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1.1 MATHMATICS, 1.3 PHYSICAL SCIENCES
We study the standard and extended Kohn-Sham models for quasi-relativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator (see article) . For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge Z of K nuclei is greater than N-1 and that Z is smaller than a critical charge (see article).
Argaez, C., Melgaard, M.: Existence of a Minimizer for the Quasi-Relativistic Kohn-Sham Model. Electronic Journal of Differential Equations, Vol 2012 (2012), no. 18, pp 1-20.