Master of Science
Viktor N. Staroverov
In density-functional theory, one can approximate either the exchange-correlation energy functional or the corresponding Kohn--Sham effective potential, which is then converted into an energy functional by functional integration. A directly approximated potential may depend on the electron density explicitly or implicitly through Kohn--Sham orbitals. A potential that depends on the electron density explicitly can be converted into an energy functional by evaluating the Leeuwen--Baerends line integral along some path of electron densities. We extend this technique to orbital-dependent potentials by integrating them along the path of scaled orbitals. Using this method, we assign energy expressions to the Slater, Becke--Johnson and van Leeuwen--Baerends model Kohn--Sham potentials. We also investigate the conditions under which the zero-force test for functional derivatives holds in finite basis set. Specifically, we show that any functional derivative of an explicitly density-dependent functional satisfies the zero-force test in any finite basis set. Approximate exchange-correlation potentials constructed by the Ryabinkin--Kohut--Staroverov (RKS) method are found to pass the zero-force test only in the basis-set limit. Our results confirm that RKS potentials obtained from Hartree--Fock wave functions are practically indistinguishable from exact exchange potentials when a large basis set is employed.
Zhao, Hanqing, "Integration of orbital-dependent exchange-correlation potentials" (2017). Electronic Thesis and Dissertation Repository. 4414.