# Publication: Density Functional Study of 13-Atom Metal Clusters M$_{13}$, M=Ta--Pt.

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Title Density Functional Study of 13-Atom Metal Clusters M$_{13}$, M=Ta--Pt.
Authors/Editors* Min Zhang and Rene Fournier
Where published* Physical Review A
How published* Journal
Year* 2009
Volume
Number
Pages 043203-1 043203-10
Publisher American Physical Society
Keywords DFT, clusters, global optimization, geometric structure, cluster analysis
We report the structures of six proposed global minima (GM) of M$_{13}$ clusters (M$=$Ta, W, Re, Os, Ir, Pt) and 62 isomers that are within roughly 1\thinspace eV of the GM. The GM and isomers were obtained after several global optimization runs using a first-principles (PBE exchange-correlation) method to evaluate the energy. The GM and lowest energy isomers can be described qualitatively as:amorphous and compact for Ta, W, and Pt; quasi-crystalline for Re; and cubic-prismatic for Os and Ir. The icosahedron is more than 1\thinspace eV above the GM (except 0.56\thinspace eV for Ta$_{13}$). The ground state electronic configuration of the atoms are essential to understanding structural trends in the clusters. Elements with a nearly closed-shell ground state atom (W, Pt) produce many more low-energy cluster isomers than elements with partially filled $d$-shells, and those isomers are generally compact and amorphous. Partially filled $d$-shells in Os and Ir lead to strong directional bonding and many 90$^{\circ}$ angles between nearest-neighbours. The predicted spin multiplicity of the GM are 2 (Ta$_{13}$), 1 (W$_{13}$), 6 (Re$_{13}$), 5 (Os$_{13}$), 4 (Ir$_{13}$), and 3 (Pt$_{13}$), and the spin multiplicity of isomers within 0.5\thinspace eV of the GM are all within $\pm 2$ of these values and are all smaller than 6.