Does spin–orbit coupling effect favor planar structures for small platinum clusters?

We have performed relativistic effective core potential calculations with and without spin-orbit coupling term in the framework of the density functional theory and investigated the geometry and binding energy of different isomers of free platinum clusters Pt(n) (n = 4-6) for 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-D 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-D isomers. Spin-orbit coupling effects change the relative stability of various isomers.