Predicting bond-strength of metal carbonyls The metal carbonyls (and similar organometallic compounds) involve a combination of sigma bond, a pi bond and backbonding. The bond strengths under consideration are the metal-carbon bond and the carbon oxygen bond. Here is the original question:- 


  Predict the order of $\ce{C-O}$ bond strength in the following:-
  I) $[\ce{Mn(CO)_6}]^+$
  II) $[\ce{Cr(CO)_6}]$
  III) $[\ce{V(CO)_6}]^-$  


All of these are isoelectronic, and hence whatever the difference of bond strengths, must arise from the difference in the resultant nuclear force of attraction. Since $\ce{Mn+}$ has the highest charge density, I would assume that the $\ce{M-C}$ bond strength of the manganese compound is the strongest (vanadium being the weakest) and therefore, the $\ce{C-O}$ bond strength must follow the opposite order, as the strengthening of the metal carbonyl bond should weaken the carbon oxygen bond.   

But the answer given is III&lt;II&lt;I, exactly the opposite of my prediction. Why is it so? A relevant factor which I didn't consider is the back bonding, but I am unsure of how to integrate that into my prediction. Also, how would we make a prediction if the given compounds were not isoelectronic?
As the π-antibonding orbital of CO is filled by electrons from the metal, they weaken the C-O bond compared with free CO.  The metal-carbon bond is strengthened in kind. That's what the books says.