Gradient Corrections in the Exchange and Correlation Energy of an Inhomogeneous Electron Gas

An exact result is derived for the coefficient Bₗ₂ which determines the first gradient corrections to the exchange and correlation energy of an inhomogeneous electron gas. A method of approximation, which is based on the random-phase approximation and is exact at high density, is given for the explicit evaluation of Bₗ₂. Numerical results are also given for the metallic density range and applications are discussed.