Many recent density functionals are numerically ill-behaved

TL;DR

This paper evaluates the numerical stability of 592 density functionals, revealing that many recent functionals, including the SCAN family, exhibit slow convergence requiring impractically large quadrature grids, which impacts their routine use.

Contribution

It provides a comprehensive assessment of the numerical behavior of a large set of density functionals, highlighting issues with their convergence and practical applicability.

Findings

Many recent DFAs show slow convergence with standard quadrature schemes.

The SCAN family of functionals requires thousands of radial points for accurate energies.

Standard quadrature grids are often insufficient for these functionals.

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 behavior 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, show impractically slow convergence with typically used numerical quadrature schemes, making these functionals unsuitable both for routine applications or high-precision studies, as thousands of radial quadrature points may be required to achieve sub-$\mu E_{h}$ accurate total energies for these unctionals, while standard quadrature grids like the SG-3 grid only contain $\mathcal{O}(100)$ radial quadrature points. These results are both a warning to users to lways check the sufficiency of the quadrature grid when adopting novel functionals, as well as a guideline to the theory community to develop better behaved density functionals.