Isomers of [(η5-C5H5)Fe(CO)2]2

The molecule [(η5-C5H5)Fe(CO)2]2 is an organometallic complex that exists in solution as a mixture of different structural isomers that are in equilibrium with each other. The primary forms observed for this compound are:

• A bridged isomer, where two carbonyl ligands act as bridging ligands between the two iron atoms. This bridged structure contains both bridging ($\mu$-CO) and terminal (CO) carbonyl ligands, and typically has an Fe-Fe bond. The bridged form can exist as cis and trans geometrical isomers, depending on the relative orientation of the $\eta$5-C5H5 (Cp) and terminal CO ligands around the Fe-Fe axis.
• An unbridged isomer, where all four carbonyl ligands are terminal, bonded directly to one iron atom each. This form also contains an Fe-Fe bond.

At room temperature (28°C), the solution of [(η5-C5H5)Fe(CO)2]2 typically contains a mixture of the bridged cis isomer, the bridged trans isomer, and the unbridged isomer, all in dynamic equilibrium.

1H NMR Signal from Cp Protons

The $\eta$5-C5H5 (Cp) ligand is a planar, cyclic system with five protons. When coordinated to a metal in an $\eta$5 fashion, the Cp ring often undergoes rapid rotation around the metal-ring axis, especially at temperatures like 28°C. This rapid rotation averages the magnetic environment experienced by the five protons on the Cp ring. As a result, the five protons become chemically equivalent on the timescale of the 1H NMR experiment.

Due to this chemical equivalence and the absence of coupling to other protons (the nearest protons are on different molecules or separated by multiple bonds), the $\eta$5-C5H5 ligand in a symmetrical or fluxional complex gives rise to a single, sharp signal in the 1H NMR spectrum. This signal appears as a singlet.

Three Singlets in the Spectrum

The question states that the 1H NMR spectrum of [(η5-C5H5)Fe(CO)2]2 solution at 28°C shows three singlet signals. Since each distinct $\eta$5-C5H5 ligand in a molecule contributes one singlet (assuming rapid rotation), observing three singlets indicates that there are three different chemical environments for the Cp ligands in the solution.

As discussed earlier, the solution at this temperature contains a mixture of the following three spectroscopically distinguishable species:

1. The bridged cis isomer of [(η5-C5H5)Fe(CO)2]2.
2. The bridged trans isomer of [(η5-C5H5)Fe(CO)2]2.
3. The unbridged isomer of [(η5-C5H5)Fe(CO)2]2.

In each of these three isomers, the two Cp rings are chemically equivalent, and the protons within each Cp ring are also equivalent due to rapid rotation. However, the overall molecular structure and electronic environment are different for the bridged cis, bridged trans, and unbridged forms. Consequently, the Cp protons in each of these three distinct species resonate at different chemical shifts in the 1H NMR spectrum.

• The Cp protons of the bridged cis isomer contribute one singlet.
• The Cp protons of the bridged trans isomer contribute one singlet at a different chemical shift.
• The Cp protons of the unbridged isomer contribute one singlet at yet another different chemical shift.

Therefore, the presence of these three distinct species in the solution at 28°C leads to the observation of three singlet signals in the 1H NMR spectrum of [(η5-C5H5)Fe(CO)2]2.

The description "1 : 1 mixture of cis- and trans-isomers" in the question likely refers to the relative amounts of the major species present, encompassing the contribution from the unbridged form as well, which together result in three observable Cp signals.