Doctor of Philosophy
Prof. Viktor N. Staroverov
The purpose of Kohn-Sham density functional theory is to develop increasingly accurate approximations to the exchange-correlation functional or to the corresponding potential. When one chooses to approximate the potential, the resulting model must be integrable, that is, a functional derivative of some density functional. Non-integrable potentials produce unphysical results such as energies that are not translationally or rotationally invariant. The thesis introduces methods for constructing integrable model potentials, developing properly invariant energy functionals from model potentials, and designing model potentials that yield accurate electronic excitation energies. Integrable potentials can be constructed using powerful analytic integrability conditions derived in this work. Alternatively, integrable potentials can be developed using the knowledge about the analytic structure of functional derivatives. When these two approaches are applied to the model potential of van Leeuwen and Baerends (which is non-integrable), they produce an exchange potential that has a parent functional and yields accurate energies. It is also shown that model potentials can be used to develop new energy functionals by the line-integration technique. When a model potential is not a functional derivative, the line integral depends on the choice of the integration path. By integrating the model potential of van Leeuwen and Baerends along the path of magnitude-scaled density, an accurate and properly invariant exchange functional is developed. Finally, a simple method to improve exchange-correlation potentials obtained from standard density-functional approximations is proposed. This method is based on the observation that an approximate Kohn-Sham potential of a fractionally ionized system is a better representation of the exact potential than the approximate Kohn-Sham potential of the corresponding neutral system. Removing 1/2 of an electron leads to the greatest improvement of the highest occupied molecular orbital energy, which explains why the Slater transition state method works well for predicting ionization energies. Removing about 1/4 of an electron improves orbital energy gaps and, when used in time-dependent density functional calculations, reduces errors of Rydberg excitation energies by almost an order of magnitude.
Gaiduk, Alex P., "Theory of Model Kohn-Sham Potentials and its Applications" (2013). University of Western Ontario - Electronic Thesis and Dissertation Repository. Paper 1099.