$I$-Au$_{\mathrm{60}}$: Chiral Symmetry Breaking Yields a Perfect Golden Shell of Singular Rigidity

The unique properties of elemental gold (Z$=$79, Au) derive from the extreme relativistic contraction of its atomic core \textit{[Xe] }5$d^{\mathrm{10}}$ orbitals. Among these manifest properties are a propensity toward planarity, 2D bonding (\textit{5d}$_{z2}$\textit{ - 6s }hybridization) and high electro-negativity (2.54) exceeding that of any other metallic or semi-metallic element. We report an astounding consequence: a chiral symmetry-breaking, i.e. the predicted spontaneous formation of a chiral-icosahedral shell ($I$-Au$_{\mathrm{60}})$ from achiral ($I_{h})$ precursor forms, accompanied by a contraction in the Au-Au bonding and hence the radius of this \textit{perfect golden sphere}, in which all 60 atomic sites are chemically equivalent. This structure, which resembles that most complex of semi-regular (Archimedean) polyhedra (3.3.3.5*), may be viewed as an optimal topological solution to the problem: how to close a 60-vertex 2D (triangular) net in 3D. The singular rigidity of the $I$-Au$_{\mathrm{60}}$ manifests in uniquely discrete structural, vibrational, electronic, and optical signatures, which are reported as a guide to its experimental detection and ultimately its isolation in material forms. Its high (implicated) electronegativity suggests routes to obtaining it as a spherically aromatic $I$-Au$_{\mathrm{60}}(^{\mathrm{6-,12-)}}$ salts of various inert counter-cations. Its large internal void could also hold a complex as large as $I_{h}$-M$_{\mathrm{12}}$C$_{\mathrm{60}}$, M $=$ a mono- or di-valent metal ion.