Metal Carbonyls & Synergic Bonding - Bond Order & Vibrational Frequency ($$\nu_{\text{CO}}$$) Trends

Trend / Formula:

$$\text{Extent of } \pi\text{-Back Donation} \propto \frac{1}{\text{Formal Charge on Metal Center}}$$

$$\text{As Back-Donation Increases } \implies \begin{cases} \text{M--C Bond Order Increases} & (\text{M--C Bond Length Shortens}) \\ \text{C--O Bond Order Decreases} & (\text{C--O Bond Length Lengthens}) \\ \text{C--O Stretching Frequency } (\nu_{\text{CO}}) \text{ Decreases} \end{cases}$$

$$\text{Stretching Frequency } (\nu_{\text{CO}}) \text{ Trend: } [\text{Mn}(\text{CO})_6]^+ > [\text{Cr}(\text{CO})_6] > [\text{V}(\text{CO})_6]^-$$

Concept:

In metal carbonyls, $$\sigma$$-donation from $$\text{CO}$$ to metal is reinforced by $$\pi$$-back donation from filled metal d-orbitals into the vacant antibonding $$\pi^*$$ orbitals of $$\text{CO}$$ (Synergic Effect). A higher negative charge on the metal increases back-donation, populating $$\pi^*(\text{CO})$$ orbitals, which weakens the $$\text{C--O}$$ bond while strengthening the $$\text{M--C}$$ bond.

Notation:

• $$\nu_{\text{CO}}$$ = Infrared vibrational stretching frequency of the carbon-oxygen bond (measured in $$\text{cm}^{-1}$$)
• $$\pi^*$$ = Antibonding molecular orbital of carbon monoxide