EDIT EDIT: I realized I was more answering @mdav2 than OP. Sorry about the confusion.
There is JuliaAtoms (disclaimer: I’m the author): https://juliaatoms.github.io/dev/index.html
It is written mainly for atomic physics, but with wider applicability in mind for the future. You could benefit from EnergyExpresions.jl that sets up symbolic energy expressions between lists of Slater determinants, which you then have to interpret, depending on what kind of orbitals you are working with. For atoms, the interpretation is done by AngularMomentumAlgebra.jl. For molecules, you need some implementation of molecular orbitals (and preferrably also some group theory). I will add that in the future, but it is not high on my priority list.
For SCF there is SCF.jl, which is also independent of which quantum system you study. So far it only works reliably on the Hartree–Fock level. It performs linear optimization by solving eigensystems for the different orbitals using ArnoldiMethod.jl. After a certain level of convergence is reached, it switches to non-linear optimization using BFGS from Optim.jl
(EDIT: Nothing from JuliaAtoms is registered as a package yet, since I don’t feel the test coverage is high enough.)
However, if you’re learning how to write quantum chemistry codes (as I am), I think it is more useful for you to write the basic building blocks yourself, to understand the details on all the levels. If you want to be productive in calculations, it would conversely be more efficient to use an already existing code (MOLPRO, &c), since it is really a multi-year (some decades) effort.
CC @antoine-levitt could have other input; I think he is also working in electronic structure