Quantum chemical accuracy from density functional approximations via machine learning

Mihail Bogojeski, Leslie Vogt-Maranto, Mark E. Tuckerman, Klaus Robert Müller, Kieron Burke

Research output: Contribution to journalArticlepeer-review


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, density-based 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.

Original languageEnglish (US)
Article number5223
JournalNature communications
Issue number1
StatePublished - Dec 1 2020

ASJC Scopus subject areas

  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology
  • General
  • General Physics and Astronomy


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