Density functional theory (DFT) is a widely used quantum mechanical method for the simulation of the electronic structure of atoms, molecules, and solids. The only part that needs to be approximated is the exchange-correlation energy as a functional of the electron density. After many-year development, there is a huge variety of exchange-correlation functionals. According to the ingredients, an exchange-correlation functional can be classified as a semi-local functional or beyond. A semi-local functional can be nonempirical or empirical and only uses locality information, such as electron density, gradient of the density, Laplacian of the density, and kinetic energy density. Unlike a non-local functional that uses non-locality information, a semi-local functional is computationally efficient and can be applied to large systems. The meta-generalized gradient approximation (meta-GGA), which is the highest-level semi-local functional, has the potential to give a good description for condensed matter physics and quantum chemistry. We built the self-consistent revised Tao-Perdew-Staroverov-Scuseria (revTPSS) meta-GGA into the band-structure program BAND to test the performances of some self-consistent semi-local functionals on lattice constant with a 58-solid test set. The self-consistent effect of revTPSS was also discussed. The vibration of a crystal has a contribution to the ground state energy of a system, which is the zero-point energy at zero temperature. It has anharmonicity at the equilibrium geometry. The standard DFT doesn’t consider the zero-point energy of a crystal. We used density functional perturbation theory (DFPT), which is a powerful and flexible theoretical technique within the density functional framework, to study the zero-point energy and make a correction to the lattice constant. The method was compared to a traditional zero-point anharmonic expansion method that is based on the Debye and Dugdale-MacDonald approximations. We also tested some new meta-GGA functionals (revTPSS, regularized revTPSS, and meta-GGA made simple) on a big molecular test set - GMTKN30 - that is composed of 30 smaller test sets and covers a large cross section of chemically relevant properties. The performances of these new meta-GGAs were compared with some other popular functionals or meta-GGAs. / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_23548 |
| Date | January 2013 |
| Contributors | Hao, Pan (Author), Perdew, John (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Format | 110 |
| Rights | Copyright is in accordance with U.S. Copyright law |
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