Electron‐Counting Rules in Cluster Bonding – Polyhedral Boranes, Elemental Boron, and Boron‐Rich Solids

An Extended Rudolph Diagram: B3H5 and B3H6+ Relate 3D-, 2D-, 1D-, and 0D-Boron Allotropes

“…The β-rhombohedral boron is not amenable to similar easy approach. We had formulated the mno rule to explain SEP required for condensed polyhedral boranes and also to explain the vacancies and extra occupancies in the β-rhombohedral boron and other B 12 -based allotropes. − The mno rule extends the n + 1 skeletal electron pair rule of Wade for single polyhedron to condensed polyhedral boranes. According to the mno rule , the number of skeletal electron pairs required for stability is m + n + o , where m = number of polyhedra, n = number of vertices, and o = number of single-atom bridge between polyhedra.…”

“…Wade’s n + 1 skeletal electron pair rules for polyhedral boranes (B n H n 2– ) and the Rudolph diagram, featuring closo-, nido-, and arachno- descriptions serve as the guiding factors here. − A well-developed chemistry of the polyhedral carboranes and other heteroboranes where some boron atoms are replaced by carbon and other fragments follows these developments. − The extra stability and 3D aromaticity of icosahedral B 12 H 12 2– invariably brought in comparisons with benzene, the planar aromatic prototype. − The structural relationship between benzenoid aromatics to graphene and graphite prompted similar strategies in understanding the 3D-allotropes of boron starting from icosahedral B 12 H 12 2– . These attempts led to the mno rule to explain the electron requirements of condensed polyhedral boranes such as B 20 H 16 and B 21 H 18 1– and relate these to β-rhombohedral boron, the most stable allotrope of elemental boron. − …”

Electron Counting and High-Pressure Phase Transformations in Metal Hexaborides

“…This diversity is unified and rationalized by polyhedral skeletal electron pair theory or the Wade–Mingos rules, , which predict the structures of boranes from their electron count using a molecular orbital theory description of π bonding in the cluster skeleton. The similarities between clusters in gas-phase boranes and solid-state borides suggest the potential for electron counting methods to predict crystal structures, which has been done for allotropes of elemental boron, boron-rich materials, and some intermetallics. − We will test the applicability of the rules to the MB 6 hexaborides (M = Ca, Sr, Ba) as they have been shown to undergo structural phase transitions under pressure. − …”