Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms

We prove that a molecule with $M$ fixed nuclei of real charges at least one and total nuclear charge $Z$ strictly binds at most $Z+CM$ electrons, where $C$ is universal. The result holds for the full nonrelativistic Coulomb Hamiltonian with two spin states and arbitrary distinct nuclear positions. For neutral atoms with integer nuclear charge $Z\ge1$, the first ionization energy and, for every ground state, the radius outside which one half of an electron remains are each bounded above and below by positive universal constants.