Wade's rules

The actually bewildering variety of structures adopted by boron-hydrogen compounds (boranes) can be rationalized by recognizing some main families, demonstrated by the series in Figure. 2.

1. Closo boranes with n boron atoms adopt closed polyhedral structures based on triangular faces like the trigonal bipyramid (five vertices), octahedron (six) and icosahedron (12); such type of polyhedra are called deltahedra. The simple most instances are the ions [B_nH_n]^2- like [B₆H₆]^2- illustrated.
2. In nido ('nest-like') boranes n boron atoms are found approximately at the positions of the vertices of an n+1-vertex deltahedron, with one vertex missing. The simple most general formula type is B_nH_n+4; for instance, B₅H₉, in which the boron atoms are placed at five of the corners of an octahedron.
3. Arachno ('web-like') boranes are still more open and can be imagined like deltahedra with two vertices missing. They create a general series of formula B_nH_n+6 (e.g. B₄H₁₀).

Wade's rules give an electronic rationalization of the regularities that is based on the MO prediction that an n atom deltahedron by s and p valence orbitals, should have n+1 skeletal bonding MOs. For instance, in [B₆H₆]^2- there are seven such type of MOs,  and electrons might be counted  as follows:  there are the 26 valence electrons; 12 are assigned to 'normal' two-center B-H bonds, leaving 14 for skeletal bonding.  There is no easy way of assigning these 14 electrons to localized two-center or even three-center bonds. Generally, we see that closo boranes with n atoms should  have  2n+2  skeletal  bonding  electrons. Isoelectronic substitutions of  atoms  should  maintain the structure; for instance, B₁₀C₂H₁₂ is based on similar icosahedron  as [B₁₂H₁₂]^2-.

As Starting by the closo ion [B_nH_n]^2-  we can imagine removing one [BH]²⁺ unit and adding 4 H⁺  to give the n-1 nido borane B_n-1H_n+3  (example [B₆H₆]^2-  gives B₅H₉).  Neither of these operations should change the number of skeletal bonding electrons, so B₅H₉  has 14, similar number  like [B₆H₆]^2-, and generally nido boranes with n atoms should have 2n +4 skeletal bonding electrons. The argument might be repeated, starting from nido B_nH_n+4, removing BH²⁺  and adding 2 H⁺, leading to the additional conclusion that arachno boranes with n atoms should have 2n+6 skeletal bonding electrons.

Wade's rules might be applied to 'naked' clusters created by p-block elements if it is assumed that each atom has one localized nonbonding electron pair. Thus in [Pb₅]^2-  there are 22 valence electrons, 10 employed in lone-pairs, hence 12 for skeletal bonding:  a closo structure  is supposed,  as found  (4). In [Sn₉]^4-  an identical count  gives 22 skeletal bonding electrons, subsequent to 2n+4 and therefore the nido structure observed (7). It should be noticed that there are exceptions. The Extension to transition metal clusters requires accommodating the d bonding electrons and leads to the Wade-Mingos rules.