TIMEDEPENDENT DENSITY FUNCTIONAL THEORY:
MOVING FROM
LINEARRESPONSE TO THE STRONGFIELD DOMAIN
E.K.U. Gross
Freie Universitaet Berlin
For large manyparticle
systems, the wave function is an illegitimate
scientific concept [Walter Kohn, Nobel Lecture],
illegitimate in the sense that it can neither be
calculated nor stored. Modern density functional
theory is based on the surprising fact that
knowledge of the groundstate density alone is
sufficient to calculate all physical observables
of a stationary quantum system. In this lecture, a
timedependent generalization of density
functional theory (TDDFT) will be presented which
treats both electrons and nuclei quantum
mechanically. TDDFT calculations of molecular
excitation spectra, of high harmonic generation
and of the Coulomb explosion will be presented.
Furthermore, a timedependent generalization of
the socalled electron localization function (ELF)
will be shown. This quantity allows one to
visualize the degree of localization of the
electron distribution and provides, in the static
limit, a topological classification of chemical
bonds. The timedependent version of the ELF
contains an additional term arising from the
phases of the timedependent KohnSham orbitals.
Movies of the timedependent ELF allow the
timeresolved 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 [1]. Movies of a laserinduced
pipi* transition and of a protonmolecule
scattering process will be presented. Finally,
optimalcontrol theory will be generalized to
treat timedependent targets. In this way, the
timedependent density may be controlleddirectly
[2].
[1] T. Burnus, M.A.L. Marques, and E.K.U.
Gross, Phys. Rev. A (Rapid Comm.) 71, 010501 (2005).
[2] I. Serban, J. Werschnik, E.K.U. Gross, Phys. Rev.
A, (2005, in press); quantph/0409124.
