Concerning the Stability of the Negative IonsH−andLi−

Abstract

The unrestricted Hartree-Fock (UHF) wave functions for ${\mathrm{H}}^{-}$ and for ${\mathrm{Li}}^{-}$ have the $Z+1\mathrm{}\mathrm{th}$ electron at infinity, and thus have the same energy as the neutral atoms. That is, the stability of these negative ions is not accounted for by Slater determinant wave functions, not even if the orbitals are allowed to split. We show that the difficulty here is that the UHF wave functions do not have the proper spin symmetry. If the Slater determinant is spin-projected and the orbitals optimized after projection (to obtain what is called the GF wave function), these negative ions are predicted correctly to be stable. Since the GF wave function leads to an independent particle interpretation, we see that instantaneous polarization of the neutralatom orbitals by the $Z+1\mathrm{}\mathrm{th}$ electron is not crucial to the stability of these negative ions. From an analysis of the differences between the UHF and GF wave functions, we find that the key term leading to stability of the negative ions is an exchange term (particularly the nuclear attraction part of this term), just like the exchange term important in the valence-bond wave function of ${\mathrm{H}}_2$.