Exchange Energy of a Strongly Inhomogeneous Electron Gas

Abstract The problem of exchange energy of a strong inhomogeneous electron gas is treated within a special model. An explicite expression for the density of exchange energy is given in dependence on the electron density as well as the gradient of the electron density, where the electron density and its gradient independently can take any arbitrary value. As a result, the relative difference between this expression and the local density approximation for the exchange energy strongly depend on the fractional change in the electron density over the local Fermi wavelength. The deformation of the Fermi‐hole in a strong inhomogeneous electron gas is considered.