Ab Initio Investigation of Strain in Group 14 polyhedrane clusters (MnHn: n = 4, 6, 8, 10, 12, 16, 20, 24)

The results of ab initio calculations on a series of [MH](n), polyhedral cages (M = C, Si, Ge, and Sn; n = 4, 6, 8, 10, 12, 16, 20, and 24) are presented. The energies are partitioned into contributions from each ring to obtain an estimate of how strain changes as a function of ring size for each of these elements. Results of these calculations indicate that three-membered rings are significantly strained for all of these elements, and five- and six-membered rings have similar stability. The relative strain in four-membered carbon rings appears to be significantly higher than the strain in four-membered rings of heavier Group 14 elements. These partitioned ring energies can be applied to predict the relative stability of other cages.