Developing New Kohn-Sham Density Functional for Molecules, Atoms, and Solids: New Methods and Applications

Abstract

The accuracy of Kohn-Sham density functional theory depends on the exchange-correlation functional. Local functionals depending on only the density (ρ), density gradient (∇ρ), and possibly kinetic energy density (τ) have been popular because of their low cost and simplicity, but the most successful functionals for chemistry have involved nonlocal Hartree-Fock exchange (HFX). Based on the mathematical form of a nonseparable gradient approximation (NGA), as first employed in the N12 functional, we developed a gradient approximation for molecules (GAM) that is parameterized with a broader data set of molecular data than N12 and with smoothness constraints. By adding the kinetic energy density (τ) to the GAM functional, we developed a new meta-NGA called MN15-L that predicts accurate results for multi-reference systems especially for transition metal ligand binding energies. Adding 44% Hartree-Fock exchange to the MN15-L functional and optimizing the linear parameters of the functional in the presence of Hartree-Fock exchange, we obtained a non-local exchange-correlation functional called MN15 that predicts accurate results for a large variety of properties including single-reference systems, multi-reference systems, and noncovalent interactions. In this thesis we presents the following studies: (1) Introduction of Density Functional Theory (DFT), (2) Development of Minnesota Database 2015B, (3) The GAM Functional, (IV) The MN15-L Functional, (V) The MN15 Functional, and (VI) Applications of Kohn-Sham Density Functionals.