“Pushing the Frontiers of Density Functionals by Solving the Fractional Electron Problem”, James Kirkpatrick, Brendan McMorrow, David H. P. Turban, Alexander L. Gaunt, James S. Spencer, Alexander G. D. G. Matthews, Annette Obika, Louis Thiry, Meire Fortunato, David Pfau, Lara Román Castellanos, Stig Petersen, Alexander W. R. Nelson, Pushmeet Kohli, Paula Mori-Sánchez, Demis Hassabis, Aron J. Cohen2021-12-09 (neural net, science; similar)⁠:

Improving DFT with deep learning: In the past 30 years, density functional theory (DFT) has emerged as the most widely used electronic structure method to predict the properties of various systems in chemistry, biology, and materials science. Despite a long history of successes, state-of-the-art DFT functionals have crucial limitations. In particular, substantial systematic errors are observed for charge densities involving mobile charges and spins.

Kirkpatrick et al 2021 developed a framework [DM21] to train a deep neural network on accurate chemical data and fractional electron constraints (see the Perspective by Perdew [see also Lowe; Quanta]). The resulting functional outperforms traditional functionals on thorough benchmarks for main-group atoms and molecules.

The present work offers a solution to a long-standing critical problem in DFT and demonstrates the success of combining DFT with the modern machine-learning methodology.

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Density functional theory describes matter at the quantum level, but all popular approximations suffer from systematic errors that arise from the violation of mathematical properties of the exact functional.

We overcame this fundamental limitation by training a neural network on molecular data and on fictitious systems with fractional charge and spin.

The resulting functional, DM21 (DeepMind 21), correctly describes typical examples of artificial charge delocalization and strong correlation and performs better than traditional functionals on thorough benchmarks for main-group atoms and molecules. DM21 accurately models complex systems such as hydrogen chains, charged DNA base pairs, and diradical transition states.

More crucially for the field, because our methodology relies on data and constraints, which are continually improving, it represents a viable pathway toward the exact universal functional.

See Also:

• “E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials”

• “Universal quantum control through deep reinforcement learning”

• “Accurate prediction of protein structures and interactions using a 3-track network”

• “Fourier Neural Operator for Parametric Partial Differential Equations”

• “Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning”

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