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An exact evaluation is given in the high-density limit of the first gradient coefficient which enters the exchange plus correlation energy in the Hohenberg-Kohn-Sham formalism for an inhomogeneous two-component (electron-hole) system. Numerical results are given for isotropic electron and hole bands for a range of values of the electron-hole mass and density ratios. An application is made to Ge under [111] strain and the surface energy is calculated in a simple model.
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Rasolt et al. (1977) studied this question.
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