Hollow Gold Cages and Their Topological Relationship to Dual Fullerenes

Golden fullerenes have recently been identified by photoelectron spectra by Bulusu et al. [S. Bulusu, X. Li, L.-S. Wang, X. C. Zeng, PNAS 2006, 103, 8326–8330]. These unique triangulations of a sphere are related to fullerene duals having exactly 12 vertices of degree five, and the icosahedral hollow gold cages previously postulated are related to the Goldberg–Coxeter transforms of C20starting from a triangulated surface (hexagonal lattice, dual of a graphene sheet). This also relates topologically the (chiral) gold nanowires observed to the (chiral) carbon nanotubes. In fact, the Mackay icosahedra well known in gold cluster chemistry are related topologically to the dual halma transforms of the smallest possible fullerene C20. The basic building block here is the (111) fcc sheet of bulk gold which is dual to graphene. Because of this interesting one-to-one relationship through Euler's polyhedral formula, there are as many golden fullerene isomers as there are fullerene isomers, with the number of isomers Nisoincreasing polynomially as (Formula presented.)). For the recently observed (Formula presented.), (Formula presented.), and (Formula presented.) we present simulated photoelectron spectra including all isomers. We also predict the photoelectron spectrum of (Formula presented.) . The stability of the golden fullerenes is discussed in relation with the more compact structures for the neutral and negatively charged Au12to Au20and Au32clusters. As for the compact gold clusters we observe a clear trend in stability of the hollow gold cages towards the (111) fcc sheet. The high stability of the (111) fcc sheet of gold compared to the bulk 3D structure explains the unusual stability of these hollow gold cages.