Wade's rule

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The Wade rule [ ˈweɪd- ] is an electron counting rule that provides information on the spatial structure, in particular the polyhedron structure of clusters such as boranes . It was set up in 1971 by Kenneth Wade . This rule was extended by Robert E. Williams and Ralph W. Rudolph . The rules were taken up by David Michael Patrick Mingos and significantly expanded, which is why they are also called Wade Mingos rules .

They are also summarized in English as Polyhedral Skeletal Electron Pair Theory (PSEPT).

Use with boranes

With it, the structure of a borane compound can easily be recognized from its molecular formula. The geometry of the framework of boranes, borane anions and carboranes is determined by the ratio of the number of framework electrons to the number of framework atoms (or framework electron pairs) n .

Framework electrons Framework electron pairs structure
2 n n hypercloso / precloso
2 n + 2 n + 1 closo
2 n + 4 n + 2 nido
2 n + 6 n + 3 arachno
2 n + 8 n + 4 hypho
2 n + 10 n + 5 clado
  • closo Latin clausus , closed
  • nido Latin nidus , nest
  • arachno Greek arachnion , spider web

The boron atoms of a closo-borane sit on the corners of a polyhedron that is only bounded by triangular surfaces ( deltahedron ). Typical known deltahedra are, for example, the trigonal bipyramid (5 corners), the octahedron (6 corners) and the icosahedron (12 corners). The borane hydrogen atoms are covalently bonded to the respective boron atom and point radially outwards. Up to now, however, closo- boranes are only known in the form of dianions (molecules with a double negative charge). One example is the most stable representative, closo-dodecaboranate B 12 H 12 2− . The structures of nido -, arachno- and hypho -Boranen result from the structures of the closo-boranes in which one, two or three adjacent corners of the closo polyhedron not with boron atoms are occupied. The resulting bodies therefore have increasingly open structures. The hydrogen atoms of these boranes again occupy all radially outer positions on the boron atoms and additional places on the open parts of the polyhedra.


The pentaborane B 5 H 9 is a nido- borane according to the Wade rules . Compared to the closed closo body, it lacks a corner. Its structure is derived from a closo -body that is one corner richer, that is, from an octahedron. One corner of the octahedron is lost - you get a tetragonal (four-sided) pyramid. 5 H atoms are located at the corners of this pyramid and point radially outward, while the remaining 4 H atoms point into the open side of the square.

hypercloso compounds are not found in the simple hydrido-boranes. They are expected to have a structure similar to that for closo compounds. However, the theoretical work on this is not finished. Examples of this are halogen-substituted boranes such as B 6 Cl 6 .

Determination of the number of framework electrons

Number of framework electrons = Sum of the valence electrons of the (boron) framework atoms
+ Valence electrons of the H atoms
+ Number of electron charges
- two electrons per main group skeleton atom or twelve per subgroup skeleton atom.

Simplified variant for calculating the framework electrons in boron clusters:

Number of framework electrons = Number of bra ties × 2
+ (Number of H atoms - number of BH bonds)
+ Number of electron charges × (−1)


W 5 H 11

n = 5 (skeleton atoms)

Framework electrons = 5 × 3 Electrons of the 5 boron atoms
+ 11 one electron each of the H-bond
+ 0
- 2 × 5 Electrons of the exo-H bond
= 16

With 16 skeletal electrons, 5 boron atoms result in 2 n + 6 = 16. This results in the arachno structure.

Alternative (for uncharged boranes)

Molecular formula structure
B n H n hypercloso
B n H n +2 closo
B n H n +4 nido
B n H n +6 arachno
B n H n +8 hypho

Individual evidence

  1. ^ K. Wade: The structural significance of the number of skeletal bonding electron pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds. In: J. Chem. Soc. D. 1971, pp. 792-793, doi : 10.1039 / C29710000792 .
  2. ^ K. Wade: Structural and bonding patterns in cluster chemistry. In: Adv Inorg Chem Radiochem . 1976, 18, pp. 1-66, doi : 10.1016 / S0065-2792 (08) 60027-8 .
  3. ^ RE Williams: Coordination Number Pattern Recognition Theory of Carborane Structures. In: Adv. Inorg. Chem. Radiochem. 1976, 18, pp. 67-142, doi : 10.1016 / S0065-2792 (08) 60028-X .
  4. RW Rudolph: Boranes and heteroboranes: a paradigm for the electron requirements of clusters ?. In: Acc. Chem. Res. 1976, 9, pp. 446-452, doi : 10.1021 / ar50108a004 .
  5. ^ DMP Mingos: A General Theory for Cluster and Ring Compounds of the Main Group and Transition Elements. In: Nature Phys. Sci. 1972, 236, pp. 99-102, doi : 10.1038 / physci236099a0 .
  6. DMP Mingos: Polyhedral Skeletal Electron Pair Approach. In: Acc. Chem. Res. 1984, 17, pp. 311-319, doi : 10.1021 / ar00105a003 .