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Many recent density functionals are numerically unstable

Authors: S. Lehtola, and M.A.L. Marques

Ref.: J. Phys. Chem. 157, 174114 (2022)

Abstract: Most computational studies in chemistry and materials science are based on the use of density functional theory. Although the exact density functional is unknown, several density functional approximations (DFAs) offer a good balance of affordable computational cost and semi-quantitative accuracy for applications. The development of DFAs still continues on many fronts, and several new DFAs aiming for improved accuracy are published every year. However, the numerical stability of these DFAs is an often overlooked problem. In this work, we look at all 592 DFAs for three-dimensional systems available in Libxc 5.2.2 and examine the convergence of the density functional total energy based on tabulated atomic Hartree-Fock wave functions. We show that several recent DFAs, including the celebrated SCAN family of functionals, suffer from strong numerical instabilities that make the functionals unsuitable for high-precision studies. In fact, their convergence with respect to quadrature is impractically slow, requiring thousands of radial quadrature points to achieve reliable total energies. These results suggest that numerical stability should be a core consideration in the development of new density functionals.

Citations: 6 (Google scholar)

DOI: 10.1063/5.0121187

URL: arxiv.org

Bibtex:

@article{Lehtola_2022,
	doi = {10.1063/5.0121187},
	url = {https://doi.org/10.1063%2F5.0121187},
	year = 2022,
	month = {nov},
	publisher = {{AIP} Publishing},
	volume = {157},
	number = {17},
	pages = {174114},
	author = {Susi Lehtola and Miguel A. L. Marques},
	title = {Many recent density functionals are numerically ill-behaved},
	journal = {The Journal of Chemical Physics}
}