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Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors

Xiangyun Lei and Andrew J. Medford
Phys. Rev. Materials 3, 063801 – Published 12 June 2019
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Abstract

In this work we explore the potential of a data-driven approach to the design of exchange-correlation (xc) functionals. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density to form a feature space to represent local electronic environments and neural networks to map the features to the exchange-correlation energy density. These features are orbital free, and provide a systematic route to including information at various length scales. This work shows that convolutional descriptors are theoretically capable of an exact representation of the electron density, and proposes Maxwell-Cartesian spherical harmonic kernels as a class of rotationally invariant descriptors for the construction of machine learned functionals. The approach is demonstrated using data from the B3LYP functional on a number of small molecules containing C, H, O, and N along with a neural network regression model. The machine learned functionals are compared to standard physical approximations and the accuracy is assessed for the absolute energy of each molecular system as well as formation energies. The results indicate that it is possible to reproduce the exchange-correlation portion of B3LYP formation energies to within chemical accuracy using orbital-free descriptors with a spatial extent of 0.2 Å. The findings provide empirical insight into the spatial range of electron exchange, and suggest that the combination of convolutional descriptors and machine learning regression models is a promising framework for xc functional design, although challenges remain in obtaining training data and generating models consistent with pseudopotentials.

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  • Received 31 January 2019
  • Revised 24 April 2019

DOI:https://doi.org/10.1103/PhysRevMaterials.3.063801

©2019 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalInterdisciplinary PhysicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Xiangyun Lei and Andrew J. Medford*

  • School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30318, USA

  • *ajm@gatech.edu

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Issue

Vol. 3, Iss. 6 — June 2019

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