of 13-atom 4d transition-metal clusters

We performed global optimization and property calculations by density-functional theory for the series of 4d transition-metal clusters M-13, M=Y-Pd. Calculated Gibbs free energies suggest the coexistence of isomers, or spin states, other than the global minimum in all cases except maybe Zr-13 and Pd-13. The calculated infrared spectra of these isomers are typically very different. Calculated ionization energies and magnetic moments agree well with available experimental results but do not allow to assign the geometric structure. Analysis of relative isomer energies and their electronic density of states suggests that these clusters tend to follow a maximum hardness principle: the lowest energy states and geometric structures are often the ones with lowest density of states near the Fermi level and lowest spin magnetic moment. In going from left to right in the 4d series, the geometric structures evolve from icosahedral (Y, Zr), to distorted compact structures (Nb, Mo), to fcc or simple-cubic crystal fragments (Tc, Ru, Rh), and icosahedron again (Pd). We rationalize this trend on the basis of the increasingly localized nature of molecular orbitals in going from left to right and the importance of d-type orbital bonding in the middle of the series.