Question #44197

In Molecular Orbital Theory, diatomic molecules like $N_2$ and $CO$ exhibit s-p mixing, rendering the HOMO of $CO$ weakly antibonding ($3\sigma$) and its LUMO as $2\pi^*$. When $CO$ acts as a ligand in homoleptic octahedral complexes, synergic bonding dictates the C-O bond order.

Consider the isoelectronic complexes $[Cr(CO)_6]$ and $[Mn(CO)_6]^+$. The standard reduction potentials are $E^\circ_{Cr^{2+}/Cr} = -0.91\text{ V}$ and $E^\circ_{Mn^{2+}/Mn} = -1.18\text{ V}$. The anomalously negative $E^\circ$ for Mn reflects the profound exchange energy stabilization of its d-orbitals, which persists in the $M(I)$ state, significantly lowering the energy of its $t_{2g}$ electrons compared to $Cr(0)$.

Given that the C-O stretching frequency ($\nu_{CO}$) for free $CO(g)$ is $2143\text{ cm}^{-1}$ and for $[Cr(CO)_6]$ is $2000\text{ cm}^{-1}$, identify the most chemically accurate $\nu_{CO}$ for $[Mn(CO)_6]^+$ from the given options.