Hartree-Fock as function minimization

[mszep]

Rather than jump straight to CI, maybe it's more interesting to explore lower-hanging fruit: The possibility of framing the Hartree-Fock approximation not as a matrix eigenvalue problem, but as a constrained minimization problem. Then we could potentially use autodifferentiation to speed up the optimization.

[jarvist]

Absolutely!
I think a few Julians have already discussed this as a possibility.

The group of Aspuru-Guzik did this last year, implemented in Python. I'm not sure how far they went, I imagine they hit some limits in what you can do with the level of abstraction available.
https://arxiv.org/abs/1711.08127
https://github.com/aspuru-guzik-group/DiffiQult

[mszep]

That's awesome! Definitely worth doing this first.