DENSITY FUNCTIONAL THEORY OF KINETIC AND EXCHANGE ENERGIES OF ATOMS AND MOLECULES.

摘要

Available from UMI in association with The British Library. Requires signed TDF.; This thesis is concerned with studying the kinetic and exchange energy functionals inside Density Functional Theory (DFT).; Chapter I is dedicated to the presentation of the basic concepts of DFT. First, the density matrix formalism is introduced as a mathematical apparatus for developing the theory. Then, the Thomas-Fermi-Dirac and Weizsacker models are given as limiting examples of kinetic and exchange energy functionals. Second, the fundamental basis of DFT are established by means of the Hohenberg-Kohn theorem. The main point to explore, namely, the research for the kinetic and exchange energy functionals, is continuously discussed along the chapter.; Next in chapter II, the research begins by working with one of the simplest physical systems; DFT is applied to closed shells in the bare Coulomb field. Important results are obtained providing the first-principles basis for the search of the kinetic and exchange energy functionals.; In Chapter III, the numerical computations are carried out for testing the, previously found, bare Coulomb field functions in real atomic and molecular systems. The method exposed here illustrates a different way to calculate energy contributions by means of variational density matrices.; Later in chapter IV, demanding more accuracy than the one obtained in the bare Coulomb field, a subshell model embracing shell structure is introduced. The model explains, up to some extent, other models previously proposed by different authors.; Because the importance of kinetic and exchange energy functionals in DFT, chapter V is dedicated to establish the relation between kinetic and exchange quantities. The relation, of non-local character, leads an alternative form to calculate either kinetic or exchange energy without the need of a density matrix; as an example, the exchange energy functional for the uniform electron gas is deduced.; Chapter VI presents a different perspective of density functional theory in order to study properties of atomic and molecular systems different to energetic calculations but linked to kinetic and exchange functionals. The relationship between electron distributions and fields is analyzed inside different approximate frameworks.; Finally, the main results are summarized at the end of this work in a form of general conclusions.