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We developed a stable Kohn-Sham (KS) inversion method to create accurate exchange-correlation potentials from electron densities. This approach, using Gaussian basis functions, offers computational efficiency and numerical stability for quantum chemistry calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Kohn-Sham (KS) theory is fundamental to density-functional theory (DFT).
  • Accurate exchange-correlation potentials are crucial for reliable DFT predictions.
  • Previous KS inversion methods faced numerical stability challenges with standard basis sets.

Purpose of the Study:

  • To develop a numerically stable Kohn-Sham (KS) inversion approach for constructing exchange-correlation potentials.
  • To enable the generation of accurate potentials from given electron densities using Gaussian basis functions.
  • To assess the method's performance on challenging atomic and molecular systems.

Main Methods:

  • An iterative KS inversion procedure utilizing linear response to update potentials.
  • Representation of all quantities (orbitals, potentials, response functions) using Gaussian basis functions.
  • Preprocessing of the auxiliary basis for improved numerical stability with standard basis sets.

Main Results:

  • The KS inversion method demonstrates numerical stability, even with standard basis sets.
  • Benchmark-quality potentials were obtained for stretched hydrogen molecules.
  • Excellent agreement between the random phase approximation (RPA) correlation potential and the KS-inverted potential for CO molecule was observed, suggesting RPA correlation potentials approximate exact ones.

Conclusions:

  • The proposed KS inversion method provides a stable and efficient way to generate accurate exchange-correlation potentials.
  • This method is valuable for creating benchmark potentials and has potential applications in quantum embedding and subsystem DFT methods.
  • The findings support the use of RPA correlation potentials as good approximations to exact ones.