Stable and Accurate Orbital-Free DFT 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. Given that decades of theoretical work have so far failed to produce this elusive exact energy functional promising great computational savings, it is 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 while also converging to meaningful electron densities. Augmenting the training data with densities obtained from perturbed potentials proved key to these advances. Altogether, we are now closer than ever to fulfilling Hohenberg and Kohn's promise, paving the way for more efficient calculations in large molecular systems.