Stable and accurate orbital-free density functional theory powered by machine learning

Hohenberg and Kohn have proven that the electronic energy and the
one-particle electron density can, in principle, be obtained by minimizing
an energy functional with respect to the density. While decades of
theoretical work have produced increasingly faithful approximations to
this elusive exact energy functional, their accuracy is still insufficient
for many applications, making it reasonable to try and learn it
empirically. Using rotationally equivariant atomistic machine learning, we
obtain for the first time a density functional that, when applied to the
organic molecules in QM9, yields energies with chemical accuracy relative
to the Kohn-Sham reference while also converging to meaningful electron
densities. Augmenting the training data with densities obtained from
perturbed potentials proved key to these advances. This work demonstrates
that machine learning can play a crucial role in narrowing the gap between
theory and the practical realization of Hohenberg and Kohn’s vision,
paving the way for more efficient calculations in large molecular systems.