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

TL;DR

This study uses relativistic density functional theory to analyze how spin-orbit coupling influences the stability and structure of small platinum clusters, revealing that 3D structures remain most stable despite some planar geometries gaining relative stability.

Contribution

It provides a comprehensive analysis of spin-orbit effects on platinum cluster geometries, challenging previous assumptions about planar structures being most stable.

Findings

3D configurations are lowest energy structures of Pt$_{n}$ clusters.

Spin-orbit coupling affects relative stabilities and vibrational properties.

Some planar geometries become more stable due to spin-orbit effects.

Abstract

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.