02/10/2025 –, Salle café
Langue: Français
We present a Julia implementation of extended Kohn-Sham models (LDA/LSDA) for computing ground states of atoms and ions using high-precision finite element methods. Originally developed to investigate the existence of negative ions, the code also serves as a versatile tool for testing new density functionals, studying numerical precision issues.
This package aims to compute the ground state of atoms and ions using extended Kohn–Sham models (LDA/LSDA). These models require solving a nonlinear eigenvalue PDE in 3D, where the nonlinearity comes from a potential depending on a finite number of eigenfunctions. As is standard in computational chemistry, a fixed-point iterative scheme is used, alternating with the resolution of the eigenvalue problem.
Thanks to spherical symmetry and the use of spherical harmonics, the eigen value problem can be reduced to a family of radial equations in 1D. The package implements a high-precision finite element method for solving these equations, using polynomials of degree up to 20 on geometric meshes. This allows for highly accurate results with fewer mesh points, making it more efficient than low-order approaches with refined meshes.
The code supports both double and quadruple floating-point precision. Such high precision is essential to resolve subtle numerical questions left open in the literature. For example, in certain extended Kohn–Sham models, it remains unclear whether the outermost orbital energies for some atoms are exactly zero or merely very small but negative — a distinction that can now be investigated numerically.
The package includes support for a wide range of exchange-correlation functionals and offers two iterative solvers: ODA and a quadratic method.
Link of the code : https://github.com/Theozeud/AtomicKohnSham
Doctorant en première année sous la direction d'Éric Cancès et Mathieu Lewin