| Density functional theory (DFT) is a rapidly growing approach to quantum theory that employs the three dimensional density for energy calculations in contrast to the many dimensional wavefunction method of traditional quantum mechanics. It also introduces the concept of F (n), a universal density functional which is independent of any external potential, that exists in theory but that in practice needs to be approximated. This is accomplished by separating F (n) into different energy functional components and then approximating these functionals. The purpose of the following research is to approximate the correlation-energy component, {dollar}rm Esb{lcub}c{rcub}lbrack nrbrack,{dollar} by trying to satisfy certain theoretical constraints.; Uniform and non-uniform coordinate scaling requirements for a correlation-energy density functional led initially to the development of the Wilson-Levy (WL) functional. The numerical results of this functional, which is Wigner-like, are compared to results of both recent and traditional functionals. Values calculated from the correlation-energy functionals of both the original Wigner and the VWN are also tabulated. Parameterization of the WL functional is explained. The advantages and disadvantages of the WL and other functionals are discussed and the functional derivative of both the closed-shell and open-shell forms of the WL is presented.; More recent developments including non-uniform coordinate scaling requirements lead to the development of a new correlation-energy Wigner-like functional. Coordinate scaling requirements along with other constraints are reviewed and investigated for the functionals of Perdew, Becke, Lee-Yang-Parr, Wilson-Levy, Perdew-Wang 91 and the newest functional. Numerous other equations that do not comply with these constraints are also evaluated. The importance of {dollar}{dollar}rmbigglvertleft({lcub}partial Esb{lcub}c{rcub}lbrack nsblambdarbrack overpartiallambda{rcub}right)sb{lcub}lambda=1{rcub}biggrvert{dollar}{dollar}is assessed and used in a new method for selecting a spin-function for open-shell species. The correlation between coordinate constraint obedience and a functional's efficiency is finally evaluated and suggestions for an improved functional are proposed. |
