Interstitial Polygonal Aromatic-Deltahedral Borane Relationships

2 Interstitial Polygonal Aromatic-Deltahedral Borane Relationships 

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 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. 

3 Aromaticity Evaluations of Three-dimensional Structures Nucleus-Independent Chemical Shift (NICS) 

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