Jemmis-Schleyer interstitial electron rule

The graph-theoretical 4N + 2 Hiickel rule analogy with the aromaticity of two-dimensional polygons requires that N = 0 in all the three-dimensional deltahedra. The Jemmis-Schleyer interstitial electron rule [55], originally introduced for nido half-sandwich species, also relates the 4N + 2 Hiickel rule to the delocalized deltahedra directly In this treatment, N is typically 1. 

In order to apply the Jemmis-Schleyer interstitial electron rule, the closo B H 2 dianions (their isoelectronic analogues are treated similarly) are dissected conceptually into two BH caps and one or two constituent (BH) rings. The BH- caps contribute three interstitial electrons each but the rings (which, formally, have zero electrons in the n MOs), contribute none. Hence, six electrons, described as interstitial, link the bonding symmetry-adapted cap and ring orbitals together perfectly. 

The Jemmis-Schleyer interstitial electron rules [41] are directly applicable to 5-, 6-, and 7-vertex deltahedra (which have one ring), and to 10-, 11-, and 12-vertex deltahedra (which have two rings) but are less obvious for 8- and 9-vertex... 

The interstitial electron rule can be applied more directly to pyramidal clusters than the graph-theoretical approximation since the latter breaks down by giving zero eigenvalues in Eq. (3) when applied to pyramids. The same ideas as those in the Jemmis-Schleyer method are needed to treat nido pyramids graph-theoretically. 

An alternative approach to aromaticity in some deltahedral boranes is based on the Jemmis and Schleyer [41] interstitial electron rule, originally introduced for nido half-sandwich species. This also relates aromaticity in deltahedral boranes to the 4A + 2 Hiickel mle, but for deltahedral boranes k is typically 0. 

---