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 φTF(R) from second- and fourth-order inhomogeneity corrections {Δ}T₂(R) and {Δ}T₄(R) to the Thomas-Fermi electronic kinetic-energy change {Δ}TTF(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}T₂(R)+{Δ}T₄(R) are major improvements over the linear response result, the remaining nonlocal corrections to the total kinetic-energy change {Δ}T(R) are substantial, as again demonstrated by explicit results for Na and Be. The importance of further study of a possible functional relation between {Δ}T(R)-{Δ}TTFG(R) and the potential V(R/2) at the midpoint of the metallic bond is finally emphasized.