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

Does Spin-Orbit Coupling Effect Favor Planar Structures for Small Platinum Clusters?