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Many recent density functionals are numerically ill-behaved.

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Many density functional approximations (DFAs) in computational chemistry exhibit slow convergence, requiring extensive numerical quadrature for accurate results. This study highlights the need to assess numerical behavior for practical applications of new functionals.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Density functional theory (DFT) is central to computational chemistry and materials science.
  • Density functional approximations (DFAs) balance accuracy and computational cost.
  • The numerical behavior of DFAs is often overlooked despite ongoing development.

Purpose of the Study:

  • To investigate the numerical convergence of 592 three-dimensional density functional approximations (DFAs).
  • To evaluate the suitability of recent DFAs, including the SCAN family, for practical computational studies.
  • To assess the impact of numerical quadrature schemes on DFA accuracy.

Main Methods:

  • Examined 592 DFAs from Libxc 5.2.2 for 3D systems.
  • Assessed energy convergence using tabulated atomic Hartree-Fock wave functions.
  • Analyzed the performance of standard numerical quadrature grids (e.g., SG-3) against required quadrature points.

Main Results:

  • Several recent DFAs, including SCAN, exhibit impractically slow convergence.
  • Achieving sub-μEh accuracy requires thousands of radial quadrature points for these functionals.
  • Standard quadrature grids are insufficient for many modern DFAs, necessitating high-precision studies.

Conclusions:

  • Users must verify quadrature grid sufficiency when employing novel DFAs.
  • The development community should prioritize DFAs with improved numerical behavior.
  • Slow convergence hinders the routine and high-precision application of advanced DFAs.