  We show that the molecular relativistic Thomas-Fermi-Weizs\"acker 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 $2.56 Z$. This gives lower and upper bounds on the
maximal ionization of heavy atoms.
