Exchange force for two-level systems such as LiH and

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 H 3 - , 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 H 3 - are utilized to calculate approximate phase angles θ(r). Finally, for H 3 - the force −∂V(r)/∂r corresponding to V(r) is calculated.