Theoretical study of the icosahedral to cuboctahedral structural transition in Rh and Pd clusters

The icosahedral to cuboctahedral structural transition in Rh-N and Pd-N clusters with closed atomic shells and increasing sizes (N = 13, 55, 147, 309, 561) is studied using a tight-binding description of the valence band including sp electrons as well as d electrons assuming an homogeneous relaxation, the effect of inhomogeneous relaxation being discussed by means of an empirical potential. The critical size at which the cuboctahedral and icosahedral clusters have roughly the same energy is similar for Rh and Pd. The potential energy profile for the Mackay transformation which distorts continuously a cuboctahedron into an icosahedron is also calculated. The cuboctahedral structure is found to be unstable for N = 13 but, for 55 less than or equal to N less than or equal to 561, the potential energy profile exhibits an activation barrier which is expected to persist at least in some range of larger sizes. This explains the coexistence of both geometries at intermediate sizes. Finally the electronic structure of these clusters is also discussed.