Machine learning accurate exchange and correlation functionals of the electronic density

Abstract

Density functional theory (DFT) is the standard formalism to study the electronic structure of matter at the atomic scale. In Kohn-Sham DFT simulations, the balance between accuracy and computational cost depends on the choice of exchange and correlation functional, which only exists in approximate form. Here, we propose a framework to create density functionals using supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to lift the accuracy of baseline functionals towards that provided by more accurate methods while maintaining their efficiency. We show that the functionals learn a meaningful representation of the physical information contained in the training data, making them transferable across systems. A NeuralXC functional optimized for water outperforms other methods characterizing bond breaking and excels when comparing against experimental results. This work demonstrates that NeuralXC is a first step towards the design of a universal, highly accurate functional valid for both molecules and solids.

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

“…Work is in progress to further develop a strategy to develop parameters entering hybrid DFT functionals using machine learning. 103…”

Perspective on integrating machine learning into computational chemistry and materials science

“…46 An alternative to the ∆-learning approach is transfer learning, 88 where a model is trained on data from a low level of theory and retrained with less data points of a more accurate method. A rule for determination of the number of data points needed in consecutive ∆-learning approaches that takes computational cost and prediction accuracy into account is proposed by Dral et al 89 . Many studies use about 10% of the original training data for ∆-learning 76,78,90,91 and transfer learning.…”

“…Besides ML models being powerful to accelerate the computation of target properties, they can also be used to predict correlated total energies of molecules based on Hartree-Fock or DFT results. Examples are NeuralXC, 107 DeepHC, 108 and OrbNet 109 which provide NN representations based on atomic orbital features.…”

“…Alternatively, an ML model may predict the electron density or a density functional. 16,83,107,124 A recent example of a deep learning framework to predict the electronic density or properties related to the density of a reference DFT method is DeepDFT. 125 A symmetryadapted method that considers geometrical covariance was proposed by Fabrizio et al 126 and Grisafi et al 127 to learn the charge density of different organic molecules via Gaussian Process Regression (GPR) models.…”

Computation sparks chemical discovery

“…Dick and Fernandez-Serra in Machine learning accurate exchange and correlation functionals of the electronic density tackle this problem by introducing a fully machine-learned functional that depends explicitly on the electronic density and implicitly on the atomic positions 3 . It approaches the accuracy of high level quantum chemistry methods at an affordable computational cost.…”