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

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)#