A Simple Molecular Orbital Description of the Bonding in Ferrocene

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 the symmetrical molecular orbital is M.O. 9

and that M.O. 12 and 13 are the other two filled p-bonding orbitals. Notice their vertical nodes are orthognal (i.e. at 90º to each other)

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. 17, 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. The outline option was deselected for this plot.


M.O. 17 the most symmetrical A₁ combination.

The less symmetrical A₁' combination has A₂' symmetry.


An E₁' combination

Another E₁' combination.

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 4p_z with less symmetrical A₂' 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 4pz A2' interaction also has poor overlap for the same reason.

Plot M.O. 23 (de-select outline) and you should see.



This is d_xz - A₁' overlap and in combination with its orthogonal d_xz - A₁' interaction 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.

The analysis of Fe - Cp bonding is similar in both the eclipsed (D_5h) and staggered (D_5d) structures and there is not much energy difference between them.

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