New Developments in Orbital-Free Density Functional Theory Enabling Simulations of Covalent Materials

Abstract

Orbital-free (OF) density functional theory (DFT) is a powerful and numerically efficient first principles quantum mechanics method. Its application has contributed to understanding a diverse set of materials properties in recent decades. However, most previous studies were confined to simple metals. In this thesis, we focus on extending OFDFT to describe covalently-bonded materials and aiming for a balance between accuracy and efficiency.

We first apply OFDFT to study diatomic molecules, with the Huang-Carter (HC) kinetic energy density functional (KEDF). OFDFT predicts reasonable equilibrium bond lengths, bond dissociation energies, and vibrational frequencies compared to Kohn-Sham (KS) DFT benchmarks. This work indicates significant progress of OFDFT in describing molecules. However, we find that the HC KEDF is computationally expensive and thus inapplicable for large-scale simulations.

Consequently, we propose an electron density decomposition formalism for covalent materials. Based on local density information, the total density is decomposed into localized and delocalized electron densities, which are then described by different KEDF models separately. The resulting Wang-Govind-Carter-decomposition (WGCD) KEDF gives accurate properties for bulk semiconductors and isolated molecules. Furthermore, it offers far superior numerical efficiency compared to the previous HC KEDF.

We then test the HC and WGCD KEDFs on Li-Si alloys and obtain accurate structures and bulk properties. The OFDFT Li adsorption energies on the Si(100) surface are also close to KSDFT values. OFDFT is thus promising to study mechanical properties of Li-Si alloys and the mixing mechanism during lithiation and delithiation processes.

We next focus on single-point KEDFs for localized densities and pointwise quantities including the local kinetic energy density (KED) and the electron localization function (ELF). Based on a transferable correlation between the reduced density and the KED/ELF discovered in bulk metals, we propose new single-point KEDFs which offer significant improvement over previous single-point KEDFs. The work emphasizes pointwise quantities and introduces the connection between KEDFs and ELFs, which should be important for future KEDF development.

We also propose a simple density decomposition method which offers more robust convergence and reliable cell relaxation. Other attempts to improve KEDFs for covalent materials and angular-momentum-dependent OFDFT for Li are also discussed.