Differentiable programming and density matrix based Hartree-Fock method

Differentiable programming is an emerging programming paradigm that allows people to take derivative of an output of arbitrary code snippet with respect to its input. It is the workhorse behind several well known deep learning frameworks, and has attracted significant attention in scientific machine learning community. In this paper, we introduce and implement a density matrix based Hartree-Fock method that naturally fits into the demands of this paradigm, and demonstrate it by performing fully variational ground state calculation on several representative chemical molecules.