Abstract

By regarding a liquid metal as a mixture of electrons and nuclei, the quantal hypernetted-chain (QHNC) equations have been derived from the density-functional theory. These integral equations for the ion-ion and electron-ion radial distribution functions (RDFS) can give the electron distribution function of a neutral pseudoatom rho (r) and the effective interionic potential upsilon eff(r) self-consistently, using the atomic number ZA as the only input data. The authors apply these equations to liquid potassium at 338 K. The ion-ion RDF gII(r) and structure factor SII(Q) obtained from QHNC agree with the experimental results from X-ray diffraction very well. The electron-ion RDF is calculated to be self-consistent with the effective interionic potential giving the ion-ion RDF in the QHNC framework. For comparison, the results of the pseudopotential method with Ashcroft's model potential (core radius rC=1.225 AA) are also shown; this method can give the same ionic structures, but it provides slightly different electron distributions from the QHNC results. These differences between the QHNC and pseudopotential methods in the electron distribution are not observed in liquid sodium, and are attributed to the fact that the Ashcroft potential omega bAC(r) cannot appropriately approximate the direct correlation function CeI(r), which plays the role of a non-linear pseudopotential.

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