Existence of minimisers for Dirac-Konh-Sham models in quantum chemistry

Long Meng (1)

1 Dipartimento di Matematica "Tullio Levi-Civita"

This article is concerned with the mathematical analysis of the Dirac-Kohn-Sham models in the local density approximation (LDA) frameworks. The difficulty is that the functional is not of class $C^{1,1}$, no critical point theory can be used to handle with this kind of problem. Nevertheless, the existence of solutions of Dirac-Koshn-Sham model can be solved in the spherical symmetric situation. And we redefine the ground state on the set of solutions. Based on an energy criteria, we can prove the existence of minimizers.

Domaines: Physique mathématique [math-ph]

Long Meng. Existence of minimisers for Dirac-Konh-Sham models in quantum chemistry. 2021. ⟨hal-03090701v2⟩