Studies On The Bounds To Density Functionals For Molecules In Density Functional Theory

The commonly-used approaches applied to many-body system are solving the Schrodinger equation and describe the electronic structures and properties of atoms, molecules and solids with the wavefunction that obtained by solving the Schrodinger equation of the system. In chapter one, we give a brief review of various approaches applied to the many-body system, such as Hartree Method,Hartree-Fock Method etc. The advantages and the disadvantages of these methods are reviewed. All of these methods are based on wavefunction, so it always called wavefunction theory. Although accurate solutions of the Schrodinger equation for the system have been found and successfully used to predict the structures and properties of atoms, molecules and solids with the development of modern computer technology. However, the physical significance of the wavefunction is still not clearly and definitely up to now as we know and it cannot be measured directly by experiments. Moreover, it is difficult to solve the Shrodinger equation of many-body system and the wavefunction theories are computationally expensive, especially for large system, since the interaction of many-body system is complicated.For ground states, Hohenberg, Kohn and Sham proved that all ground state properties of the system is a unique functional with electron density. In other words, Electron density determines all ground state properties of the system. They made a suggestion that ascribed the electron density as a basic variable to study the electronic structure and properties of many-body system. This allows one to replace the complicated 3N-dimensional wavefunction and the associated Schrddinger equation by the 3-dimensional single particle density which can be measured from diffraction experiments and readily visualized and its associated calculational scheme. Since then, The density functional theory (DFT) has been widely-used in condensed-matter physics and increasingly applied to chemistry for the prediction of these properties, chemical reaction trend and rate, and the properties of biologically interesting molecules. The prediction of these properties will contribute to design of new materials, chemicals, and pharmaceuticals. With the contributions of development for the density functional theory, the 1998 Nobel Prize was awarded to the American scholar Walter Kohn. In chapter Two, we give a concise description of the density functional theory, various ingredientsof the total energy are defined as functional of the electron density and some formal properties of these functionals are discussed.However, In the studies of the density functional theory, big challenges remain, the exact and rigorous form of the universal energy functional has still not been found, especially, in the momentum space so far. Largely having to do with the need to construct or improve functional of the electron density. Thus Construction or improvement of exchange-correlation functionals has been the focus of the density functional theory. There are two major directions in this domain: one is construction or improvement of approximations the kinetic and exchange-correlation energy functionals by various approximate methods. Such as local density approximation (LDA), local spin density approximation (LDA), general expansion approximation (GEA) and general gradient approximation(GGA) etc. Various approximate methods and their application in atom and molecules are reviewed briefly and descripted concisely in the chapter 3. The other is study on the bounds to the kinetic and exchange-correlation energy functionals. Studies on the bounds to density functional are very interesting and important approaches in density functional theory (DFT), and they could indicate the directions and provide much reliable information for finding or constructing the approximate and rigorous forms of the energy functional which could simplify and improve the computational methods. These are the major project we have done in present thesis. Based on the brief review of the works have been done by previ...