Structure of Mg$_n$ and Mg$_n^+$ clusters up to n=30

TL;DR

This study uses advanced density functional theory methods to determine the structures and electronic properties of Mg and Na clusters up to 30 atoms, revealing stability patterns and electronic gaps without a non-metal to metal transition.

Contribution

It introduces a new coordinate-space algorithm for solving Kohn-Sham equations, enabling high-resolution electronic structure calculations of metal clusters on parallel computers.

Findings

Identified ground-state structures for Mg clusters up to 30 atoms.

Analyzed HOMO-LUMO gaps and stability of Mg clusters.

Found no non-metal to metal transition in the examined regime.

Abstract

We present structure calculations of neutral and singly ionized Mg clusters of up to 30 atoms, as well as Na clusters of up to 10 atoms. The calculations have been performed using density functional theory (DFT) within the local (spin-)density approximation, ion cores are described by pseudopotentials. We have utilized a new algorithm for solving the Kohn-Sham equations that is formulated entirely in coordinate space and, thus, permits straightforward control of the spatial resolution. Our numerical method is particularly suitable for modern parallel computer architectures; we have thus been able to combine an unrestricted simulated annealing procedure with electronic structure calculations of high spatial resolution, corresponding to a plane-wave cutoff of 954eV for Mg. We report the geometric structures of the resulting ground-state configurations and a few low-lying isomers. The energetics and HOMO-LUMO gaps of the ground-state configurations are carefully examined and related to their stability properties. No evidence for a non-metal to metal transition in neutral and positively charged Mg clusters is found in the regime of ion numbers examined here.