Abstract
We show that the molecular relativistic Thomas–Fermi–Weizsäcker functional consisting of atoms of atomic numbers Z 1, …, Z k has a minimizer, if the particle number N is constrained to a number less or equal to the total nuclear charge Z ≔ Z 1 + ⋯ + Z K . Moreover, there is no minimizer, if the particle number exceeds 2.56Z. This gives lower and upper bounds on the maximal ionization of heavy atoms.
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