Nuclear gradients: Forces

[jackbaker1001]

Implementing ionic forces in Grad DFT would be useful as this provides information beyond the total energy and density for training neural functionals. There is potential here to strongly improve generalization performance of our models.

There are two ways to proceed here:

(1) Auto-diff computation of forces. This would also require a differentiable implementation h1e and the ERI's as these quantities evolve with the nuclear positions.

(2) Direct implementation of the Hellman-Feynmann theorem, with additional Pulay forces (a must-have since we are using a local basis).

Route 1 will probably take longer but comes with the benefit of having access to other nuclear gradients (like stresses for example).