| Summary: | 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. In this thesis we describe an accurate and efficient extension of Chawla and Voth's planewave 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. The theory and numerical results show that the computational effort scales almost linearly with the number of plane waves and quadratically with the number of k vectors. To obtain high accuracy with relatively few k vectors, we use an adaptation of Gygi and Baldereschi's method for reducing Brillouin zone integration errors. We then generate a large database of highly accurate exchange energy densities in 106 artificial but realistic solid-state systems. We use the database not only to examine the accuracy of some important existing exchange functionals, but also to show that there exists a smooth function of the local electron density, its gradient and Laplacian that fits our data well. We also study 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. In the case of the Ewald interaction, this investigation is carried out in both the canonical (fixed particle number) and grand-canonical (fixed Fermi wave vector) ensembles. Finally, we study the new reciprocal-space approach to the . Coulomb finite-size errors introduced by Chiesa et al. and find that it is almost equivalent to the use of the MPC interaction.
|
|---|
