Exchange Energy Density Functional

Density Functional Theory (DFT) is an important tool in the treatment of quantum many-body problems. In spite of being exact in principle, the application of DFT requires the use of approximations, because it involves an unknown universal functional called the exchange-correlation energy. This book starts with a review of the theory and then introduces an accurate and efficient extension of a plane-wave based algorithm for calculating exchange energies, exchange energy densities, and exchange energy gradients with respect to wave function parameters in systems of electrons subject to periodic boundary conditions, and shows a way to build a more accurate exchange energy density functional. It also discusses the effects of twist-averaging on the finite-size errors in the exchange energy of a uniform electron gas, using the Ewald, model periodic Coulomb (MPC) and screened Coulomb interactions.