A ternary rhodium-centered bipyramidal dibismuth complex is an example of subhalide complexes with interesting geometry and unusual electronic properties, particularly what has been reported as an example of Möbius aromaticity. The complex exhibits a 4-electron-5-centered bond in the central plane occupied by a Bi equatorial pentagon with the rhodium center in the middle. Based on the electronic analysis carried out by Ruck (2003), the bismuth bonding consists of 2-centered-2-electron bonds, namely, Bi-Rh and Bi-Br one (see structure on the right).
The electronic analysis was carried out starting with counting the available skeletal electrons. Each of the 7 bismuth atoms contribute a total of 3x7=21 electrons (3 per each atom), while Rh gives all of its 9 electrons and the 8 bridging bromide atoms yield 3 electrons each. The total skeletal electron count is thus 54. The total skeletal electron count gets distributed as follows: 2 electrons per each of the 16 2c-2e Bi-Br bond, 2 electrons per each of the 7 2c-2e Rh-Bi metallic bond, 2 rhodium lone pairs remaining on the Rh centre (total of 4e), and 4 electrons for 5c-4e bond pertaining to the central pentagon. The sum of electrons used in bonding is therefore 54. Hence, the subhalide complex is electron-precise, i.e., with all of its skeletal electrons involved in chemical bonding.
The bonding in such a system was compared to the aromatic cyclopentadienyl aromatic anion. Contrary to the π-type all in-phase orbital overlap exhibited by the organic cyclopentadienyl anion, σ-type bonding of the RhBi unit yields a phase change for an orbital pair (see figure).
The relative orbital energy diagram is rationalized for each of the systems relying on the Frost-Musulin mnemonic. The two lone pairs stemming from the rhodium metallic center are localized on the lowest-lying twicely degenerate set of molecular orbitals, consistent with the Möbius-type aromaticity. For reference, the electronics of the aromatic organice cyclopentadienyl unit is shown to the right of the rhodium-centered pentagonal Bi unit. As can be seen, Hückel rules dictate the molecular orbital splitting is inverted compared to its metallic counterpart, the highest-occupied molecular orbitals this time being twicely degenerate.