The Hartree-Fock approximation (HFA) works by assuming each electron sees the effective electric field from all the other electrons as some self-consistent field.
The HFA is known to give pretty decent results, but often gets the last quantitative bit of accuracy wrong. This last bit is attributed to mysterious many-body or "strongly-correlated" effects.
There are many examples of HFA quantitatively giving wrong answers (energies are wrong, incorrect numerical results, etc.). But, are there general phenomena that HFA gets totally wrong? I'm thinking of something where the chemistry/physics is fundamentally different from what HFA would tell you. Said differently, when do "strong correlations" actually matter and fundamentally change things in a chemical context?
I've tried reading up on this topic in the physics literature, and it is incomprehensible despite being an ex-physicist myself. Most of the discussion is about high temperature superconductors and complicated transition metal oxides. I can't understand the basic phenomena without all the specific details.