The maximal negative ion of molecules in Schrödinger, Hartree-Fock, and Müller theories

Abstract

Bounds are studied for the maximum number, $N_c$, of electrons that can be bound to $K$ atoms of the total nuclear charge $Z$. It is proved that $N_c<\min \{2Z+1,1.22Z+3Z^{1/3}\}$ in Schrödinger theory. This improves Lieb's bound $N_c<2Z+K$ and extends Nam's results for an atom to the molecule. Moreover, the ionization conjectures for the molecules in Hartree-Fock and Müller theories are proved, i.e., $N_c\le Z+CK{R}_{\min }^{-3}$, where $R_{\min }$ is the minimal distance between atoms and $C$ is a universal constant.

The proof is incorrect