MATHPH
In the literature: open
Excess charge of molecules bounded by a constant per nucleus
In plain words
A molecule with several nuclei can also hold extra electrons. Show that the number of extra electrons is at most a fixed constant times the number of nuclei, whatever the nuclear charges and positions.
Precise statement
For $K$ static nuclei with charges $Z_1, ..., Z_K$ at positions $R_1, ..., R_K$, $Z_{\mathrm{tot}} = \sum_k Z_k$, and $N$ electrons with Coulomb interactions, let $N_c$ be the largest N for which the electronic ground state is bound. Prove $N_c \le Z_{\mathrm{tot}} + C K$ with C independent of the Z_k, R_k and K, or give a counterexample family.
What would settle it
A proof of the bound uniform in nuclear charges and positions, or an explicit configuration violating it.
Status in the literature
Lieb's 1984 bound $N_c < 2 Z_{\mathrm{tot}} + K$ holds for all nuclear positions.