Trimetallic deltahedral Zintl ions [Sn(9-m-n)Ge(m)Bi(n)]((4-n)-) for n = 1-4 and m = 0-(9 - n): a theoretical survey with prediction and rationalization of the possible structures.

The recent discovery of trimetallic deltahedral Zintl ions based on Sn, Ge, and Bi revealed the possibility to obtain such clusters with a variety of different Sn/Ge/Bi ratios. Although only the dimer [(BiSn(6)Ge(2))-(Ge(2)Sn(6)Bi)](4-) was structurally characterized, a number of other nine-atom clusters with various stoichiometries were detected by electrospray mass spectrometry. The lack of structural data for the latter persuaded us to use relativistic density functional calculations in order to determine and rationalize theoretically the most stable structure conformation of each cluster and the positional preferences for the different atoms in the series [Sn(9-m-n)Ge(m)Bi(n)]((4-n)-) where n = 1-4 and m = 0-(9 - n). The analysis revealed strong dependence of the cluster geometry on the cluster stoichiometry and revealed sites with significantly different charge distribution. In addition, we introduce a parameter ϕ based on certain angles in order to rationalize the obtained structures as monocapped square antiprisms (C(4v)), tricapped trigonal prisms (D(3h)), or intermediates (C(2v)).