Binding in pair potentials of liquid simple metals from nonlocality in electronic kinetic energy

An explicit expression is obtained for the pair potential φ(R) in liquid simple metals from low-order density-gradient theory when the superposition of single-center displaced charges is employed. Corrections are thereby explicitly exhibited to the local Thomas-Fermi result ${\mathrm{\phi }}_{\mathrm{TF}}$(R) from second- and fourth-order inhomogeneity corrections Δ${\mathit{T}}_2$(R) and Δ${\mathit{T}}_4$(R) to the Thomas-Fermi electronic kinetic-energy change Δ${\mathit{T}}_{\mathrm{TF}}$(R). The important point to emphasize is that, in each order, the potential V(R/2) and displaced charge Δ(R/2) of a single screened ion at the midpoint of the metallic bond completely determines the pair potential in the density-gradient theory. These approximate results are illustrated by explicit calculations on liquid Na and liquid Be near their respective freezing points. While the pair potentials obtained by including Δ${\mathit{T}}_2$(R)+Δ${\mathit{T}}_4$(R) are major improvements over the linear response result, the remaining nonlocal corrections to the total kinetic-energy change ΔT(R) are substantial, as again demonstrated by explicit results for Na and Be. The importance of further study of a possible functional relation between ΔT(R)-Δ${\mathit{T}}_{\mathrm{TFG}}$(R) and the potential V(R/2) at the midpoint of the metallic bond is finally emphasized.