Since the gradients are computed with jax, the library can be used to differentiate with respect to all inputs including nuclear charge and basis set parameters (exponents and contraction coefficients). I agree that computing gradients for the nuclear charges could be interesting in the context of molecular design.

But for the colab demo I thought that sticking to nuclear positions (i.e atomic forces) would be easier to visualize.

In a nutshell, the only approximation in Hartree Fock is the assumption that the electronic wave function has a very specific form. Namely, that it is a Slater determinant of orbitals, and that each orbital is a linear combination of atomic orbitals from a fixed basis set. The linear coefficients of the orbitals are then solved for via the (exact) variational method.

Of course, the true wave function is generally not a Slater determinant. In particular, electrons in a Slater determinant with different spins are uncorrelated.

The standard approach to resolving this is density functional theory. In that model, the main approximation is the choice of an “exchange correlation functional” which approximates the electron exchange and correlation energy. The choice of a functional is unfortunately a dark art in the sense that they can only be evaluated empirically rather than from first principles.

The classic reference for Hartree Fock is Modern Quantum Chemistry by Szabo and Ostland: https://books.google.com/books/about/Modern_Quantum_Chemistr...

It is very well written and I highly recommend it.

I also wrote up some notes here: https://www.daniellowengrub.com/blog/2025/07/26/scf

The short answer is yes, but either memory (if the electron integrals are cached) or runtime (if they are not cached) currently scales like O(n^4) where n is the number of atoms.

In cached mode, it can currently jit compile the graph for molecules of around 10 atoms in ~5 minutes on one T4 gpu. Once the graph is compiled, the actual geometry optimization only takes a few seconds.

I’m working on optimizations that improve the scaling behavior (such as density fitting) with the goal of achieving similar or even better performance for molecules with ~50 atoms.

Thanks!

Theoretically yes, but the method that is currently implemented (Hartree Fock) is notoriously inaccurate for molecular interactions. For example it does not predict the Van Der Waals force between water molecules.

I’m planning to add support for an alternative method called density functional theory which gives better results for molecular interaction.

In quantum chemistry, you decide where the bonds should be drawn. Internally, it's all an electron density field. So yes, you can model chemical reactions, for example by constraining the distance between two atoms, and letting everything else reach an equilibrium.

Thanks!