BIOINORGANIC CHEMISTRY A Short Course Second Edition

Many organometallic complexes are clusters involving multiple metals that
feature metal – metal bonds. The electrons in Me – Me bonds are counted by
contributing one electron to each metal connected. Bridging ligands contrib-
ute one - half of their electrons to each metal center. Some simple examples in
Figure 1.9 illustrate application of the rules.
Iron – sulfur clusters, such as those found in the enzyme aconitase discussed
in Section 7.9.2.1 , cannot be treated using the 16 - e or 18 - e rules. Other frame-
works exist to treat large metal clusters, and these have some utility in treating
[Fe x S y ] n + clusters. One method treats the number of metal atoms and the metal -
metal bonds in a cluster according to the following formula^13 :

Valence electrons of cluster Me atoms

no of metal metal bo

=×

−−

∑ #

(.

18

nnds)× 2

Applying this formula to the cubane [Fe(II) 4 ( η^5 - C 5 H 5 )(( μ 3 - S) 4 ] shown in Figure
1.10A results in the following electron count:

(^) ∑Valence electrons=× − × =418 62 60()electrons
the so - called “ magic number ” for four metal atoms in a cluster.
If one applies the same procedure to Figure 1.10B , an iron – sulfur cluster
often used as a model for those in biological systems, the same magic number
of 60 would be obtained. Cluster magic numbers would occur as: 48 e for a
triangular clusters, 60 e for tetrahedral, 72 e for trigonal bipyramidal, 74 e for
square pyramidal, 84 e for octahedral complexes like Zr 6 I 14 C or [Mo 6 Cl 14 ] 2 − or
86 e for octahedral complexes such as Rh 6 (CO) 16 and [Os 6 (CO) 18 ] 2 − , 90 e for
trigonal prisms, and 120 e for cubic structures. Reference 13a contains a more
complete discussion of cluster valence electron counting.
For biological systems such as ferredoxins, problems arise when counting
electrons by the valence electron method. This system assumes six Fe – Fe
bonds within the tetrahedral iron – sulfur clusters, but Fe – Fe bond distances
within biological iron – sulfur clusters, as found by X - ray crystallography, often
Figure 1.10 Cubanes (A) [Fe(II) 4 ( η^5 - C 5 H 5 ) 4 ( μ 3 - S) 4 ] and (B) [Fe(II) 4 (SR) 4 ( μ 3 - S) 4 ] 4 −.
S
S
S
Fe
Fe
S
Fe
S
S
S
Fe
Fe
Fe
S
SR
RS
RS
SR
[(Fe(II)) 4 (η^5 -C 5 H 5 ) 4 (μ 3 -S) 4 ] [(Fe(II)) 4 (SR) 4 (μ 3 -S) 4 ]4-
Fe Fe
A B
BIOORGANOMETALLIC CHEMISTRY 21