Isolobal Analogy
Isolobal Analogy
Isolobal Analogy
6.1 Introduction
The outline of Wade's rule given above showed how quite different groups of atoms can give rise to similar
shaped clusters. For example, the C-H group and the P atom have 5 electrons and can contribute 3 electrons
to a cluster,
C-H has 4+1 electrons and uses 2 electrons for the C-H bond
N
T
Both fragments are 3 electrons short of making maximum use of their 4 valence orbitals (s and 3 p) by
achieving an octet. The clusters C4H 4 or (CH)4 (tetrahedrane) and P 4 have the same number of cluster
electrons and therefore adopt the same shape:
B and C are more conventionally thought of as (m 3-P)[CoCO) 3]3 and (h 3-C3H 3)Co(CO)3 respectively but this
hides the structural and electronic links between all these clusters.
The similarity between these fragments and between other groups of fragments has been investigated in
detail by Roald Hoffmann. Fragments are deemed to be isolobal if
"the number, symmetry properties, approximate energy and shape of the frontier
orbitals and the number of electrons in them are similar"
The isolobal relationship is symbolized by a double-headed arrow with a tear-drop,
The isolobal analogy relates the orbitals and bonding in inorganic, organometallic and cluster chemistry to that
in organic and main group chemistry. The utility of the isolobal analogy is that one should be able to replace
a (transition metal) MLn fragment in a molecule with the isolobal (main group) AHn fragment, and vice versa,
The transition metal fragments are generated in an analogous way. For example, from the starting point of
CrL 6, 2, where L is a two electron donor such as CO, (or any molecule obeying the eighteen electron rule
such as 3), the fragments 2a, 2b and 2c are generated by successive homolytic cleavage of ML bonds on one
octahedral face. As L is a two-electron donor, homolytic cleavage of CrL 6 gives CrL 5- and L + . To remove the
charge, the metal is then replaced by Mn (the element one to the right in the 3d series):
8electron
18-electron
16electron
1a
2a
3a
4a
1b
2b
3b
4b
1c
2c
3c
4c
As long as the electron count is maintained or consistent changes are made, the metal or main group element
can be substituted. Thus,
CH3
Me3Sn
Mn(CO) 5
Fe(PPh3) 5+
Mo(CO) 5
CH3+
BH3
Mn(CO) 5+
Cr(CO)5
Rh(PPh3)3+
CH3
NH 3
Mn(CO) 5
Fe(CO) 5
Rh(CO)5+
It should be noted that the main use of the isolobal analogy is in generating alternative fragments in
molecules. The geometry of the fragment in a molecule not as an isolated species is important. Thus, CH3 and
BH3 are considered as pyramidal (not planar) species and Cr(CO)5 is considered as a square-based pyramid
(not trigonal bipyramid).
6.4 Applications
The isolobal analogy between CH3 and d7 MnL 5 implies similar bonding in the following compounds:
The isolobal relationship of CH2, with Fe(CO) 4 generates the compounds illustrated below. The transition
metal molecule has been drawn as a metallocyclopropane. A more common description is to consider it as an
ethene complexes, (h2C2H 4)Fe(CO) 4. The isolobal relationship shows that cyclopropane itself can be consider
as (h2C 2H 4)CH2.