On the electronic structure and stability of icosahedral r-X2Z10H12 and Z12H(12)(2-) clusters; r = {ortho, meta, para}, X = {C, Si}, Z = {B, Al}.

We report on the electronic structure of the 12-vertex icosahedral clusters r-X(2)Z(10)H(12) and Z(12)H(12)(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-X(2)Z(10)H(12) 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-C(2)Al(10)H(12). Substitution of two atoms of carbon or silicon into the icosahedral cage B(12)H(12)(2-) enhances considerably the stability of the system as analyzed from E(g) gaps, as opposite to Al(12)H(12)(2-), 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.