Question

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

Answer 1

If we build the MO diagram for `"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 `"*"` notation. In here, `sigma` `"*"` and `pi` `"*"` are both antibonding. However, I will provide both if you want to compare.

If we write the configurations, they look like this:

`"N"_2`:

`["core 1"s]^2(1sigma_(g))^2(1sigma_(u))^2(pi_u^x)^2(pi_u^y)^2 (2sigma_(g))^2color(red)((pi_g^x)^0(pi_g^y)^0(2sigma_u)^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 `"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 `"*"` notation because I find it easier to remember which MOs are antibonding/bonding.

`"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)`

`"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)`

`"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)`

`"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)`