APPLICATIONS OF DENSITY FUNCTIONAL THEORY TO HOMONUCLEAR DIATOMIC MOLECULES: A COMPLEMENTARY VARIATIONAL PRINCIPLE APPROACH

Homonuclear diatomic systems are studied within a density functional formalism. Preliminary investigations of simple density functional theories yield few positive results. The major portion of this work is concerned with the application of complementary variation principles to more sophisticated density functional models.; In the first chapter, an analysis of the relationship between electron density and bare-nuclear potential is presented. Topological similarities between the contour maps of these two fields are shown to exist. A calculation on the hydrogen molecular ion demonstrates that 80% of the binding energy can be obtained from a wavefunction forced to produce a density dependent only on bare-nuclear potential.; A method for extending the local density functional theory of Parr et al. to molecules is developed in the second chapter. Bound molecular systems arise without incorporating a gradient correction term into the energy functional. Unfortunately, rather poor estimates for the equilibrium internuclear distance (2.70 bohr) and energy (-1.205 hartree) of H(,2) result.; In Chapter III, complementary variational principles are used to derive a general 'Poisson' lower bound energy functional complementary to a large class of upper bound energy functionals. Tests are performed on atomic systems. Employing the Thomas-Fermi functional along with its Poisson complement, a zero-parameter trial function bounds the energy of neutral Thomas-Fermi atoms to within better than 1.4%. Extensive calculations on the Thomas-Fermi-Diracvon Weizsacker neutral atoms with a six-parameter trial density show that the absolute percent error in total energy increases with nuclear charge, but even for argon, the error is less than 4%. A Poisson complement to the Hohenberg-Kohn energy functional is also presented.; Lower bound techniques are applied to diatomic systems in the final chapter. After a direct derivation of the density functional Poisson complement, the Thomas-Fermi-Dirac-(1/5) von Weizsacker potential energy curve for N(,2) is calculated; less binding than previously thought to exist results. Following by analogy, a Poisson complement for orbital theories is derived. The complement to the Hartree-Fock energy functional is used to obtain a potential energy curve for the hydrogen molecule; without performing any two electron integrals, the Hartree-Fock dissociation energy is exceeded by less than 6%.