Nonlocal Machine-Learned Exchange Functional for Molecules and Solids

Abstract

The design of better exchange-correlation functionals for Density Functional Theory (DFT) is a central challenge of modern electronic structure theory. However, current developments are limited by the mathematical form of the functional, with efficient semilocal functionals being inaccurate for many technologically important systems and the more accurate hybrid functionals being too expensive for large solid-state systems due to the use of the exact exchange operator. In this work, we use machine learning combined with exact physical constraints to design an exchange functional that is both orbital-dependent and nonlocal, but which can be evaluated at roughly the cost of semilocal functionals and is significantly faster than hybrid DFT in plane-wave codes. By training functionals with several different feature sets, we elucidate the roles of orbital-dependent and nonlocal features in learning the exchange energy and determine that both types of features provide vital and independently important information to the model. Having trained our new exchange functional with an expressive, nonlocal feature set, we substitute it into existing hybrid functionals to achieve hybrid-DFT accuracy on thermochemical benchmark sets and improve the accuracy of band gap predictions over semilocal DFT. To demonstrate the scalability of our approach as well as the practical benefits of improved band gap prediction, we compute charged defect transition levels in silicon using large supercells. Due to its transferability and computational efficiency for both molecular and extended systems, our model overcomes the cost-accuracy trade-off between semilocal and hybrid DFT, and our general approach provides a feasible path toward a universal exchange-correlation functional with post-hybrid DFT accuracy and semilocal DFT cost.

34 pages, 10 figures, 5 tables (main body); 17 pages, 4 figures, 17 tables (supporting information); 51 pages combined. v2 changes: reformatting, more point defect results, figure revisions, new SI figures, revised theory section. v3 changes: improved clarity and organization. v4 changes: new data for Fig. 8a, clearer exposition in the main text, and additional figures in the SI

References in corpus (30)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Van der Waals density functionals applied to solids
• Optimized norm-conserving Vanderbilt pseudopotentials
• A real-space grid implementation of the Projector Augmented Wave method
• Efficient implementation of a van der Waals density functional: Application to double-wall carbon nanotubes
• Nonlocal van der Waals density functional: The simpler the better
• Recent developments in the PySCF program package
• van der Waals forces in density functional theory: The vdW-DF method
• Understanding Band Gaps of Solids in Generalized Kohn-Sham Theory
• Electrostatics-based finite-size correction for first-principles point defect calculations
• More-Realistic Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme
• Adaptively Compressed Exchange Operator
• Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space
• Efficient nonparametric $n$-body force fields from machine learning
• The derivative discontinuity of the exchange-correlation functional
• Orbital-Free Density Functional Theory Implementation with the Projector Augmented-Wave Method
• Learning the exchange-correlation functional from nature with fully differentiable density functional theory
• DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory
• Design and Analysis of Machine Learning Exchange-Correlation Functionals via Rotationally Invariant Convolutional Descriptors
• Predictive Power of the Exact Constraints and Appropriate Norms in Density Functional Theory
• Bayesian Force Fields from Active Learning for Simulation of Inter-Dimensional Transformation of Stanene
• Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based $Ab$ $Initio$ Molecular Dynamics I: Theory, Algorithm, and Performance
• Nonlocal Pseudopotential Energy Density Functional for Orbital-Free Density Functional Theory
• Accurate non-empirical range-separated hybrid van der Waals density functional for complex molecular problems, solids, and surfaces
• Machine learning density functionals from the random-phase approximation
• DeePKS+ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials
• Faster Exact Exchange in Periodic Systems using Single-precision Arithmetic
• Data-driven and constrained optimization of semi-local exchange and non-local correlation functionals for materials and surface chemistry
• Simple and accurate exchange energy for density functional theory

Cited by in corpus (4)

• Bridging electronic and classical density-functional theory using universal machine-learned functional approximations
• Multi-channel machine learning based nonlocal kinetic energy density functional for semiconductors
• Shifting sands of hardware and software in exascale quantum mechanical simulations
• Neural network distillation of orbital dependent density functional theory