One of the more famous species in coordination chemistry is the Creutz-Taube complex: It is named for the two scientists who discovered it and initially studied its properties. The central ligand is pyrazine, a planar six-membered ring with nitrogens at opposite sides. (a) How can you account for the fact that the complex, which has only neutral ligands, has an odd overall charge? (b) The metal is in a low-spin configuration in both cases. Assuming octahedral coordination, draw the \(d\)-orbital energy-level diagram for each metal. (c) In many experiments the two metal ions appear to be in exactly equivalent states. Can you think of a reason that this might appear to be so, recognizing that electrons move very rapidly compared to nuclei?

To account for the odd overall charge in the Creutz-Taube complex with only neutral ligands, it is essential to consider the oxidation states of the two metal ions present in the complex. The oxidation states of the metal ions combined with the charges contributed by ligands (neutral in this case) will result in the overall charge of the complex.

To draw the \(d\)-orbital energy-level diagram for each metal in the Creutz-Taube complex, we need to consider the following steps: 1. Determine the oxidation state of each metal. The oxidation states will give the electron configuration of each metal ion. 2. Identify the ligands' nature in the complex, i.e., whether they are strong field or weak field ligands. The strength of the ligand determines whether it will produce a high or low crystal field splitting. 3. Assuming octahedral coordination, draw the energy levels of the \(d\)-orbitals, splitting them into three lower-energy orbitals (dz^2 and dx^2-y^2) and two higher-energy orbitals (dxy, dyz, and dxz) due to the octahedral crystal field splitting. 4. Fill the electrons based on the electron configuration determined in step 1, following the low-spin configuration rule, i.e., pairing the electrons in the lower-energy orbitals before occupying the higher-energy orbitals.

The reason why the two metal ions might appear to be in exactly equivalent states in many experiments is the rapid electron transfer between the metal ions. Since electrons move very rapidly compared to the nuclei, it could create a situation where the two metal ions appear to be in equivalent states. The rapid electron transfer can be facilitated by the ligand bridging the two metal ions, causing the metal ions to share the electrons effectively, making them behave as if they are in identical chemical environments.