18-electron rule and synergic bonding in metal carbonyls; ν(CO) of [V(CO)₆]⁻, Cr(CO)₆, [Mn(CO)₆]⁺

Apply the 18-electron rule to $\ce{Ni(CO)4}$, $\ce{Fe(CO)5}$, $\ce{Mn2(CO)10}$ and $\ce{V(CO)6}$, and explain why manganese carbonyl is a dimer while $\ce{V(CO)6}$ is easily reduced. Describe synergic bonding in metal carbonyls. Explain the trend in C–O stretching frequency: $\ce{[V(CO)6]^-}$ ≈ 1860, $\ce{Cr(CO)6}$ ≈ 2000 and $\ce{[Mn(CO)6]^+}$ ≈ 2090 cm⁻¹, compared with free CO at 2143 cm⁻¹.