There are a lot of examples on the G16 manual, each with different levels of difficulty. But, if you want to show a simple reaction, it could be this: 10.1007/s00214-015-1774-8
There are some exercises on Levine's "Quantum Chemistry" that may also be usable for students. Which makes me wonder course' level you want to teach them how to use computational chemistry as a tool.
Francisca J. Benítez I would like to find a paper, explaining steps of the DFT SCF procedure including worked out examples of the integrals and numerical grid calculation. Quite a lot are already very well explained by R. L. Snow and J. L. Bills in their 1975 paper,.
DFT it is the most effective method for calculating density in terms of energy , and deponding on code Wien2k where we can calculate all the structural, electronic and optic properties of the material (solid).
I think the answer to this depends on what you want to teach (is this DFT as a physicist or a chemist?) and which code you want to use to do the teaching with.
Either way, you probably want something that runs quickly and reliably; the obvious suggestions being bulk Si if you are interested in solid state, or a simple molecule such as benzene if you are approaching it from a chemical perspective.
Either way, if you are asking students to run it themselves, go for something quick (small with relatively few electrons) so they can make mistakes and still have time to get the answer!
I'd also be inclined to avoid systems which are strongly correlated (3d and 4f block) as the extra complication of these systems are probably a bit much for a new DFT user to take in.
Naturally, all of this depends on *what* it is you actually want to teach!
Not to seem immodest, but Chapter 7 in my book Beyond Classical Physics (Springer) has a lengthy discussion of chemistry/chemical bonding. I use the open-source code NWChem to perform the calculations.