**
**

E.K.U. Gross

*Institut für Theoretische Physik, Freie Universität Berlin,
Arnimallee 14, D-14195 Berlin, Germany
*

This lecture deals with excited electrons.
In the first part, a time-dependent generalization of
the electron localization function (ELF) will be shown. The static
ELF represents a tool to visualize the degree of localization of
the electron distribution and, thereby, allows the classification of
chemical bonds. The time-dependent version of the ELF contains an
additional term arising from the phases of the time-dependent Kohn-Sham
orbitals. Movies of the time-dependent ELF allow the *time-resolved*
observation of the formation, the modulation, and the breaking of
chemical bonds, and can thus provide a visual understanding of complex
reactions involving the dynamics of excited electrons. We illustrate
the usefulness of the time-dependent ELF by two examples: A p- p^{*}
transition induced by a laser field, and the destruction of bonds and
the formation of lone-pairs in a scattering process.

Although time-dependent density functional theory (DFT) enjoys increasing
popularity as a method of calculating molecular excitation spectra, it
often has difficulties -just like ground-state DFT- in dealing with
degeneracies or near-degeneracies. To get a grip on this kind of situations
we explore, in the second part of the lecture, a stationary approach to
excitation energies, known as ensemble DFT. We observe that the direct Coulomb
(Hartree) term appearing in the ensemble DFT for excited states contains an
unphysical ``ghost" interaction which has to be corrected by the ensemble
exchange and correlation functional. We propose a simple additive
correction to the conventional ensemble exchange energy in the form of an
orbital functional. By treating this corrected exchange energy functional
self-consistently within the optimized effective potential method one finds
a significant improvement of excitation energies.

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On 25 Oct 2003, 16:16.