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Two topics will be covered in this lecture: (i) The visualization and
analysis of electronic motion by means of the so-called electron
localization function (ELF), and (ii) optimal control theory of
electronic dynamics. The ELF provides a way to visualize chemical bonds.
It is derived from the conditional probability of finding an electron in
the vicinity of a point r if one knows with certainty that there is
another electron with the same spin at r. The shape of the ELF (as
function of r) allows a topological classification of the different
types of chemical bonds [1]. Here we generalize the ELF to the
time-dependent case [2]. Two movies of the time-dependent ELF will be
presented, one that shows the formation and breaking of chemical bonds
in a proton-ethylene scattering process and another one that visualizes
a laser-induced π-π* transition in acetylene in a time-resolved
fashion.
In the context of optimal control we first present two generalizations
of the standard formulation [3] of optimal-control theory: The first
generalization [4] allows the calculation of optimized pulses with
frequency constraints. The second generalization [5] achieves the
optimization of **
[1] A. Savin et al, Angew. Chem.

[2] T. Burnus, M.A.L. Marques, E.K.U. Gross, Phys. Rev. A (Rapid Comm.)

[3] W. Zhu, J. Botina, H. Rabitz, J. Chem. Phys.

[4] J. Werschnik, E.K.U.Gross, J. Opt. B

[5] I Serban, J. Werschnik, E.K.U.Gross Phys. Rev. A

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