Physical Sciences and Mathematics Commons^™

Construction And Analysis Of Accurate Exchange-Correlation Potentials, Sviataslau V. Kohut

Electronic Thesis and Dissertation Repository

Practical Kohn–Sham density-functional calculations require approximations to the exchange-correlation energy functional, E_XC[ρ], or the exchange-correlation potential, v_XC(r), defined as the functional derivative of E_XC[ρ] with respect to the electron density, ρ. This thesis focuses on the following problems: (i) development of approximate exchange-correlation potentials by modelling the exchange-correlation charge distribution; (ii) accurate approximation of functional derivatives of orbital-dependent functionals; (iii) generation of exchange-correlation potentials from many-electron wavefunctions; (iv) analysis of accurate exchange-correlation potentials in atoms and molecules.

The advantage of modelling the exchange-correlation potential through the exchange-correlation …

Integration Of Orbital-Dependent Exchange-Correlation Potentials, Hanqing Zhao

Electronic Thesis and Dissertation Repository

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 …