Closed-shell to split-shell stability of isovalent clusters

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Metallic clusters containing 2, 8, 18, and 20 electrons are now known to exhibit enhanced stability that can be reconciled because of filled 1S, 1P, 1D, and 2S electronic shells within a simplified confined nearly free electron (NFE) gas. Here, we present first-principles studies on three isovalent clusters, i.e., ZnMg${}_{8}$, CuMg${}_{8}$${}^{\ensuremath{-}}$, and AuMg${}_{8}$${}^{\ensuremath{-}}$, each with 18 valence electrons. All the clusters exhibit local energetic stability but with differing origins. Although the stability of ZnMg${}_{8}$ can be reconciled within the conventional confined NFE picture with filled 1S${}^{2}$, 1P${}^{6}$, and 1D${}^{10}$ shells, CuMg${}_{8}$${}^{\ensuremath{-}}$ and AuMg${}_{8}$${}^{\ensuremath{-}}$ are shown to be stable despite the unfilled D-shell. Their stability can be understood as a crystal field--like splitting of the otherwise degenerate D-shell because of internal electric fields of the positive ion cores that lead to a filled 1S${}^{2}$, 1P${}^{6}$, 1D${}^{8}$, 2S${}^{2}$ sequence separated by unfilled D${}^{2}$ states that form a large gap. We also examine the progression toward the metallic character in ZnMg${}_{\mathrm{n}}$ clusters, because isolated Mg and Zn atoms have filled valence 4s${}^{2}$ and 3s${}^{2}$ atomic states. As Mg atoms are added to a Zn atom, the excited atomic p-states in the Mg atoms hybridize rapidly with Zn and Mg s-states to promote a metallic character that evolves more rapidly than in pure Mg${}_{\mathrm{n}}$ clusters.