| This dissertation is divided into four chapters. The first is a review, in which the Born-Oppenheimer approximation is presented for the purpose of orientation, and the density functional theorems of Hohenberg and Kohn, and of Levy, are discussed at length. In addition, the point of view is advanced that density functional theory may be considered as a renormalization scheme, in that system expectation values and external potentials may be expressed solely in terms of the observable single particle density.; In the second chapter, a new class of density functionals is exhibited whereby excited state energies and electron densities may, within the Born-Oppenheimer approximation for molecules, be calculated by direct minimization. The density functional R(,2){lcub}(rho),(alpha){rcub} obeys the bound R(,2){lcub}(rho),(alpha){rcub} (GREATERTHEQ) (E(,b) - (alpha))('2) where (alpha) is an arbitrary fixed constant, and E(,b) is the bound state energy closest to (alpha). Also, some properties of reduced density-matrix functionals are presented, as well as a brief excursion into the area of N-representability.; It is shown in the third chapter that the Hohenberg-Kohn-Levy density functional theory of molecular structure is not restricted by the Born-Oppenheimer approximation. The existence of the corresponding ground state density functionals for the case of the exact nonadiabatic, nonrelativistic, field-free Hamiltonian of a molecular system, in terms of the one-particle electronic and nuclear densities, is proven and the associated Euler equations are discussed. Extensions to the case of a system in an external field and to bound excited states are examined. As an example, the non-Born-Oppenheimer Hartree-Fock theory of Thomas is discussed from the density functional viewpoint. In addition, possible applications of the theory to the analysis of molecular structure and chemical reactivity are identified.; The final chapter contains an analysis of Legendre transformed representations of the non-Born-Oppenheimer density functional theory, as well as a derivation of the corresponding Maxwell relations. These relations are shown to exhibit various couplings between parameters of the non-Born-Oppenheimer energy hypersurface E{lcub}{lcub}N(,i),Z(,i),M(,i){rcub}{rcub} where N(,i),Z(,i), and M(,i) denote, respectively, the number of particles i, and their charge and mass. Also included are criteria for intrinsic equilibrium and stability of molecular systems. Finally, the physical content of these criteria are intepreted via the principle of Le Chatelier. |
