Studies in density functional theory: Chemical reactivity; kinetic energy

This dissertation consists of two sets of studies:; I. Chemical reactivity. Presented in Chapter 1 is a density-functional viewpoint of the frontier-electron theory of chemical reactivity. Corresponding to frontier orbitals, fukui functions, defined as the derivatives of electron density with respect to number of electron, are identified to be the chemical reactivity indices. The frontier-electron principle is thus transcribed: the preferred direction of chemical reaction is the one for which the initial change in chemical potential is a maximum. A follow-up analysis, within Kohn-Sham density functional theory, of the relationship between fronteir orbitals and fukui functions is given in Chapter 2, where their equivalence is established on the frozen-core approximation.; In an extension to theory of metals in Chapter 3, hardness defined recently by Parr and Pearson (J. Am. Chem. Soc. 105, 7512 (1983)), and fukui functions proposed in Chapter 1 are respectively shown to be equal to the inverse of the density of electronic states, and the normalized local density of electronic states, at Fermi energy. Then concepts of softness and local softness are naturally introduced, relating to hardness and fukui functions.; Chapter 4 demonstrates that to a reasonable approximation, softness for a molecule is the average of the softness of its constituent atoms--the proposed arithmetic average principle for molecular softness.; II. Kinetic energy. A functional of both electron density and its scaling parameter is proposed in Chapter 5 through a constrained minimization; it, unlike the customary Hohenberg-Kohn density functionals, exhibits homogeneous scaling both for kinetic and potential components. The implications and possible application of the new functional are discussed. In Chapter 6, a variational analysis of the energy functionals is carried out. The conditions of stationarity of the kinetic energy and collapse to the given electron density require that each of the pure state wave functions involved in the density matrix be a single determinant in the same eigenspace of a particular N-electron Hamiltonian.; The last two chapters involve explicit approximations of kinetic energy functional.