Physical Sciences and Mathematics Commons^™

Approximation Of Exchange-Correlation Potentials For Orbital-Dependent Functionals, Alexei Kananenka

Electronic Thesis and Dissertation Repository

Density-functional theory (DFT) is the most widely used method of modern computational chemistry. All practical implementations of DFT rely on approximations to the unknown exchange-correlation functional. These approximations may be devised in terms of energy functionals or effective potentials. In this thesis, several approximations of the latter type are presented.

Given a set of canonical Kohn–Sham orbitals, orbital energies, and an external potential for a many-electron system, one can invert the Kohn–Sham equations in a single step to obtain the corresponding exchange-correlation potential, vXC(r). We show that for orbitals and orbital energies that are solutions of the Kohn–Sham equations with …

Theory Of Model Kohn-Sham Potentials And Its Applications, Alex P. Gaiduk

Electronic Thesis and Dissertation Repository

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. …