We study why gold forms planar and cage-like clusters while copper and silverdo not. We use density functional theory and norm-conserving pseudo-potentialswith and without a scalar relativistic component. For the exchange-correlationfunctional we use both the generalized gradient (GGA) and the local density(LDA) approximations. We find that planar Au_n structures, with up to n = 11,have lower energy than the three-dimensional isomers only withscalar-relativistic pseudopotentials and the GGA. In all other calculations,with more than 6 or 7 noble metal atoms, we obtain three dimensionalstructures. In the total energy balance, kinetic energy favors planar and cagestructures, while xc-energy favors 3D structures. As a second step, weconstruct cluster structures having only surface atoms with Oh, Td, and Ihsymmetry. Then we select those with 2(l+1)**2 electrons (with l integer), whichcorrespond to the filling of a spherical electronic shell formed by node-lessone electron wave functions. Using scalar relativistic GGA molecular dynamicsat T = 600K, we show that the cage-like structures of neutral Au32, Au50, andAu162 are meta-stable. The dipole polarizability of gold clusters correspondsto the linear response of 1.6 delocalized valence electrons, suggesting astrong screening of the valence interactions due to the d-electrons.
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