Why are there two infrared vibrational frequencies for the terminal CO ligands of Fe2(CO)9?

Question

I am struggling to rationalise why there are two infrared vibrational frequencies ($\pu{2082 cm^-1}$ and $\pu{2019 cm^-1}$) for the stretching of the terminal $\ce{CO}$ ligands of $\ce{Fe2(CO)9}$. From my understanding of the structure, all six terminal $\ce{CO}$ ligands are equivalent and thus I would expect only one vibrational frequency. Why there are two?

The structure is as follows:

The bridging ligands are accounted for by a vibrational frequency at $\pu{1829 cm^-1}$.

Answer 1

Despite the title of the publication, Fletcher et al. both present an IR spectrum of diiron nonacarbonyl in a matrix of ($\ce{Ar}$ + 10% $\ce{CO}$, recorded at $\pu{15 K}$) in the $\nu(\ce{C-O})$ region of about $2080 \dots \pu{1820 cm^-1}$ (left to right hand side) as below:

(composite of two illustrations by Fletcher et al.)

Given the data recorded, the authors' assignment is (emphasis in the original publication):

«The spectrum of $\ce{Fe2(CO)9}$ shows two striong bands in the terminal $\ce{C-O}$ stretching region, ~$\pu{2000 cm^-1}$, as expected ($a''_2$ + $e'$) for a $D_{3h}$ structure, 1. In the bridging $\ce{C-O}$ stretching region, ~$\pu{1840 cm^-1}$, there is a single band, again as predicted, $e'$.»

Reference:

Fletcher, S. C.; Poliakoff, M.; Turner, J. J. Structure and reactions of octacarbonyldiiron: An IR spectroscopic study using carbon-13 monoxide, photolysis with plane-polarized light, and matrix isolation. Inorg. Chem. 1986, 25, 3597–3604; doi 10.1021/ic00240a014.

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Since there is an entry about this compound in Wikipedia, you have access to the/a CAS registry number (here, 15321-51-4). If your school has the corresponding subscriptions, you may use this as a search criterion e.g., in Reaxys (by Elsevier) or SciFinder (by ACS) to identify more recent publications with an assigned IR spectrum of said compound. You may complement the search with checking the publications citing the work by Fletcher et al. (landing page of the publication already lists 63 works known to the journal).

There is a good chance Martyn Poliakoff, co-author of the paper, and Sir Martyn Poliakoff, a chemist at University of Nottingham and still engaged in popularization of chemistry on youtube/The periodic videos, are the very same person.

Answer 2

It basically comes down to molecular symmetry and since Buttonwood provided an answer just seconds ago, I'll leave the following as visualisations for it.

An optimisation of $\ce{Fe2(CO)9}$ at the DF-B97D3/def2-SVP level of theory results in a D_3h symmetric molecule.

This in term results in degenerate vibrations (E') for the bridging $\ce{CO}$ at $\pu{1922 cm-1}$.

There are degenerate vibrations (E') for the terminal ligands at $\pu{2059 cm-1}$

Furthermore, there is another vibration (A2'') at $\pu{2085 cm-1}$.

Please bear in mind that this is an instructional answer (if it really is one) and the level of theory chosen for it is simple enough to make some approximate observations. Without further checking, the modes are surprisingly close to the values you have posted.