If you
really want to learn how a quantum chemistry algorithm works the only way is really to write it (or a simplified version of it) yourself. Daniel Crawford has made
this wonderful page of projects that covers everything from harmonic vibrational analysis to coupled cluster (no DFT unfortunately).
It's geared towards C++ so this might also be a good way to learn that. However, if you are familiar with python you should be able to complete the exercises in that language.

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