Time-dependent density-functional theory (TDDFT) is widely used to describe
electronic excitations in complex finite systems with large numbers of atoms,
such as biomolecules and nanocrystals. The first part of this paper will give a
simple and pedagogical explanation, using a two-level system, which shows how
the basic TDDFT formalism for excitation energies works. There is currently an
intense effort underway to develop TDDFT methodologies for the charge and spin
dynamics in extended systems, to calculate optical properties of bulk and
nanostructured materials, and to study transport through molecular junctions.
The second part of this paper highlights some challenges and recent advances of
TDDFT in these areas. Two examples are discussed: excitonic effects in
insulators and intersubband plasmon excitations in doped semiconductor quantum
wells.Comment: 15 pages, 2 figures, International Conference on Materials Discovery
and Databases: Materials Informatics and DF
