The structure of ferrocene was famously analysed by Woodward and Wilkinson in 1952 (DOI: 10.1021/ja01128a527), symmetrically straddled in history by Pauling (1951) and Watson and Crick (1953). Quite a trio of Nobel-prize winning molecular structural analyses, all based on a large dose of intuition. The structures of both proteins and DNA succumbed to models built from simple Lewis-type molecules with covalent (and hydrogen) bonds; ferrocene is intriguingly similar and yet different. Similar because Lewis postulated an octet of electrons as being key to the (quadri)valencies of e.g. carbon via four electron pair bonds. He did not (in 1916) realise that 8 = 2(1 + 3), and that the next in sequence would be 18 = 2(1 + 3 + 5). That would have to wait for quantum mechanics, and of course inorganic chemists now call it the 18-electron rule (for an example of the 32-electron rule, or 2+6+10+14, as first suggested by Langmuir in 1921[1] (see also here).
Iron has an argon core, and 6 (of a maximum of 10) 3d electrons, 2 (of a maximum of 2) 4s, and 0 (of a maximum of 6) 4p electrons. Or, 8 = 2 + 0 + 6 rather than 18 = 2 + 6 + 10. So Woodward and Wilkinson argued that sharing a further 10 electrons would bring iron up to, in effect, a Lewis shell (albeit one using not just s and p shells, but d shells too). These 10 electrons would be provided by two cyclopentadienyl radicals. Thence a Nobel prize (for Wilkinson)! But wait!
QTAIM analysis for Ferrocene. Green=bcp, red=rrp, blue=ccp.
Firstly, let me adjust slightly the counting above. Rather than starting with neutral Fe, we ionise it to Fe2+. Rather than starting with two cyclopentadienyl radicals, let us use two aromatic cyclopentadienyl anions. But now, Lewis’ idea of covalency via shared electron pair bonds struggles. If 18 electrons really are being deployed (12 from the cyclopentadienyl anions, 6 from the Fe2+), does that imply 9 shared electron-pair bonds? How might the bonds in ferrocene be represented? This matters. Since the 1970s, the idea of searching for molecules via what is called its connectivity (a simple index which ignores bond order, and simply specifies whether two atoms are connected by a bond, any kind of bond, or not) has revolutionised searching for molecules. Think of CAS, Pubchem, REAXYS, CCDC, and SMILES and InChI. So is it useful to try to partition 9 bonds into ferrocene (it kind of difficult, since it has five-fold symmetry)? Indeed, most students trying to search for a ferrocene in any of the aforementioned databases will scratch their head over this one. The normal solution is to draw 10 bonds from the iron, one to each of the ten carbon atoms (and the databases accept this as a valid search query). But what can that mean?
To find out, I show here a QTAIM and an ELF analysis of the bonds (in italics, since we do not know if these conform to Lewis covalent bonds or not). The QTAIM is shown above, and it shows a bond-critical point along all ten of the Fe…C regions. The electron density, ρ(r) at each of these is 0.083 au. In truth, this is rather low, even for a single bond. The Laplacian ∇2ρ(r) at each of these points is +0.29, which is in what Hiberty and Shaik have called the charge-shift category (i.e. NOT a covalent bond). The Laplacian isosurface is shown below, contoured at 0.25, and you can see each of the bond-critical points for the ten Fe-C regions is shrouded in blue (a positive Laplacian). So, NOT a pure covalent two-electron bond of the Lewis variety then(?).
Electronic Laplacian for ferrocene. Click for 3D
Centroids of ELF basins for ferrocene. Click for 3D.
ELF isosurface for ferrocene. Click for 3D
References
- I. Langmuir, "Types of Valence", Science, vol. 54, pp. 59-67, 1921. https://doi.org/10.1126/science.54.1386.59