  We have performed full-relativistic density functional theory calculations to
study the geometry and binding energy of different isomers of free platinum
clusters Pt$_{n}$ ($n=4-6$) within the spin multiplicities from singlet to
nonet. The spin-orbit coupling effect has been discussed for the minimum-energy
structures, relative stabilities, vibrational frequencies, magnetic moments,
and the highest occupied and lowest unoccupied molecular-orbital gaps. It is
found in contrast to some of the previous calculations that 3-dimentional
configurations are still lowest energy structures of these clusters, although
spin-orbit effect makes some planar or quasi-planar geometries more stable than
some other 3-dimentional isomers.
