On the electronic structure and stability of icosahedralr-X2Z10H12 and Z12H122−clusters; r = {ortho, meta, para}, X = {C, Si}, Z = {B, Al}

Abstract

We report on the electronic structure of the 12-vertex icosahedral clusters r-X₂Z₁₀H₁₂ and Z₁₂H₁₂^2–, where X = {C, Si} and Z = {B, Al}. The least stable cluster—with the lowest HOMO–LUMO gap (E_g)—corresponds to the ortho-X₂Z₁₀H₁₂ isomers for all values of X = {C, Si} and Z = {B, Al}. The well-known energetic order E(para) < E(meta) < E(ortho) for r-carboranes is also valid for all compounds except r-C₂Al₁₀H₁₂. Substitution of two atoms of carbon or silicon into the icosahedral cage B₁₂H₁₂²⁻ enhances considerably the stability of the system as analyzed from E_g gaps, as opposite to Al₁₂H₁₂²⁻, where similar gaps are found upon double carbon or silicon substitution regardless of the positions in the cage. In order to highlight similarities and differences in the title clusters, topological analysis of the electron density was performed, together with analysis of the deviation from polyhedron icosahedral form with (i) volumes, skewness and kurtosis calculations; and (ii) continuous shape measures.