Submitted by Gerard Rowe / University of South Carolina Aiken on Mon, 11/04/2013 - 10:38
My Notes

This activity is meant to teach students an MO theory interpretation of hypervalency that goes beyond the simple (and somewhat unsatisfying) explanation that atoms that are in the third row and below use d-orbitals for bonding in addition to s- and p-orbitals. Specifically, students will be learning how to construct MO diagrams for multicenter bonding schemes (i.e., 3c4e).  

I have seen other articles in J. Chem. Ed. about how to treat hypervalent molecules, or even how to construct multicenter bonding schemes, but not one that uses what I believe to be a more systematic approach that I am tentatively calling the "missing orbital method".  

This activity builds upon the ideas presented in Adam Johnson's VIPER activity and J. Chem. Ed. paper on building LGOs, which my class completes two classes before undertaking this activity.

Learning Goals

A student should be able to apply their knowledge of group theory to construct ligand group orbitals of polyatomic molecules

A student should be able to construct a molecular orbital diagram using ligand group orbitals.

A student should be able to identify orbitals that do not participate in bonding in hypervalent molecules.

A student should be able to interpret the meaning of bonding and nonbonding orbitals.

Equipment needs

Some students find molecular models helpful in visualizing orbital overlap

All my students found it very helpful to have a table of the orbital hybridizations for the different molecular geometries, which can be found in Adam Johnson's J. Chem. Ed. article.

Related activities
Implementation Notes

It is important that students are grounded in constructing LGOs before attempting this activity, because it requires them to quickly build them and combine them with orbitals on the central atom to form MOs.  My class gets a week of lecture and activities on LGOs, MO theory, and hypervalent molecules before this activity.

Time Required
One 50 minute class period


Evaluation Methods

Students are graded on this activity based on the questions and how well they constructed the LGOs and translated them into a molecular orbital diagram, with a specific focus on which LGO was chosen to be nonbonding.

The year before creating this activity, students in this course in had a question on their exam where they were asked to construct the MO diagram of XeF4, being warned that the molecule was hypervalent.  They had seen lectures about hypervalency, but never got an opportunity to practice this systematized approach.  

This year, my students received essentially the same question on their exam.  Comparing results from the two years, every one of my current students scored higher on that question than anyone in the class last year.

Evaluation Results

One particularly sticky point for many students is seeing how px and py overlap with atoms on a trigonal plane.  Since the molecule in this activity is trigonal bipyramidal, about half of the class struggled with drawing the appropriate LGOs.  Others were so stuck on the rules they learned about LGOs previously that they forgot to eliminate one of the bonding LGOs before constructing the MO diagram.  The last two questions in the activity were also problematic, but that may have been because students were burned out by the end or ran out of time.

Creative Commons License
Adam Johnson / Harvey Mudd College


I was looking at this LO with Hilary Eppley over the past week. I think its a great example problem. You say in your table for XeF2 that deciding between dz2 and s as the LGO generator vs the lone pair symmetry predictor is too difficult and that you give the students the answer. After talking this through with a few people, I think I see where you are coming from but I disagree.

To predict the LGOs, we need an in-phase and out-of-phase combination. I tell my students that when there are only 2 ligands, that is always what they will be. Obviously one of them will have s (or dz2) symmetry, a1 type, and the other will be pz, a2 type.

But, when constructing the table, you do obviously have to make a choice. I'm going to try to reconstruct the table here and then give my comments... note that I have dropped to a dxh character table (where x is an odd number)...

Generator    symm label     LGO?     LP?

s                   a1                   yes         yes

px/py            e                     no          yes

pz                a2                    yes        no

dz2               a1                   yes         yes


ok, we need to LGOs so we must pick a2, pz, and then either s or dz2 as a1. then we have 3 LPs, and we predict symmetry to be e and then the remaining s or dz2, a1.

Here is the part that trips up my students (and my colleagues). Once we assign the symmetry label for the LGO, forget where it came from. we have an in-phase of a1 and out-of-phase of a2 symmetry. Those will interact with the orbitals on Xe (s, px, py, pz only). In your key, you say that the s is too low in energy to interact, thus you get a bonding combination with a2 only and an a1 non-bonding LP on the fluorines. This makes sense to me. Alternatively, you can bond with s, to form one bond, and then the LP is an antibonding interaction of s and the fluorines, but the net bond order is the same.

I hope this helps and doesn't confuse further. Dealing with lone pairs is tough, kludgy, and the reason it took me almost 10 years to finally decide to pull the trigger an publish the J. Chem. Educ. article!!


Mon, 10/20/2014 - 12:06 Permalink