Submitted by Joanne Stewart / Hope College on Wed, 05/22/2019 - 09:38
My Notes

This is the sixth in a series of exercises used to teach computational chemistry. It has been adapted, with permission, from a Shodor CCCE exercise ( It uses the WebMO interface for drawing structures and visualizing results. WebMO is a free web-based interface to computational chemistry packages (

In this exercise, students perform molecular orbital calculations, which generate electron densities, electrostatic potentials, and reactivity indices. They compare electron distribution in H2, HF, and LiH. They learn about electrophilic and nucleophilic reactivity indices. They use HOMO and LUMO shapes and energies to predict reactivity in a Diels-Alder reaction.

The exercise provides detailed instructions, but does assume that students are familiar with WebMO and can build molecules and set up calculations.


Learning Goals

After completing this exercise, students will be able to:

  1. Calculate and visualize electron densities, electrostatic potentials, HOMO/LUMO, and reactivity indices.
  2. Use these visualizations to predict or understand reactivity.
Equipment needs

Students need access to a computer, the internet, and WebMO (with Mopac and Gaussian). 

Implementation Notes

I use this as an in-class exercise. Students bring their own laptops and access our institution's installation of WebMO through wifi.

In Exercise 1, students compare the electron density distributions in H2, HF, and LiH. It is not always obvious to them that these can be considered models for covalent, polar covalent, and ionic bonding, so I debrief those concepts after they have completed the exercise.

In Exercise 2, students compare electron density distributions in benzene and pyridine. Although they have studied aromatic compounds in organic, they are still somewhat surprised by the benzene results, with its negative region in the middle of the ring and positive region around the outside of the ring. They are reluctant to suggest T-shaped packing in the solid state.

In Exercise 3, students are introduced to the concept of reactivity indices and asked to consider the "Electrophilic (HOMO) Frontier Density," which is used to predict where an electrophile might attack. There are several interesting discoveries for students here. First, they are happy to see that the methoxybenzene calculation predicts an ortho, para preference for electrophilic substituion, which is what they learned in organic chemistry. Second, they see that semi-empirical calculations can sometimes be misleading, when their PM3 thiophene calcuation gives them the "wrong" result, but a DFT calculation gives them the "right" result. The DFT calculation clearly predicts that electrophilic subsitution is most likely at the alpha-carbon atoms. (The PM3 calculation gets the "wrong" order for the HOMO and LUMO, so the electrophilic (HOMO) frontier density ends up on sulfur instead of on the alpha carbons.

It is worth mentioning that the WebMO colors for the electrophilic (HOMO) frontier density may seem counterintuitive. We are used to visualizing electrostatic potentials, where red means negative and blue means positive. Intuitively, we might think that the site for electrophilic attack would be red because it is electron-rich. However, it is blue.

In Exercise 4, students visualize the HOMOs and LUMOs for the diene and dienophile in a Diels-Alder reaction. This exericise takes students longer than you might think. First, they must figure out which orbitals are the HOMOs and LUMOs, by looking at the long list of orbitals and finding the last full one and the first empthy one. Also, it is difficult for them to visualize/understand the orbitals and twist the molecules into useful views.

Time Required
1.5 hours


Evaluation Methods

This exercise usually takes longer than a 50 minute class period. Students record their answers directly onto their handouts, and I collect the handouts at the beginning of the next class.


Evaluation Results

Some common student struggles:

In Exercise 2, students don't always understand how to use simple electrostatic arguments to explain the possible packing of benzene molecules in the solid.

In Exercise 3, students are confused by the fact that the PM3 and DFT calculations give them different answers.

In Exercise 4, students find it challenging to sketch how the HOMO and LUMO come together in the Diels-Alder reaction.

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