Hückel's Rule of Aromaticity Categorizes Aromatic closo Boron Hydride Clusters

A direct connection is established between three-dimensional aromatic closo boron hydride clusters and planar aromatic [n]annulenes for medium and large boron clusters. In particular, the results prove the existence of a link between the two-dimensional Hückel rule, as followed by aromatic [n]annulenes, and Wade-Mingos' rule of three-dimensional aromaticity, as applied to the aromatic [Bn Hn ](2-) closo boron hydride clusters. The closo boron hydride clusters can be categorized into different series, according to the n value of the Hückel (4 n+2) π rule. The distinct categories studied in this work correspond to n=1, 2, and 3. Each category increases in geometrical difficulty but, more importantly, it is possible to associate each category with the number of pentagonal layers in the structure perpendicular to the main axis. Category 1 has one pentagonal layer, category 2 has two, and category 3 has three.