closohedral

Closohedral refers to a class of cluster compounds in inorganic chemistry whose skeletal framework forms a closed polyhedron. The term is used especially for boron hydride and carborane clusters, where the atoms at the vertices create a tight, fully connected cage. Closo denotes a closed, self-sustaining polyhedral framework in contrast to more open cage types.

In the language of Wade’s rules, closo borane and carborane clusters contain the maximum possible connectivity for a given number of vertices. Specifically, a cluster with n vertices (n atoms in the cage) requires n+1 skeletal electron pairs to stabilize the closed cage. This electron count drives the deltahedral geometries commonly observed, such as octahedral B6H6^2− (n = 6) and icosahedral B12H12^2− (n = 12). Carboranes such as closo-C2B10H12 also adopt highly symmetric icosahedral-like frameworks, with carbon atoms occupying vertex positions within the cage.

Closo clusters are contrasted with nido, arachno, and hypho classifications, which describe progressively more open cages with one, two, or more missing vertices, respectively. In these other classes, the skeletal electron requirement differs, leading to different shapes and reactivity.

These closo cages are notable for their chemical stability, diverse substituent patterns, and applications in materials science, catalysis, and medicine (including boron neutron capture therapy). Their rigid, well-defined architectures make them useful scaffolds for functionalization and as models for studying polyhedral chemistry.