Exchange force for two-level systems such as LiH and H₃⁻

Abstract

Using the Dawson-March transformation, the Dirac density matrix γ(r, r') can be written in terms of the density amplitude √ρ(r) and a phase θ(r), where ρ(r)≡γ(r, r) is the ground-state electron density. Here, for systems such as LiH or H₃⁻, it is shown how the force −∂V(r)/∂r corresponding to the one-body potential V(r) can be written, given the ground-state density ρ(r) from a high-level ab initio calculation or a diffraction experiment. The Hartree-Fock ground-state densities for LiH and H₃⁻ are utilized to calculate approximate phase angles θ(r). Finally, for H₃⁻ the force −∂V(r)/∂r corresponding to V(r) is calculated.