Electron-deficient bonding in ◊ rhomboid rings

The bonding environment of boron is usually thought about in terms of localized 2c-2e/3c-2e bonding (as in diborane) or completely delocalized polyhedral bonding (as in B12H122-). Recently, a number of boron compounds having a rhomboidal B-4 framework have been synthesized; these show an amazing variation in their skeletal electron count, one that cannot be interpreted in familiar ways. In this report, we systematically explore the origin of the range of electron counts in these compounds. We find that four skeletal MOs are primarily responsible for keeping the B-4 skeleton together. As a subunit in a macropolyhedral environment, termed rhombo-B-4, such an arrangement of B atoms deviates from Wade's rule by three electron pairs (if treated as a distorted arachno system derived from B6H62-). Aided by this analysis, we examine the nature of bonding in Na3B20, where the rhombo-B-4 unit forms linear chains fusing closo-B-7 units. Theory suggests that this structure requires one more electron per formula unit for optimal bonding. Finally, we study the nature of bonding in beta-SiB3, where silicon atoms also adopt the rhomboid framework.