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Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory

Authors: J. Schmidt, C.L. Benavides-Riveros, and M.A.L. Marques

Ref.: J. Phys. Chem. Lett. 10, 6425-6431 (2019)

Abstract: We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and potential. This functional is extremely non-local, but retains the computational scaling of traditional local or semi-local approximations. It therefore holds the promise of solving some of the delocalization problems that plague density-functional theory, while maintaining the computational efficiency that characterizes the Kohn-Sham equations. Furthermore, by using automatic differentiation, a capability present in modern machine-learning frameworks, we impose the exact mathematical relation between the exchange-correlation energy and the potential, leading to a fully consistent method. We demonstrate the feasibility of our approach by looking at one-dimensional systems with two strongly-correlated electrons, where density-functional methods are known to fail, and investigate the behavior and performance of our functional by varying the degree of non-locality.

Citations: 38 (Google scholar)

DOI: 10.1021/acs.jpclett.9b02422

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Bibtex:

@article{Schmidt_2019,
	doi = {10.1021/acs.jpclett.9b02422},
	url = {https://doi.org/10.1021%2Facs.jpclett.9b02422},
	year = 2019,
	month = {oct},
	publisher = {American Chemical Society ({ACS})},
	volume = {10},
	number = {20},
	pages = {6425--6431},
	author = {Jonathan Schmidt and Carlos L. Benavides-Riveros and Miguel A. L. Marques},
	title = {Machine Learning the Physical Nonlocal Exchange{\textendash}Correlation Functional of Density-Functional Theory},
	journal = {The Journal of Physical Chemistry Letters}
}