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.