Effective interionic interaction in liquid metals: liquid metallic hydrogen

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Abstract
A formula for an effective interionic interaction in a liquid metal is derived by means of the density-functional method. The effective interaction is described in terms of the direct correlation function (DCF) of an electron-ion mixture: the electron-electron DCF Cee and the electron-ion DCF Cel. In this formula, the influence of ions on the exchange-correlation effect for electrons can be introduced appropriately through the DCF Cee, which involves the local-field correction (LFC) Gee in the presence of ions, and the non-linear effects are taken into account by the DCF Cel, which plays the role of a 'non-linear' pseudopotential. Also, an expression for the internal energy of a perfectly ionised electron-ion mixture is derived by following the usual pseudopotential method with a modification that ions are taken as a component of a liquid metal, instead of being treated as a uniform positive background. This expression proves to lead to the same expression for an effective interatomic interaction. As an application, effective proton-proton interactions in liquid metallic hydrogen are calculated. In this system, it is shown to be inappropriate to use the fundamental approximation that the LFC Gee in a metal should be equal to the LFC Gjell in the jellium. Furthermore, non-linear effects, characterised by the LFC Gep between electrons and protons, are found to be important. As a consequence, effective proton-proton interactions show a strong dependence on the proton configuration.