Gradient Corrections to Exchange Energies within Density Functional Theory
The small-wavector expansions for the first- and second-order exchange energy kernels (second-and third-order functional density derivatives of the exchange energy) have been investigated. Expansion coefficients are found, both in the case of a statically screened Coulomb interaction and a 'bare' interaction. The ensuing series of gradient corrections to the local density approximation (LDA) is th