4d and 5d bimetal doped tubular silicon clusters Si12M2 with M = Nb, Ta, Mo and W: a bimetallic configuration model

Abstract

Geometries and electronic properties related to the ground state stabilities of several Si₁₂M₂ clusters (M: second-row (Nb and Mo) and third-row (Ta and W) transition metals, and their mixed bimetallic clusters M₂: NbMo and TaW) were explored using density functional theory (DFT) computations. The computed results show that two different structural motifs emerge as the global energy minima of such clusters. They are basically singlet tubular structures in either a C_2v prism (¹A₁) or a C_6v antiprism (¹A₁) form. Other structural shapes are also possible for higher-energy isomers and in higher spin states. 58-valence electron systems including Nb₂Si₁₂, Ta₂Si₁₂, Mo₂Si₁₂²⁺, W₂Si₁₂²⁺, NbMoSi₁₂⁺ and TaWSi₁₂⁺ are thermodynamically stable as C_2v prism global minima on the corresponding potential energy surfaces. Clusters containing 60 valence electrons include Mo₂Si₁₂, W₂Si₁₂, Nb₂Si₁₂²⁻, Ta₂Si₁₂²⁻, NbMoSi₁₂⁻ and TaWSi₁₂⁻ and they prefer a C_6v anti-prism form. In the mixed MoNbSi₁₂ and TaWSi₁₂ open-shell systems, both resulting C₂ (²A) and C_2v (²A₁) forms are nearly degenerate. The formation of Si₁₂M₂ clusters in such specific ground state symmetry is explained using the Jellium model and orbital interaction analyses. The investigations lead further to a proposal for a simple model of a bimetallic configuration using the nature of interactions of the transition metal d–d dimeric bond with the Si₁₂ host, to interpret the formation of such M₂Si₁₂ clusters.