Existence of minimizers for Kohn–Sham within the local spin density approximation

Abstract

The purpose of this article is to extend the work by Anantharaman and\nCanc\\`es [1], and prove the existence of minimizers for the spin-polarized\nKohn-Sham model in the presence of a magnetic field within the local spin\ndensity approximation. We show that for any magnetic field that vanishes at\ninfinity, the existence of minimizers is ensured for neutral or positively\ncharged systems. The proof relies on classical concentration-compactness\ntechniques.\n