The maximal negative ion of molecules in Schr\"odinger, Hartree-Fock, and M\"uller theories

TL;DR

This paper establishes new bounds on the maximum number of electrons that molecules can bind in Schrödinger, Hartree-Fock, and M"uller theories, improving previous results and confirming ionization conjectures.

Contribution

It provides improved bounds for electron binding in molecules and proves ionization conjectures in Hartree-Fock and M"uller theories.

Findings

Bound $N_c < ext{min}igrace 2Z+1, 1.22Z + 3Z^{1/3}ig\}$ in Schrödinger theory.

Proved ionization bounds $N_c extless Z + CK R_ ext{min}^{-3}$ in Hartree-Fock and M"uller theories.

Extended Lieb's and Nam's results from atoms to molecules.

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 Schr\"odinger 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 M\"uller theories are proved, i.e., $N_c \le Z + CKR_\mathrm{min}^{-3}$, where $R_\mathrm{min}$ is the minimal distance between atoms and $C$ is a universal constant.