  We study why gold forms planar and cage-like clusters while copper and silver
do not. We use density functional theory and norm-conserving pseudo-potentials
with and without a scalar relativistic component. For the exchange-correlation
functional 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 with
scalar-relativistic pseudopotentials and the GGA. In all other calculations,
with more than 6 or 7 noble metal atoms, we obtain three dimensional
structures. In the total energy balance, kinetic energy favors planar and cage
structures, while xc-energy favors 3D structures. As a second step, we
construct cluster structures having only surface atoms with Oh, Td, and Ih
symmetry. Then we select those with 2(l+1)**2 electrons (with l integer), which
correspond to the filling of a spherical electronic shell formed by node-less
one electron wave functions. Using scalar relativistic GGA molecular dynamics
at T = 600K, we show that the cage-like structures of neutral Au32, Au50, and
Au162 are meta-stable. The dipole polarizability of gold clusters corresponds
to the linear response of 1.6 delocalized valence electrons, suggesting a
strong screening of the valence interactions due to the d-electrons.
