Wade's rules

Boranes and carboranes come in dozens of cage shapes, and for a long time chemists simply memorized them. Then Kenneth Wade noticed something wonderful: you do not have to know the structure to predict the shape. If you just count the electrons that go into building the cage skeleton, the count itself tells you whether the cage will be closed, have one corner missing, or two. Wade's rules are the recipe for that count.

Wade's rules (polyhedral skeletal electron pair theory, PSEPT) say that the shape of a cluster is governed by the number of skeletal electron pairs that bind its framework, not by the number of atoms alone. Count the skeletal pairs, call it the number that fits a parent polyhedron with n vertices. A cluster with (n+1) skeletal pairs is closo (a closed n-vertex polyhedron, like the octahedron of B6H6^2-); with (n+2) pairs it is nido (the same polyhedron with one vertex removed); with (n+3) pairs it is arachno (two vertices removed); and (n+4) gives hypho (three removed). To get the skeletal count for a borane, a handy version is: each B-H unit gives 2 skeletal electrons, each extra hydrogen gives 1, and you add any overall charge, then divide by 2 for pairs. For carboranes a C-H unit gives 3 skeletal electrons (carbon has one more than boron).

Wade's rules matter because they turn a zoo of cage compounds into one predictable family, and the same electron-counting idea, extended by Mingos, reaches into transition-metal clusters and even gold and bare-metal Zintl clusters. They embody a deep lesson of cluster chemistry: structure follows from total delocalized electron count, the same spirit as molecular-orbital thinking, rather than from drawing localized two-atom bonds. They are guidelines with exceptions, but astonishingly good ones.