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, 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.

Pure non-local machine-learned density functional theory for electron correlation

“…Of course, the work of Burke, Müller, Tuckermann, and co-workers on ML-based DFT is also highly pertinent 10 , 11 , 13 – 15 . Their most recent method focuses on the integrated prediction of both the valence electron density and the exchange-correlation energy 14 .…”

“…Their most recent method focuses on the integrated prediction of both the valence electron density and the exchange-correlation energy 14 . This work was originally aimed at accelerating the computation of established DFAs, but has very recently been extended to also learn corrections to higher-level methods like CCSD(T) 15 . The main difference to our work is their choice of density representation.…”

“…Furthermore, grid-based models are not in general size-extensive, particularly if they require the grid to be of constant size. Very recently, Burke and co-workers developed ML-based DFT models, which represent the density in a plane-wave basis 14 , 15 . These models have successfully been applied to real molecules, though they are still not size-extensive.…”

Dynamical strengthening of covalent and non-covalent molecular interactions by nuclear quantum effects at finite temperature

“…There have been many attempts to accurately learn molecular force fields by using mainly neural networks 65 – 69 and kernel-based models 70 – 77 , cf. also refs.…”

Machine learning dielectric screening for the simulation of excited state properties of molecules and materials

“…Another important advantage of the ML-derived dielectric screening is that it provides insight into the approximate screening parameters used in the derivation of hybrid functionals for time-dependent DFT (TDDFT) calculations, including dielectric-dependent hybrid (DDH) functionals. [44][45][46][47][48] We emphasize that the strategy adopted here is different in spirit from strategies that use ML to infer structure-property relationships [49][50][51][52][53][54][55][56][57] or relationships between computational and experimental data. 58 We do not seek to relate structural properties of a molecule or a solid to its absorption spectrum.…”