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.
