4n rules Polyhedral skeletal electron pair theory

pb2−

10

when counting electrons each cluster, number of valence electrons enumerated. each transition metal present, 10 electrons subtracted total electron count. example, in rh6(co)16 total number of electrons 6 × 9 + 16 × 2 − 6 × 10 = 86 – 6 × 10 = 26. therefore, cluster closo polyhedron because n = 6, 4n + 2 = 26.

s2+

4

other rules may considered when predicting structure of clusters:

in general, closo structures n vertices n-vertex polyhedra.

to predict structure of nido cluster, closo cluster n + 1 vertices used starting point; if cluster composed of small atoms high connectivity vertex removed, while if cluster composed of large atoms low connectivity vertex removed.

to predict structure of arachno cluster, closo polyhedron n + 2 vertices used starting point, , n + 1 vertex nido complex generated following rule above; second vertex adjacent first removed if cluster composed of small atoms, second vertex not adjacent first removed if cluster composed of large atoms.

os6(co)18, carbonyls omitted

example: pb2−

10

electron count: 10 × pb + 2 (for negative charge) = 10 × 4 + 2 = 42 electrons.
since n = 10, 4n + 2 = 42, cluster closo bicapped square antiprism.

example: s2+

4

electron count: 4 × s – 2 (for positive charge) = 4 × 6 – 2 = 22 electrons.
since n = 4, 4n + 6 = 22, cluster arachno.
starting octahedron, vertex of high connectivity removed, , non-adjacent vertex removed.

example: os6(co)18

electron count: 6 × os + 18 × co – 60 (for 6 osmium atoms) = 6 × 8 + 18 × 2 – 60 = 24
since n = 6, 4n = 24, cluster capped closo.
starting trigonal bipyramid, face capped. carbonyls have been omitted clarity.


b

5h4−

5, hydrogens omitted

example: b

5h4−

5

electron count: 5 × b + 5 × h + 4 (for negative charge) = 5 × 3 + 5 × 1 + 4 = 24
since n = 5, 4n + 4 = 24, cluster nido.
starting octahedron, 1 of vertices removed.

the rules useful in predicting structure of carboranes. example: c2b7h13

electron count = 2 × c + 7 × b + 13 × h = 2 × 4 + 3 × 7 + 13 × 1 = 42
since n in case 9, 4n + 6 = 42, cluster arachno.

the bookkeeping deltahedral clusters carried out counting skeletal electrons instead of total number of electrons. skeletal orbital (electron pair) , skeletal electron counts 4 types of deltahedral clusters are:

n-vertex closo: n + 1 skeletal orbitals, 2n + 2 skeletal electrons
n-vertex nido: n + 2 skeletal orbitals, 2n + 4 skeletal electrons
n-vertex arachno: n + 3 skeletal orbitals, 2n + 6 skeletal electrons
n-vertex hypho: n + 4 skeletal orbitals, 2n + 8 skeletal electrons

the skeletal electron counts determined summing total of following number of electrons:

2 each bh unit
3 each ch unit
1 each additional hydrogen atom (over , above ones on bh , ch units)
the anionic charge electrons




^ cotton, f. albert; wilkinson, geoffrey; murillo, carlos a.; bochmann, manfred (1999), advanced inorganic chemistry (6th ed.), new york: wiley-interscience, isbn 0-471-19957-5 
^ cotton, albert (1990). chemical applications of group theory. john wiley & sons. pp. 205–251. isbn 0-471-51094-7.