Date of Award
Doctor of Philosophy (PhD)
This thesis reports results of the author's investigations along the theme that both dynamic and static properties of molecules and solids can be expressed in terms of their parts from theoretical and applied aspects. Specifically, the following four main results are obtained: (1) A topological analysis of the charge density in crystals has been developed. This is an extension of the theory of molecular structure to crystalline systems. Relationships between the bulk properties of a crystal and its topological properties of molecules and crystals have been made. (2) The theory of atoms in molecules has been extended to a crystal and yields a variational definition of Wigner-Seitz cell. This definition maximizes the relation of the cell to the physical form exhibited by the charge density and the derived structure factors that account, in a natural way, for the observed intensities of scattered electrons and X-rays. It has been demonstrated that the theory of atoms in molecules and crystals can provide a way to model the behaviors of solids. This is done through the use of the fact that atomic properties are often transferable from one system to another. (3) The subsystem variational principle has been reformulated in terms of quantum field theoretical language and the subsystem Feynman path integrals of electrons have been obtained using the coherent representation. This part contributes to the foundation of the theory of atoms in molecules and crystals. (4) Both dynamic and static quantum mechanical subspace techniques have been extensively investigated. A new variational method has been derived for embedding one system in another using the R-matrix formalism within the density functional approach. A formal subspace perturbation scheme has been proposed. These methods aim to obtain the charge distribution of a subsystem starting from known reference systems.
Zou, Peng Fei, "Subsystem Quantum Mechanics and Its Applications to Crystalline Systems" (1993). Open Access Dissertations and Theses. Paper 2805.