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In this activity, students construct molecular orbital correlation diagrams for several species (H2, He2, HeH), in a semi-quantitative fashion using a ruler and a list of first ionization energies. All the MO schema are placed on a common energy scale, and the stability of each orbital is reported using "cm from the top of the paper" as the unit of energy. Once the correlation diagrams for all the species are completed, students calculate the total energy of each molecule by adding together the energies of all the electrons in their respective orbitals.
Once the energies of each species are calculated, students use those values to determine why the molecule HeH is unstable with respect to H2 and He.
I developed this in-class activity for my introductory inorganic chemistry course after running into some issues with my advanced students' inability to interpret the results of density funcational theory calculations. Mainly, it was a great challenge to get them to understand that the total energy of a molecule was (to a first approximation) simply the sum of all the electron orbital energies times their respective occupancies. They also had trouble in shifting their thinking about the stability of a molecule from a simple number to a more sophisticated concept along the lines of "X is unstable with respect to Y".
| Attachment | Size |
|---|---|
| Semi-Quantitative Molecular Orbital Diagrams (PDF) | 154.2 KB |
| Semi-Quantitative Molecular Orbital Diagrams (DOCX) | 22.55 KB |
A student should be able to use ionization energies to place atomic orbitals of different elements on a common energy scale
A student should be able to properly construct a molecular orbital digram for first-row diatomic molecules
A student should be able to recognize the meaning of 0 energy as applied to electrons in molecules
A student should be able to calculate the energy of molecules based on orbital energies/occupancies
A student should be able to apply their understanding of thermodynamics and molecular energy to estimate the stability of a particular molecule (HeH)
Unlined paper, ruler
The previous class, I gave a lecture introducing molecular orbital theory up to second-row diatomic molecules, so the concepts were fresh in their minds.
Students worked in groups of 3.
If they are careful about using their ruler to place the bonding and antibonding orbitals the appropriate distance away from their respective atomic orbitals, students will obtain energies that result in the correct answer for the final question about the stability of HeH.
The only issue any group ran into was that they didn't remember to make the antibonding orbital sets more destabilizing than the bonding sets were stabilizing (they had learned about the nuclear repulsion term in the previous lecture). If the two MO sets were equidistant from the corresponding atomic orbitals, they could determine that HeH should be a perfectly stable molecule.
Evaluation
Students handed in their MO digrams and energy calculation at the end of class. They were graded on the accuracy of the correlation digrams (including the relative energies of different species), their ability to estimate molecular energy, and to determine the stability of HeH.
I was a little surprised at how well my students performed. I was walking around the classroom coaching groups through the exercise, but most of that was encouraging them to hurry up a bit when drawing their MO diagrams. Apparently, when you hand some people a ruler, they feel the need to make sure everything lines up to the nearest mm.
The interesting thing about this activity is that every group ended up estimating a different absolute magitude for the bonding-antibonding energy gap, with some barely having any gap at all, and some having them take up half the page. As long as they were consistent in their methods, the molecular energies they calculate will lead to the correct answer in the end.
All this is predicated on them correctly placing the relative energies of the 1s orbitals of H and He based on ionization energies, with the magnitude of helium's orbital energy being roughly double that of hydrogen.
I'd like to add something that I'm embarrassed I didn't think of until this year. This activity goes much more quickly and smoothly if you ditch the rulers and give everyone graph paper. Nobody spent 10 minutes trying to figure out how large 1 eV should be on their page like some students did in years past.