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I know that metal carbonyl complexes that do not follow EAN rule or 18 electron rule try to achieve that by gaining electron (forming carbonylate) or loosing electron (forming carbonyl cations). But this question is way too dicey. It came in a national level exam in our country. I am yet to find a solution.

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Yes there are more carbonylate ions than metal carbonyl cations, but the latter do exist. A salt $\ce{[Mn(CO)6^+][BF4^-]•SO2}$ has been synthesized in a superacid medium.

Metal carbonyl cations are often disfavored because they have to contend with counterions that are anions, which may compete with the carbon monoxide ligands. Such a competition is tilted towards the anion winning out if the metal is positively charged. Solvents with significant Lewis-base character are also apt to displace carbon monoxide from the coordination sphere, for a similar reason. Carbonylate anions do not face this situation (or at least not as severely) because cations are more likely to bind with the solvent than with an an ionic metal center that is dispersing its charge through pi donation to the carbon monoxide ligands.

Going back to the referenced salt, we can see features that protect $\ce{[Mn(CO)6^+]}$ from such an ignominious fate. First note the counterion, $\ce{[BF4^-]}$which is a very weak nucleophile and has its negative charge buried inside the relatively bulky fluorine "shield". Then note the superacid medium; perforce the solvent is not competing as a Lewis base either.

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