##
Density Functionals for Dynamic Linear Response in Finite
Systems

### Maria Hellgren

**Monday, 31 August 2009, 15:15**

Lundmarksalen, Astronomihuset, Sölvegatan 27

**Abstract**:

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.