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 ≥ 1, 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.

We prove the energy part of the generalized ionization conjecture for full nonrelativistic Coulomb atoms with two electron spin states. The energy needed to remove m electrons is asymptotic to $a_{\mathrm{TF}}m^{7/3}$ whenever $m\to\infty$ and $Z/m\to\infty$, with the Thomas–Fermi constant in atomic units. We also obtain both conjectured iterated limits.

We prove the radius part of the generalized ionization conjecture for neutral nonrelativistic Coulomb atoms with two spin states. For every choice of ground states, the upper and lower large-nuclear-charge limits of the radius defined by an expected exterior electron mass m are both asymptotic to $(81\pi^2/2)^{1/3}m^{-1/3}$ as m tends to infinity.