Why is the bond length of CO+ less than that of CO?

According to molecular orbital theory, the bond order of $\ce{CO}$ is 3. When $\ce{CO+}$ is formed, the bond order decreases to 2.5, and thus the bond length should increase.


However, the bond length of $\ce{CO+}$ is found to be less than $\ce{CO}$. How is that so?




Unfortunately, the arguments presented by `buckminst` and `Uncle Al` aren't completely right. The MO schemes are correct but the HOMO-$\sigma$ orbital ($s\_{\sigma}^{\*}(5\sigma)$ in `buckminst`'s diagramm, $\sigma\_{3}$ in `Uncle Al`'s diagram) is not antibonding but slightly bonding in character because there is some mixing with the $\ce{p}$ atomic orbitals of the right symmetry (in this respect the MO scheme of `Uncle Al` is better than the one of `buckminst` because it indicates this mixing).


So, the original problem still persists.
One possible explanation for the bond shortening after ionization is that the ionization leads to a shift of the $\ce{CO}$-electron-polarization (on ionization an electron is lost from the mostly $\ce{C}$-centered HOMO-$\sigma$ orbital and this leads to a formation of a positive partial charge on the $\ce{C}$ atom).
This strengthens the covalence of the $\ce{CO}$-bond and thus reduces the bond length (since the HOMO-$\sigma$ orbital is only slightly bonding there is not much bonding lost by taking away one of its electrons - the lost bonding is outweighed by the gain in covalency).
You can think of this strenghtening of the bond covalence in the following way: Two atomic orbitals can interact better (form stronger bonds) if their energies are close. Without the positive partial charge on $\ce{C}$ the AOs of $\ce{O}$ lie energetically a lot below the AOs of $\ce{C}$ (this is most pronounced for the $\ce{s}$ AOs which form the HOMO-$\sigma\*$ orbital). But with the positive partial charge on $\ce{C}$ the AOs of $\ce{C}$ are shifted down in energy and thus their energies are closer to the related AOs of $\ce{O}$ which leads to a stronger interaction when bonds are formed.


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<http://www.meta-synthesis.com/webbook/39_diatomics/co.jpg>   

Measured $\ce{CO}$ bond length is 1.128 Å, $\ce{CO^{+}}$ is 1.115 Å. Given the following carbon monoxide MO diagram, from where is the electron removed to afford the cation with a shorter bond length? $\ce{CO}$ has a dipole moment of 0.122 debyes, net negative charge on the carbon. One then suspects the electron is removed from the sigma anti-bonding orbital on carbon.


![carbon monoxide MO diagram](https://i.stack.imgur.com/w6qNx.jpg)


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Molecular Orbital theory does NOT predict a longer bond. It correctly predicts a shorter bond. The HOMO for $\ce{CO}$ is a sigma antibonding orbital. When it is ionized, the bond order is increased to 3.5, and the bond length decreases.


![enter image description here](https://i.stack.imgur.com/nWjgj.gif)


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