Octahedral Co(II) Ground State

Cobalt in the +2 oxidation state, Co(II), has a $d^7$ electron configuration.

In a high-spin octahedral environment, the $d$ orbitals split into lower-energy $t_{2g}$ and higher-energy $e_g$ sets.

For a $d^7$ configuration, the electron distribution is $(t_{2g})^5 (e_g)^2$. This configuration leads to 5 unpaired electrons.

According to Crystal Field Theory and Hund's rules, the ground state term symbol for $d^7$ in an octahedral field originating from the free ion $^4F$ state is $^4T_{1g}$.

• The superscript '4' indicates the spin multiplicity ($2S+1 = 4$, since $S=3/2$).
• 'T' denotes a triply degenerate orbital state.
• '$_{1g}$' specifies the particular term derived from the $F$ state and its symmetry under octahedral ($O_h$) point group (g = gerade/even parity).

Tetrahedral Co(II) Ground State

In a high-spin tetrahedral environment, the $d$ orbitals split into lower-energy $e$ and higher-energy $t_2$ sets. The splitting is inverted compared to octahedral complexes, and the energy gap ($\Delta_t$) is smaller, ensuring a high-spin configuration.

For a $d^7$ configuration in a tetrahedral field, the electron distribution is $(e)^2 (t_2)^5$.

The ground state term symbol for $d^7$ in a tetrahedral field, derived from the free ion $^4F$ state, is $^4A_2$.

• The superscript '4' again indicates the spin multiplicity ($S=3/2$).
• 'A' denotes a non-degenerate orbital state.
• No parity subscript ('g' or 'u') is used in tetrahedral symmetry as it lacks an inversion center.

Conclusion

Therefore, the ground states of high-spin octahedral and tetrahedral Co(II) complexes are $^4T_{1g}$ and $^4A_2$, respectively.