The correct geometries for the metal carbonyl clusters, A-C

$$\text{A. } [\text{Ru}_6(\text{CO})_{17}\text{B}]^{-} \\\text{B. } [\text{Os}_6(\text{CO})_{18}\text{P}]^{-} \\\text{C. } [\text{Os}_4(\text{CO})_{16}]$$

are

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Correct option is D

​The structures of many polynuclear organometallic species considers the total valence electron count, also called the Mingos cluster valence electron count. 

Each low oxidation state metal cluster cage possesses a characteristic number of valence electrons (ve). A and B are examples of a cage containing an interstitial atom which contributes all of its valence electrons to cluster bonding. An interstitial C atom contributes four electrons, a B atom three, an N or P atom five, and so on.

Each CO contributes two electrons.

Electronic configuration of Ru is ⦏Kr⦐4d⁷5s¹. 

Electronic configuration of Os is [Xe] 4f¹⁴5d⁶6s²

A: Total valence electron count=8×6+2×17+3+1=86

B: Total valence electron count= 8×6+2×18+5+1=90

C: Total valence electron count= 8×4+2×16=64

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