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

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

BH-DFTB/DFT calculations for iron clusters

We present a study on the structural, electronic, and magnetic properties of Fen(n  =  2  −  20) clusters by performing density functional tight binding (DFTB) calculations within a basin hopping (BH) global optimization search followed by density functional theory (DFT) investigations. The structures, total energies and total spin magnetic moments are calculated and compared with previously reported theoretical and experimental results. Two basis sets SDD with ECP and 6-31G** are employed in the DFT calculations together with BLYP GGA exchange-correlation functional. The results indicate that the offered BH-DFTB/DFT strategy collects all the global minima of which different minima have been reported in the previous studies by different groups. Small Fe clusters have three kinds of packing; icosahedral (Fe9−13), centered hexagonal antiprism (Fe14−17, Fe20), and truncated decahedral (Fe17(2), Fe18−19). It is obtained in a qualitative agreement with the time of flight mass spectra that the magic numbers for the small Fe clusters are 7, 13, 15, and 19 and with the collision induced dissociation experiments that the sizes 6, 7, 13, 15, and 19 are thermodynamically more stable than their neighboring sizes. The spin magnetic moment per atom of Fen(n = 2 − 20) clusters is between 2.4 and 3.6 μB for the most of the sizes. The antiferromagnetic coupling between the central and the surface atoms of the Fe13 icosahedron, which have already been reported by experimental and theoretical studies, is verified by our calculations as well. The quantitative disagreements between the calculations and measurements of the magnetic moments of the individual sizes are still to be resolved