Au${}_{40}$: A large tetrahedral magic cluster

40 is a magic number for tetrahedral symmetry predicted in both nuclear physics and the electronic jellium model. We show that Au${}_{40}$ could be such a a magic cluster from density functional theory-based basin hopping for global minimization. The putative global minimum found for Au${}_{40}$ has a twisted pyramid structure, reminiscent of the famous tetrahedral Au${}_{20}$, and a sizable HOMO-LUMO gap of 0.69 eV, indicating its molecular nature. Analysis of the electronic states reveals that the gap is related to shell closings of the metallic electrons in a tetrahedrally distorted effective potential.

Figure 1

Energy landscape of a DFT-based basin-hopping search for the global minimum of Au${}_{38}$, started with the octahedral structure.

Figure 2

Energy landscape of a DFT-based basin-hopping search for the global minimum of Au${}_{40}$.

Figure 3

The global minimum for Au${}_{40}$ featuring a twisted pyramid with a missing corner: (a) top view, the missing corner is at the top of the figure; (b) side view, the Au${}_4$ tetrahedral core is highlighted.

Figure 4

An isomer of Au${}_{40}$ featuring a twisted pyramid with $C_3$ symmetry: (a) top view; (b) side view, showing the Au${}_3$ triangle core; (c) bottom view, showing the base of the pyramid.

Figure 5

The density of states relative to Fermi energy projected on angular momentum eigenfunctions relative to the clusters center of mass. In (a), (b) only the Au(6s) electrons are treated as valence electrons, whereas in (c), (d) the Au(5d) electrons are also allowed to rearrange.