# MO diagram for pentaamminechlorocobalt(III)?

I was considering the MO diagram for [Co(NH3)5Cl]2+, and figured it’d be as follows:

5 sigma interactions from the NH3 ligands; by reducing a reducible representation one obtains 2A1 + B1 + E

2 pi interactions (pi donation from Cl- px and pz orbitals), which have symmetry E

And the cation atomic orbitals, which we just read off the character table.

Unfortunately this results in a lot of confusing interactions in the MO diagram.

What would the MO diagram look like, and are my group orbitals correct?

Thanks!

• One approach you may find helpful is to break this down into steps. First figure out the MOs for a square planar $\ce{[Co(NH3)4]^3+}$, then add in the axial ligands and see how that changes things. Feb 13 '19 at 16:23
• Since no one's followed up on this - a couple more comments. 1) It appears you're missing the Cl- sigma interaction. 2) One your lower image, you have all the group orbitals at the same energy. It might help you with overall ordering to order those by energy first. I may have time to write out a full answer in a little bit. Feb 15 '19 at 15:21

Let's start at the bottom. There will be three a1 bonding orbitals. First, we can have the metal $$4s$$ orbital interact with all six ligands in phase. Let's call this $$1a_1$$. Next, the metal $$d_{z^2}$$ can interact with all six ligands as well, but the axial ligands are now opposite phase from the equatorial. Let's call that $$2a_1$$. Both will of course have antibonding counterparts. The third $$a_1$$ orbital is an interaction of the metal $$p_z$$ with out of phase axial ligand orbitals. The equatorial ligands do not contribute to this orbital because they are on the nodal plane. Let's call this $$3a_1$$.
Mixed in with these a1 orbitals will be the $$b_1$$ orbital comprised of the equatorial ligand orbitals interacting with $$d_{x^2-y^2}$$. That will be $$1b_1$$. It is lower in energy than $$3a_1$$ but likely higher than $$1a_1$$ and $$2a_1$$. (This $$1b_1$$ and the $$2a_1$$ correspond to the $$1e_g$$ orbitals of an $$O_h$$ complex.)
Near $$3a_1$$ we have the two $$e$$ orbitals comprised of the metal $$p_x$$ and $$p_y$$, each interacting with a pair of equatorial ligands. Let's call these $$1e$$. (These along with $$3a_1$$ correspond to the $$1t_{1u}$$ orbitals of an $$O_h$$ complex).
If we are only considering sigma interactions, we next have the $$e$$ and $$b_1$$ orbitals representing metal $$d_{xy}$$, $$d_{xz}$$, and $$d_{yz}$$, all of which are nonbonding for sigma. However, the pi interactions with Cl mean that the $$e$$ orbitals are stabilized and have antibonding destabilized counterparts. Let's call those $$2e$$. The $$b_1$$ orbital ($$d_{xy}$$) remains nonbonding.