Determination of the pair potential and the ion-electron pseudopotential for aluminum from experimental structure-factor data for liquid aluminum

A method of inverting a given structure factor ${\mathrm{}\left[S\right(k\left)\right]}_{\mathrm{expt}}$ of a liquid metal using a hypernetted-chain equation containing bridge-diagram contributions is presented. Starting from parametrized local pseudopotential and a parametrized model local field (or a theoretical local field), a pair potential is constructed. The $S\left(k\right)\mathrm{}$ calculated from it is fitted to the given ${\mathrm{}\left[S\right(k\left)\right]}_{\mathrm{expt}}$. The method is first applied to a molecular-dynamics-generated $S\left(k\right)\mathrm{}$ derived from an ab initio aluminum potential and shown to yield the pair potential, the pseudopotential, and the charge density in excellent quantitative agreement with the original ab initio potential and other quantities. The method is then applied to the experimental $S\left(k\right)\mathrm{}$ of aluminum from x-ray data at 943 K. The Al-Al pair potential, Al-electron pseudopotential, and electron charge densities as well as the electron-gas response function (i.e., the model local field) are obtained self-consistently, to within the accuracy of the experimental data. The calculated electrical resistivity is in excellent agreement with experiment. These investigations provide a comparative examination of the electron-gas local fields of Geldart-Taylor, Vashishta-Singwi, Ichimaru-Utsumi, and the density-functional local-density approximation. The hard-sphere parameter defining the bridge term is found to be essentially the same for the different ion-ion potentials determined from all but one of the different local fields, thus supporting the "universality" hypothesis of Rosenfeld and Ashcroft.