Exchange-correlation functionals from ab initio potentials

Abstract

An accurate description of the exchange-correlation energy is central to density functional theory (DFT). In this thesis a series of exchange-correlation functionals are developed using new approaches based on exchange-correlation potentials and enhancement factors. The functionals are assessed for a wide range of molecular properties. Chapter 1 describes Hartree Fock theory, introducing the key concepts of exchange and correlation. Chapter 2 describes the fundamental ideas of DFT and the implementation of Kohn-Sham theory. Chapter 3 describes a new approach for determining exchange-correlation functionals solely from ab initio potentials. A series of functionals are developed and assessed. Chapter 4 investigates the performance of one of these functionals, which provides particularly high quality structural predictions. A challenging benchmark of sulfur-containing compounds and a new benchmark of diatomic molecules are considered. Results are assessed in terms of the enhancement factor. In Chapter 5, the enhancement factor is used to develop new functionals that satisfy several exact physical conditions. The potential energy curve of the Helium dimer is investigated, since this is known to be sensitive to the enhancement factor. In Chapter 6 a series of hybrid functionals are determined. Particular attention is paid to their performance for chemical reactions and the relationship of these results to self-interaction errors. Chapter 7 investigates a new definition of the exchange-correlation charge (hole), which is directly related to the exchange-correlation potential. The first such calculations on molecular systems are presented. Concluding remarks are presented in Chapter 8.