LDA exchange-energy functional

Using exact results for the nonlocal exchange potential for an electron in a semi-infinite metal, it is shown that in the tail region of the electron density, the exact exchange energy density functional (EEDF) exhibits a behavior that is linear with respect to the electron density. Furthermore, in the Friedel-oscillation region of the electron density a weak dependence of the EEDF on the sign of the gradient of the electron density is observed. These results and similar ones obtained from calculations on the free Be and Na atoms, suggest that a more appropriate way to improve the local electron density approximation (LDA)-EEDF is one in which the LDA functional is not retained as the leading term on which gradient corrections are to be applied. [S0163-1829(98)03727-8].