Geometries, electronic and magnetic properties of hafnium clusters: A density functional calculation

The geometries, electronic and magnetic properties of Hfn (n = 2–13,14,18) clusters are studied by using density functional methods. Particularly, the studies focus on the averaged atomic binding energies, equilibrium geometries, detachment energies, and magnetic characteristics of Hfn clusters. Relative stabilities of Hfn clusters in terms of the calculated detachment energies are discussed, exhibiting that the magic numbers of stabilities are n = 4, 7, 9, and 12, and that the nonmagnetic Hf12 geometry is the most stable isomer and ground state. Furthermore, the calculated highest occupied orbital and lowest unoccupied orbital gap of Hfn (n = 6–13) displays a small odd–even oscillation feature. The calculated ground state magnetic moments for Hfn are respectively 4.0 μB (n = 4,11), 2.0 μB (n = 2,5,7–9,13), and 0.0 μB (n = 3,6,10,12,14,18); the averaged atomic magnetic moment of Hfn is generally decreased as the number of n being increased. Comparison of our calculated results with available experimental data is made.