Browsing by Subject "Multi-reference Systems"

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    Density functional theory: toward better understanding of complex systems in chemistry and physics
    (2014-06) Luo, Sijie
    Density functional theory (DFT) has become the workhorse of computational chemistry and physics in the past two decades. The continuous developments of high-quality exchange-correlation functionals (xcFs) have enabled chemists and physicists to study complex as well as large systems with high accuracy at low-to-moderate computational expense. Although a wide range of normal systems have been well understood by DFT, there are still complex ones presenting particular challenges where most commonly used xcFs have failed due to the complex nature of the system, lack of or difficulty to obtain reliable reference data, or the practical limitations of the Kohn-Sham DFT (KS-DFT) formulation.This thesis presents studies with various exchange-correlation functionals on a wide selection of complex systems in chemistry and solid-state physics, including large organic molecules, adsorption on metallic surfaces, transition states, as well as transition metal atoms, ions, and compounds, to (i) draw conclusions upon recommendations of xcFs for important practical applications; (ii) understand the root of errors to help design better xcFs or propose new theoretical schemes of DFT; (iii) explore the utility of noncollinear spin orbitals in KS-DFT for better description of multi-reference systems.
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    Developing New Kohn-Sham Density Functional for Molecules, Atoms, and Solids: New Methods and Applications
    (2016-06) Yu, Haoyu
    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.