skip to main content

Attention:

The NSF Public Access Repository (PAR) system and access will be unavailable from 11:00 PM ET on Friday, December 13 until 2:00 AM ET on Saturday, December 14 due to maintenance. We apologize for the inconvenience.


Title: 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.

 
more » « less
PAR ID:
10171392
Author(s) / Creator(s):
;
Publisher / Repository:
Nature Publishing Group
Date Published:
Journal Name:
Nature Communications
Volume:
11
Issue:
1
ISSN:
2041-1723
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Within density functional theory (DFT), adding a HubbardUcorrection can mitigate some of the deficiencies of local and semi-local exchange-correlation functionals, while maintaining computational efficiency. However, the accuracy of DFT+U largely depends on the chosen HubbardUvalues. We propose an approach to determining the optimalUparameters for a given material by machine learning. The Bayesian optimization (BO) algorithm is used with an objective function formulated to reproduce the band structures produced by more accurate hybrid functionals. This approach is demonstrated for transition metal oxides, europium chalcogenides, and narrow-gap semiconductors. The band structures obtained using the BOUvalues are in agreement with hybrid functional results. Additionally, comparison to the linear response (LR) approach to determining U demonstrates that the BO method is superior.

     
    more » « less
  2. Abstract

    The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity—the electron density—without resorting to multi-electron wave functions. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore. This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities. We cast the inverse DFT problem as a constrained optimization problem and employ a finite-element basis—a systematically convergent and complete basis—to discretize the problem. We demonstrate the accuracy and efficacy of our approach for both weakly and strongly correlated molecular systems, including up to 58 electrons, showing relevance to realistic polyatomic molecules.

     
    more » « less
  3. 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−1with 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-basedΔ-learning (learning only the correction to a standard DFT calculation, termedΔ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness ofΔ-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, thatΔ-DFT  facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails.

     
    more » « less
  4. Abstract

    Various methods going beyond density functional theory (DFT), such as DFT+U, hybrid functionals, meta-GGAs, GW, and DFT-embedded dynamical mean field theory (eDMFT), have been developed to describe the electronic structure of correlated materials, but it is unclear how accurate these methods can be expected to be when applied to a given strongly correlated solid. It is thus of pressing interest to compare their accuracy as they apply to different categories of materials. Here we introduce a novel paradigm in which a chosen set of beyond-DFT methods is systematically and uniformly tested on a chosen class of materials. For a first application, we choose the target materials to be the binary transition metal oxides FeO, CoO, MnO, and NiO in their antiferromagnetic phase and present a head-to-head comparison of spectral properties as computed using the various methods. We also compare with available experimental angle-resolved photoemission spectroscopy (ARPES), inverse-photoemission spectroscopy, and with optical absorption. For the class of compounds studied here, we find that both B3LYP and eDMFT reproduce the experiments quite well, with eDMFT doing best, in particular when comparing with the ARPES data.

     
    more » « less
  5. The redox potential is a powerful thermodynamic and kinetic tool used to predict numerous chemical and biochemical mechanisms. However, despite the improving predictive power of density functional theory (DFT), chemically accurate theoretical redox potentials are often difficult to achieve with DFT. For example, calculated redox potentials are sensitive to density functional choice and often fall short of the desired accuracy. Thus, ranges of errors for computed redox potentials between different density functionals can become quite large. The current study presents a cost-effective protocol that utilizes effective error cancellation schemes in order to accurately predict the redox potentials of a wide range of organic molecules. This computational protocol, called CBH-Redox, is an extension of the connectivity-based hierarchy (CBH) method, and produces thermochemical data with near-G4 accuracy. Herein, we test the CBH-Redox protocol against both experimental and G4 reference values and compare these results to DFT alone. Considering 46 C, O, N, F, Cl, and S atom-containing molecules, when using the CBH-Redox correction scheme, the MAEs for all eight density functionals tested are within the 0.09 V target accuracy versus both experiment and G4. Moreover, CBH-Redox achieves an impressive accuracy, with a MAE of 0.05 V or below when compared to G4 for six of the eight density functionals tested. In addition, when the CBH correction is applied, the error range across all functionals tested decreases from 0.12 V to about 0.05 V versus G4, and from 0.13 V to 0.04 V versus experiment. 
    more » « less