# Is C_2^+ paramagnetic or diamagnetic? Is C_2 paramagnetic or diamagnetic?

Apr 5, 2016

${\text{C}}_{2}$ has a similar MO ordering to ${\text{N}}_{2}$.

From bottom to top, we have the following valence MOs:

1. $\setminus m a t h b f \left({\sigma}_{2 s}\right)$, generated from the linear combination $2 {s}_{A} + 2 {s}_{B}$ (head-on, in-phase)
2. $\setminus m a t h b f \left({\sigma}_{2 s}^{\text{*}}\right)$, generated from the linear combination $2 {s}_{A} - 2 {s}_{B}$ (head-on, out-of-phase)
3. $\setminus m a t h b f \left({\pi}_{2 {p}_{x}}\right)$, generated from the linear combination $2 {p}_{x , A} + 2 {p}_{x , B}$ (sidelong, in-phase)---degenerate with (4)
4. $\setminus m a t h b f \left({\pi}_{2 {p}_{y}}\right)$, generated from the linear combination $2 {p}_{y , A} + 2 {p}_{y , B}$ (sidelong, in-phase)---degenerate with (3)
5. $\setminus m a t h b f \left({\sigma}_{2 {p}_{z}}\right)$, generated from the linear combination $2 {p}_{z , A} + 2 {p}_{z , B}$ (head-on, in-phase)
6. $\setminus m a t h b f \left({\pi}_{2 {p}_{x}}^{\text{*}}\right)$, generated from the linear combination $2 {p}_{x , A} - 2 {p}_{x , B}$ (sidelong, out-of-phase)---degenerate with (7)
7. $\setminus m a t h b f \left({\pi}_{2 {p}_{y}}^{\text{*}}\right)$, generated from the linear combination $2 {p}_{y , A} - 2 {p}_{y , B}$ (sidelong, out-of-phase)---degenerate with (6)
8. $\setminus m a t h b f \left({\sigma}_{2 {p}_{z}}^{\text{*}}\right)$, generated from the linear combination $2 {p}_{z , A} - 2 {p}_{z , B}$ (head-on, out-of-phase)

You can see the compatible bonding orbital combinations here (reverse one of the orbitals' signs to achieve the corresponding antibonding orbital combination):

As a result, we have the following MO diagram (with atomic orbital energies from Inorganic Chemistry, Miessler et al., pg. 134):

Thus, with no unpaired electrons, neutral ${\text{C}}_{2}$ is diamagnetic.

If ${\text{C"_2 -> "C}}_{2}^{+} + {e}^{-}$, then is ${\text{C}}_{2}^{+}$ paramagnetic or diamagnetic? Paramagnetism requires unpaired electrons.