How do you write the orbital diagram for phosphate?

I interpreted this as the molecular orbital diagram... and it became rather complicated (I honestly don't think you want to know the minor details!).

Here's the scratchwork when I was getting the reducible representations #Gamma_(S(O))#, #Gamma_(p_y(O))#, #Gamma_(p_x(O))#, and #Gamma_(p_z(O))#, and the decomposed irreducible representations (#A_1 + T_2#, #E + T_1 + T_2#), for the four oxygen atoms transforming as a group:

The whole point of that was to see how the oxygen orbital energies split up (and which were two-fold or three-fold degenerate). It was also to figure out which orbitals on phosphorus interact with which orbitals on the oxygen atoms.

The resultant MO diagram was:

Takeaways:

• This is only qualitative, so take it with a grain of salt.
• Phosphate has all electrons paired.
• The nonbonding orbitals are nonbonding either due to mismatched symmetries, overly different inner-atom/outer-atom orbital energies, or interactions between both high-lying and low-lying orbitals.
• There are #22# nonbonding electrons, which accounts for all #11# lone pairs of electrons that belong to the oxygen atoms. The remaining #2# nonbonding electrons account for the #bb(pi)# bond that is delocalized.
• The #sigma# bond order that this MO diagram seems to account for is #1# for all four #bb(sigma)# bonds, as there are four clearly-bonding MOs (#a_1 + t_2#), one for each bond.