Quantum chemical accuracy from density functional approximations via machine learning
Abstract
Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry,
but accuracies for many molecules are limited to 2-3 kcal ⋅ mol−1 with presently-available
functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher
accuracy, but computational costs limit their application to small molecules. In this paper, we
leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching
quantum chemical accuracy (errors below 1 kcal ⋅ mol−1
) on test data. Moreover, densitybased Δ-learning (learning only the correction to a standard DFT calculation, termed Δ-DFT )
significantly reduces the amount of training data required, particularly when molecular
symmetries are included. The robustness of Δ-DFT is highlighted by correcting “on the fly”
DFT-based molecular dynamics (MD) simulations of resorcinol (C6H4(OH)2) to obtain MD
trajectories with coupled-cluster accuracy. We conclude, therefore, that Δ-DFT facilitates
running gas-phase MD simulations with quantum chemical accuracy, even for strained
geometries and conformer changes where standard DFT fails.