# What are the molecular orbital configurations for N_2^+, N_2 ^(2+), N_2, N_2^-, and N_2^(2-)?

Nov 2, 2015

If we build the MO diagram for ${\text{N}}_{2}$, it looks like this: First though, notice that the $p$ orbitals are supposed to be degenerate. They weren't drawn that way on this diagram, but they should be. Anyways, for the electron configurations, you would use a notation like the above.

g means "gerade", or even symmetry upon inversion, and u means "ungerade", or odd symmetry upon inversion. It's not crucial that you memorize which ones are gerade and which ones are ungerade, because the ${\pi}_{g}$ are antibonding, yet the ${\sigma}_{u}$ are also antibonding, for example.

That is why I will use the easier notation to understand---the $\text{*}$ notation. In here, $\sigma$$\text{*}$ and $\pi$$\text{*}$ are both antibonding. However, I will provide both if you want to compare.

If we write the configurations, they look like this:

${\text{N}}_{2}$:

${\left[\text{core 1} s\right]}^{2} {\left(1 {\sigma}_{g}\right)}^{2} {\left(1 {\sigma}_{u}\right)}^{2} {\left({\pi}_{u}^{x}\right)}^{2} {\left({\pi}_{u}^{y}\right)}^{2} {\left(2 {\sigma}_{g}\right)}^{2} \textcolor{red}{{\left({\pi}_{g}^{x}\right)}^{0} {\left({\pi}_{g}^{y}\right)}^{0} {\left(2 {\sigma}_{u}\right)}^{0}}$

or

["core 1"s]^2(sigma_"2s")^2(sigma_"2s"^"*")^2(pi_"2px")^2(pi_"2py")^2 (sigma_"2pz")^2color(red)((pi_"2px"^"*")^0(pi_"2py"^"*")^0(sigma_"2pz"^"*")^0)

The red labels indicate that they are empty for neutral ${\text{N}}_{2}$ and you do not have to write them out.

Then if you want to do it for the ions, you just take out or add in electrons to the red-labeled configuration portions. Again, I will use the $\text{*}$ notation because I find it easier to remember which MOs are antibonding/bonding.

${\text{N}}_{2}^{+}$:

["core 1"s]^2(sigma_"2s")^2(sigma_"2s"^"*")^2(pi_"2px")^2(pi_"2py")^2 (sigma_"2pz")^1color(red)((pi_"2px"^"*")^0(pi_"2py"^"*")^0(sigma_"2pz"^"*")^0)

${\text{N}}_{2}^{2 +}$:

["core 1"s]^2(sigma_"2s")^2(sigma_"2s"^"*")^2(pi_"2px")^2(pi_"2py")^2 color(red)((sigma_"2pz")^0(pi_"2px"^"*")^0(pi_"2py"^"*")^0(sigma_"2pz"^"*")^0)

${\text{N}}_{2}^{-}$:

["core 1"s]^2(sigma_"2s")^2(sigma_"2s"^"*")^2(pi_"2px")^2(pi_"2py")^2 (sigma_"2pz")^2(pi_"2px"^"*")^1color(red)((pi_"2py"^"*")^0(sigma_"2pz"^"*")^0)

${\text{N}}_{2}^{2 -}$:

["core 1"s]^2(sigma_"2s")^2(sigma_"2s"^"*")^2(pi_"2px")^2(pi_"2py")^2 (sigma_"2pz")^2(pi_"2px"^"*")^1(pi_"2py"^"*")^1color(red)((sigma_"2pz"^"*")^0)