Density Functionals for Dynamic Linear Response in Finite Systems

Maria Hellgren

Monday, 31 August 2009, 15:15
Lundmarksalen, Astronomihuset, Sölvegatan 27

This dissertation investigates a new method for obtaining excited- state properties of finite, many-electron systems such as atoms, molecules and nano-systems. The method combines the merits of many- body perturbation theory and time-dependent perturbation theory and yields approximate density response functions which preserve basic physical conservation laws. Furthermore, advanced density functionals for ground-state properties like total energies and van der Waals coefficients can be constructed from these approximations. The thesis begins with an introduction that discusses in more detail the concepts and formulas used in the papers attached. It is followed by a summary of the main findings and an outlook. In total, four original papers are included. Paper I is concerned with the random phase approximation for the total energy and the corresponding Kohn-Sham (KS) potential. While total energies are far too negative the potentials produce very accurate ionization potentials. Paper II investigates the response function of the time-dependent exact-exchange (TDEXX) approximation for obtaining static polarizabilities, van der Waals coefficients and some low excitation energies. The results are very close to results obtained from time- dependent Hartree-Fock theory showing that the method accurately reproduce results from the more demanding Bethe-Salpeter approach. In Paper III some important findings regarding the exact-exchange kernel are presented. The optical absorption spectra is calculated and the results show that at higher energies the approximation is ill- behaved leading to a response function with the wrong analytic structure. A new derivation of Fano-parameters based on adiabatic TDDFT is also given. In Paper IV the adiabatic approximation to TDEXX is used to obtain an advanced functional for the total energy, yielding both excellent total energies and KS potentials. van der Waals coefficients are shown to be very sensitive to the ground-state density and when calculated in TDEXX using a correlated density, results are remarkably improved.