Physics 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 …

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. …