{"id":"openai-math/Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms","pdf":"https://github.com/openai/math/blob/main/preprints/Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026","tags":["quantum-chemistry","coulomb-systems","schrodinger-operators","mathematical-physics"],"score":0,"title":"Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms","domain":"Mathematical physics","family":"263","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The ionization and generalized ionization conjectures"}