Step 1: Understanding CO stretching frequency.
The CO stretching frequency is influenced by the electron density on the metal. Higher electron density on the metal leads to a lower stretching frequency because the metal-carbon bond becomes weaker.
Step 2: Analyzing the options.
- (1) \( \text{V(CO)}_6^+ \): Vanadium has a positive charge, which attracts electron density from the CO ligands, increasing the CO stretching frequency.
- (2) \( [\text{Co(CO)}_4]^- \): Cobalt in this complex is in a negative oxidation state, which increases electron density on the CO ligands, slightly decreasing the CO stretching frequency.
- (3) \( \text{Ni(CO)}_4 \): Nickel in this complex is neutral, and the electron density on the CO ligands is balanced, leading to a moderate CO stretching frequency.
- (4) \( \text{Fe(CO)}_4^{2-} \): Iron in this complex is in a negative oxidation state, which greatly increases electron density on the CO ligands, leading to the lowest CO stretching frequency.
Step 3: Conclusion.
The correct answer is (4) \( \text{Fe(CO)}_4^{2-} \), as the increased electron density on the CO ligands lowers the CO stretching frequency.