| Summary: | The first part of the work is an attempt to develop improved exchange-correlation. This is initially approached by separating the exchange-correlation functional into an exchange functional and a correlation functional. The simplest chemical systems, atoms, are used to help develop new functionals. This leads to a proposal for an exchange functional, OPTX, and a correlation functional, OPTC. A total exchange-correlation functional, HCTH, is then developed by choosing a functional form with several parameters. These parameters are chosen to minimise the error in a least squares fit to energy, potential, and geometry of 93 chemical species. To further understand the nature of exchange, molecules are examined. In molecules the separation of exchange and correlation is not as simple as in atoms. By studying the geometries and the energetic contributions to dissociation energies of the molecules, it is seen that local exchange functionals do not approximate Hartree-Fock exchange. It is concluded that local exchange functionals also include non-dynamical correlation. In the next part the performance of a wide range of exchange-correlation functionals, ranging from LDA (containing just the density, <IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif">) to GGA (containing <IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif"> and <img src=/inline/symbol_209.gif><IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif">) to meta GGA (containing <IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif">, <img src=/inline/symbol_209.gif><IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif">, <img src=/inline/symbol_209.gif><SUP>2</SUP><IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif"> and the kinetic energy density, <IMG WIDTH=7 HEIGHT=7 ALIGN=BOTTOM SRC="/maths/tau.gif">) and hybrid functionals (containing a fraction of exact exchange), are assessed. By looking at two sets of molecules it is concluded that more recently developed functionals are an improvement over the older functionals.
|
|---|
