The ionization and generalized ionization conjectures
OpenAI research collection · 3 manuscripts · Source checked 2026-10-19
OpenAI's result summary
For the full nonrelativistic Coulomb model with two electron spin states, proves that a molecule with M fixed nuclei of charges at least one and total charge Z strictly binds at most Z+CM electrons. Neutral-atom first ionization energies and radii containing all but an expected half-electron have universal positive upper and lower bounds. The energy cost of removing m electrons has Thomas–Fermi asymptotics as m→∞ and Z/m→∞; neutral-atom outer radii have the corresponding iterated-limit asymptotics, taking Z→∞ first.
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MANUSCRIPT 01
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…
Full source abstract
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.
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Generalized ionization energies for full Coulomb atoms
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_{TF}m^{7/3} whenever m→∞ and Z/m→∞, with the Thomas–Fermi constant in atomic units. We also obtain both conjectured iterated limits.
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Generalized outer-electron radii of neutral Coulomb atoms
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 (81π^2/2)^{1/3}m^{-1/3} as m…
Full source abstract
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 (81π^2/2)^{1/3}m^{-1/3} as m tends to infinity.
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