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I'm struggling to understand the trend of $\ce{CO}$-vibration in isoelectronic metal carbonyls.

$$ \begin{array}{lr|lr} \hline \text{Compound} & ν/\pu{cm-1} & \text{Compound} & ν/\pu{cm-1} \\ \hline \ce{Ni(CO)4} & 2060 & \ce{[Mn(CO)6]+} & 2090 \\ \ce{[Co(CO)4]-} & 1890 & \ce{Cr(CO)6} & 2000 \\ \ce{[Fe(CO)4]^2-} & 1790 & \ce{[V(CO)6]-} & 1860 \\ & & \ce{[Ti(CO)6]^2-} & 1750 \\ \hline \end{array} $$

Since the complexes are isoelectronic, the reason behind the trend should lie in the atomic charge $(\ce{Ni} > \ce{Co} > \ce{Fe}).$ Higher atomic charge means more attraction between metal cation and the ligand electron pair → higher electron density → more π-backbonding → weaker $\ce{C#O}$ bond → lower wavenumber.

But it is not the case here. I'm not sure why. I think it has something to do with the energy level of HOMO.

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I think the mistake you're making is this conclusion: "Higher atomic charge. . . -> higher electron density -> more pi-backbonding". With higher (ie more positive or less negative) atomic charge, there is less electron density donation towards the ligand, because the electron density is pulled to the metal center more strongly. Thus, $\pi$ back-bonding is weaker and C-O bond is stronger.

The more positively charged metal centers do not pull enough electron density from CO in the sigma interaction to be able to donate more back through pi interaction, which seems to be the way you're looking at it.

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