Determined Unpaired Electrons in Metallocene Complexes

To find the number of unpaired electrons in transition metal complexes like metallocenes, we first need to determine the oxidation state of the metal and its electron configuration in that oxidation state. The ligand involved here is cyclopentadienyl (Cp), which is $C_5H_5^-$. The Cp ligand is a $\pi$ ligand and typically donates 6 electrons.

Understanding the Cp Ligand and Metal Oxidation State

The cyclopentadienyl anion ($C_5H_5^-$) carries a $-1$ charge. In complexes of the form $[M(C_5H_5)_2]$, there are two Cp ligands, contributing a total charge of $2 \times (-1) = -2$. Since the overall complex is neutral, the metal M must be in the $+2$ oxidation state to balance the charge.

Therefore, for $[Cp_2Fe]$, $[Cp_2Ni]$, and $[Cp_2Co]$, the metal is in the $+2$ oxidation state ($Fe^{2+}$, $Ni^{2+}$, and $Co^{2+}$, respectively).

Electron Count and Unpaired Electrons

Now, let's determine the number of unpaired electrons for each complex:

Fe: Unpaired Electrons in [Cp2Fe]

• Metal: Iron (Fe)
• Neutral Fe electron configuration: $[Ar] 3d^6 4s^2$. Valence electrons = 8.
• Oxidation state in $[Cp_2Fe]$: $Fe^{2+}$
• $Fe^{2+}$ electron configuration: $[Ar] 3d^6$ (loses the two $4s$ electrons). $d$-electron count = 6.
• In ferrocene, $Fe^{2+}$ ($d^6$) forms a stable 18-electron complex ($6 + 2 \times 6 = 18$). This complex is low spin $d^6$, meaning all 6 $d$ electrons are paired in the lower energy orbitals according to the molecular orbital diagram for metallocenes.
• Number of unpaired electrons in $[Cp_2Fe]$ = 0.

Ni: Unpaired Electrons in [Cp2Ni]

• Metal: Nickel (Ni)
• Neutral Ni electron configuration: $[Ar] 3d^8 4s^2$. Valence electrons = 10.
• Oxidation state in $[Cp_2Ni]$: $Ni^{2+}$
• $Ni^{2+}$ electron configuration: $[Ar] 3d^8$ (loses the two $4s$ electrons). $d$-electron count = 8.
• In nickelocene, $Ni^{2+}$ ($d^8$) forms a 20-electron complex ($8 + 2 \times 6 = 20$). Unlike ferrocene, nickelocene deviates from the 18-electron rule and is paramagnetic. The extra two electrons beyond the 18-electron count occupy antibonding orbitals, leading to unpaired electrons. For a $d^8$ configuration, these two electrons occupy degenerate or near-degenerate antibonding orbitals, resulting in 2 unpaired electrons (following Hund's rule).
• Number of unpaired electrons in $[Cp_2Ni]$ = 2.

Co: Unpaired Electrons in [Cp2Co]

• Metal: Cobalt (Co)
• Neutral Co electron configuration: $[Ar] 3d^7 4s^2$. Valence electrons = 9.
• Oxidation state in $[Cp_2Co]$: $Co^{2+}$
• $Co^{2+}$ electron configuration: $[Ar] 3d^7$ (loses the two $4s$ electrons). $d$-electron count = 7.
• In cobaltocene, $Co^{2+}$ ($d^7$) forms a 19-electron complex ($7 + 2 \times 6 = 19$). Cobaltocene is also paramagnetic. The extra electron beyond the 18-electron count occupies a higher energy antibonding orbital, which is singly occupied. This leads to 1 unpaired electron.
• Number of unpaired electrons in $[Cp_2Co]$ = 1.

Summary of Unpaired Electrons

The number of unpaired electrons in the complexes are as follows:

The number of unpaired electrons in $[Cp_2Fe]$, $[Cp_2Ni]$ and $[Cp_2Co]$ are 0, 2, and 1, respectively.