We have determined the coefficients of the first- and second-order gradient corrections to the exchange-correlation energy of an inhomogeneous electron gas using a slightly modified version of the theory of Vashishta and Singwi. We find that the correction to the surface energy of metal-vacuum interface due to the first gradient term is of the order of +20%, and that due to the second gradient term is negative and amounts to only a few percent. It is concluded that the gradient expansion of the exchange-correlation energy is a rapidly convergent series even for the metallic surface problem. It provides justification of using local-density approximation in the self-consistent Kohn-Sham calculations in cases where the total exchange-correlation energy is not the dominant part of the total energy.

• Received 22 July 1976

DOI:https://doi.org/10.1103/PhysRevB.15.1801