A Simple Molecular Orbital Description of the Bonding in Ferrocene

The structure of ferrocene in the gas phase was established by A. Haaland (Acc. Chem. Res.1979, 12, 415-422) to be eclipsed point group D5h. The original staggered D5d structure from X-ray diffraction was actually disordered with respect to ring rotation. There no seems little doubt that the ground state is D5h but that the rotation barrier is low and is estimated to be 2 kJ/mol (N. Mohammadi et al.,J. Organometal. Chem. 2012, 713, 51-59). Thus it does not matter which structure is used to analyse the bonding and both structures yield closely related bonding patterns. Ring rotation is symmetry allowed.

It is possible to derive a reasonable bonding model by considering the interaction of the molecular orbitals fromed by the p-p orbitals of two cyclopentadienyl (Cp) anions and an Fe²⁺ cation. The strategy is to consider the orbital interactions in three steps:
1    the orbitals of one ring,
2    the orbitals of two rings combined
3    the orbitals of two rings interacting with Fe²⁺.

The Orbitals of One Ring

The ring and the hydrogens are bonded by an sp² framework. This leaves one p_z orbital on each carbon unused. There are five ways to combine the five p_z orbitals. The most symmetrical combination has the lowest energy and one node (A₁' symmetry, D_5h point group). Higher in energy lie a degenerate pair which have two nodal planes (E₁' symmetry). At the highest energy are a pair of orbitals with three nodes. There are 6 p-electrons in Cp^- and thus the three lowest energy orbitals are filled. Build Cp^- using Moilin with the ptest jobname and run Mopac to obtain orbital plots you will see that M.O. 9 is the symmetrical lowest energy M.O. MCE was used to obtain the plots. It is necessary to adjust the iso-levels using View/Level Control for Primary and Secondary Maps.

and that M.O. 12 and 13 are the other two filled p-bonding orbitals. Notice that this pair have their nodal planes orthognal to each other(i.e. at 90º to each other when viewed from above)

 



 

The Orbitals of Two Rings

To examine the orbitals of two rings combined. Purge the display and load ferrocene_d5h from the Moilin library into the ptest job. Delete the Fe atom and use Iconc to calculate the energy of the system. Do not forget to set the charge to -2. Look at the orbitals shown here: M.O. nos. 15, 18, 25 and 26. Molecular orbital 26 is the HOMO and it has the same energy as (is degenerate with) 25. You can see this degeneracy if you examine the energies in the LST file. These four orbitals are clearly combinations of the orbitals of one ring. Orbital 17 is the most symmetrical way to combine two A₁' orbitals and 17 has A₁' symmetry. Notice the hole in the centre of the blue density.


M.O. 15 the most symmetrical A₁ combination.




M.O.s 24 and 25 (both e1) have nodal planes which are orthogonal with respect to rotation about the 5 fold axis..


 

Iron Orbital Interactions with the Two Ring Orbitals

The valence orbitals of Iron are the 4s, 4p and 3d orbitals. The 4s and the 3d_z2 have the same symmetry type as the most symmetrical A₁' combination. The 3d_xz and 3d_yz have the same symmetry type as the E₁' combinations. Thus some of the possible interactions are
4s or 3d_z2 with the most symmetrical A₁' combination.
The 3d_xz and 3d_yz with the E₁' combinations.
Purge the display and load ferrocene_d5h from the Moilin library and use Iconc to calculate the energy of the system. Plot the molecular orbitals and look at the HOMO.



The ferrocene HOMO looks like the 3d_z2 and there is not much overlap with the ring orbitals. The hole in the centre of the blue density above is the reason for this poor overlap. The HOMO plot for the ferrocene_d5d structure is exactly the same.
The plots for MO 24 of ferrocene_d5d and ferrocene_d5h are shown here.

 

They show the d_xz - E₁' overlap and they are both essentially the same and this is the principal bond holding the rings and the iron together.


There is general agreement that the E₁ - E₁ interaction is the most important one and that the other interactions are non-bonding or anti-bonding. Thus 18 valence electrons are in bonding or non-bonding levels.

N.B. Ring rotation is symmetry allowed -This bond between dxz/ dyz and the the degenerate E1 pair has degenerate orthogonal pairs overlapping. If you rotate the ring you will break one E1 metal d overlap and make another this is equivalent to saying that there is in this approximation no barrier to rotation of the rings about five fold axis. See Inorganic Chemistry, Holleman and Wiberg page 1620.

The analysis of Fe - Cp bonding is similar in both the eclipsed (D_5h) and staggered (D_5d) structures.

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