Jemmis mno rules

Wade's rules were formulated to explain the electronic requirement of monopolyhedral borane clusters.

To account for the existence of B20H16 as a neutral species, and to understand the electronic requirement of condensed polyhedral clusters, a new variable, m, was introduced and corresponds to the number of polyhedra (sub-clusters).

Thus the skeletal electron pair (SEP) requirement of closo-condensed polyhedral clusters is m + n. Single-vertex sharing is a special case where each subcluster needs to satisfy Wade's rule separately.

The rule can be modified to m + n + 1, or generally m + n + o, where o corresponds to the number of single-vertex sharing condensations.

As such, the generalized Jemmis rule can be stated as follows: m + n + o + p − q = 2 + 20 + 0 + 0 + 0 = 22 SEPs are required; 16 BH units provide 16 pairs; four shared boron atoms provide 6 pairs, which describes why B20H16 is stable as a neutral species.

Removing the electron corresponding to the positive charge of the complex leads to a total of 22+1⁄2 + 2 − 1⁄2 = 24 pairs.

The structure of β-rhombohedral boron is complicated by the presence of partial occupancies and vacancies.

[9][10][11] The idealized unit cell, B105 has been shown to be electron-deficient and hence metallic according to theoretical studies, but β-boron is a semiconductor.

[12] Application of the Jemmis rule shows that the partial occupancies and vacancies are necessary for electron sufficiency.

The requirement of 8 electrons by the B48 fragment can be satisfied by 2+2⁄3 boron atoms and the unit cell contains 48 + 56 + 2+2⁄3 = 106+2⁄3, which is very close to the experimental result.