*Ab initio *methods, such as coupled-cluster, routinely produce much higher accuracy, but
computational costs limit their application to small molecules. We create density functionals
from coupled-cluster energies, based only on DFT densities, via machine learning. These functionals attain quantum chemical accuracy (errors below 1 kcal/mol). Moreover, density-based
∆-learning (learning only the correction to a standard DFT calculation, ∆-DFT) significantly
reduces the amount of training data required. We demonstrate these concepts for a single water
molecule, and then illustrate how to include molecular symmetries with ethanol. Finally, we highlight the robustness of ∆-DFT by correcting DFT simulations of resorcinol on the fly to obtain
molecular dynamics (MD) trajectories with coupled-cluster accuracy. Thus ∆-DFT opens the
door to running gas-phase MD simulations with quantum chemical accuracy, even for strained
geometries and conformer changes where standard DFT is quantitatively incorrect.