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 beh avior 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 an d Na atoms, suggest that a more appropriate way to improve the local electr on density approximation (LDA)-EEDF is one in which the LDA functional is n ot retained as the leading term on which gradient corrections are to be app lied. [S0163-1829(98)03727-8].